Institutional Design and Voting Power in the European Union [1 ed.] 9780754694960, 9780754677543

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Institutional Design and Voting Power in the European Union

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Institutional Design and Voting Power in the European Union

Edited by Marek A. Cichocki Natolin European Centre, Poland and Karol Życzkowski Jagiellonian University, Poland

© Marek A. Cichocki and Karol Życzkowski 2010 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. Marek A. Cichocki and Karol Życzkowski have asserted their right under the Copyright, Designs and Patents Act, 1988, to be identified as the editors of this work. Published by Ashgate Publishing Limited Ashgate Publishing Company Wey Court East Suite 420 Union Road 101 Cherry Street Farnham Burlington Surrey, GU9 7PT VT 05401-4405 England USA www.ashgate.com British Library Cataloguing in Publication Data Institutional design and voting power in the European Union. 1. European Union. 2. Voting--European Union countries. 3. Balance of power. 4. Power (Social sciences)--European Union countries. I. Cichocki, Marek A. II. Życzkowski, Karol. 324.6’5’094-dc22 Library of Congress Cataloging-in-Publication Data Cichocki, Marek A. Institutional design and voting power in the European Union / by Marek A. Cichocki and Karol Życzkowski. p. cm. Includes bibliographical references and index. ISBN 978-0-7546-7754-3 (hardback) -- ISBN 978-0-7546-9496-0 (ebook) 1. Voting--European Union countries. 2. European Union countries--Politics and government. 3. European Union. I. Zyczkowski, Karol, 1960- II. Title. JN45.C43 2010 324.6094--dc22 2010011717 ISBN 9780754677543 (hbk) ISBN 9780754694960 (ebk)

Contents List of Figures   List of Tables   List of Abbreviations   Notes on Contributors   Preface   Introduction   Desmond Dinan

ix xi xv xvii xxiii 1

Part I  Voting System for the Council of European Union 1

Is the Double Majority Really Double? The Voting Rules in the Lisbon Treaty   Axel Moberg

19

2

Penrose’s Square-Root Rule and the EU Council of Ministers: Significance of the Quota   Moshé Machover

35

3

Jagiellonian Compromise – An Alternative Voting System for the Council of the European Union   Wojciech Słomczyński and Karol Życzkowski

43

4

The Double Majority Voting Rule of the EU Reform Treaty as a Democratic Ideal for an Enlarging Union: An Appraisal Using Voting Power Analysis   Dennis Leech and Haris Aziz

5

The Blocking Power in Voting Systems   Tadeusz Sozański

6

The Distribution of Power in the Council of Ministers of the European Union   Werner Kirsch

59 75

93

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Part II  Distribution of Power in the European Union 7

The Distribution of Power in the European Cluster Game   Jesús Mario Bilbao

111

8

The Constitutional Power of Voters in the European Parliament   125 Silvia Fedeli and Francesco Forte

9

Decision Rules and Intergovernmentalism in the European Union  151 Madeleine O. Hosli

10

On the Relative Unimportance of Voting Weights: Observations on Agenda-Based Voting Procedures   Hannu Nurmi

11

Patterns of Voting in the Council of Ministers of the European Union. The Impact of the 2004 Enlargement   181 Rafał Trzaskowski

12

Decision-Making in the EU Council after the First Eastern Enlargement: The Relevance of the Empirical Findings for the Voting Rules   Běla Plechanovová

171

201

Part III Allocation of Seats in the European Parliament 13

Degressive Proportionality: Composition of the European Parliament. The Parabolic Method   victoriano Ramírez González

215

14

Putting Citizens First: Representation and Power in the European Union   Friedrich Pukelsheim

235

15

Comparative Analysis of Several Methods for Determining the Composition of the European Parliament   José Martínez Aroza and Victoriano Ramírez González

255

16

On Bounds for Allocation of Seats in the European Parliament   Wojciech Słomczyński and Karol Życzkowski

269

Contents

17

vii

Conclusions: The System of Equal Influence of the Citizens in the EU – The Polish Proposal Submitted During the 2007 Reform Treaty Negotiations   283 Marek A. Cichocki and Ewa Ośniecka-Tamecka

Index  

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List of Figures 3.1 3.2 3.3 4.1 4.2 4.3 5.1 8.1.1 8.1.2 8.1.3 8.2.1 8.2.2 8.2.3 8.3.1 8.3.2 8.3.3 9.1 10.1 10.2 12.1 12.2 13.1 13.2

The weights attributed to the member states   The ‘square root’ weights attributed to member states   Jagiellonian Compromise compared with the Treaty of Nice and with the Constitution proposals   Relative citizen power: large countries   Relative citizen voting power: middle-sized countries   Relative citizen voting power: small countries   The relation between France and Germany in two voting games    Performance of PPE-DE in terms of representation in the three games in EU15   Performance of PPE-DE in terms of representation in the three games in EU25   Performance of PPE-DE in terms of representation in the three games in EU27   Performance of PSE in terms of representation in the three games in EU15   Performance of PSE in terms of representation in the three games in EU25   Performance of PSE in terms of representation in the three games in EU27   Performance of ELDR in terms of representation in the three games in EU15   Performance of ELDR in terms of representation in the three games in EU25   Performance of ELDR in terms of representation in the three games in EU27   Uni-dimensional bargaining game between the European Parliament and the Council of the European Union: The effects of changing Win Set Size   The successive agenda   The amendment agenda   Dissenting votes cast by member states in the Council 2004–2006 (negative votes and abstentions)   Voting in the Council 2004–2006 (207 observations, complete linkage)   Parabolic allocation and adjusting function for H = 750 and n = 27 Lisbon proposal (points) and parabolic adjusting curve  

49 50 52 70 71 71 89 137 137 138 138 139 139 140 140 140 152 173 173 204 206 225 225



Institutional Design and Voting Power in the European Union

13.3 Parabolic allocation EU28 = EU27 + Croatia (assuming EP size of 750)   14.1 Compensating balance of citizen-based procedures: Seat deviation of ‘AFCO+1’ from ‘Fix+Prop’ and power deviation of ‘DM’ from ‘JC’  15.1 Allotment of the EP seats by means of the Balinski method   15.2 Allocation by FPuk from Table 15.4   15.3 Allocation by ParF and SplF methods from Table 15.4   16.1 Allocation of seats in the European Parliament (all countries)   16.2 Allocation of seats in the European Parliament (countries from Malta to Greece)   17.1 Change in voting power under the Nice Treaty   17.2 Change in voting power under the Constitutional Treaty  

227 249 258 265 266 278 279 284 286

List of Tables 1.1 1.2 3.1 4.1 4.2 4.3 5.1 5.2 5.3 6.1 6.2 6.3 6.4 6.A.1 6.A.2 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.A.1 8.A.2 8.A.3 9.1 9.2

Changes in voting weight and blocking potential    28 Votes in Nice and with equal degressivity   32 Comparison of voting power of EU27 member states   53 Voting power analysis of the EU27   67 Citizen indirect power indices under all scenarios: Reform Treaty   68 Citizen indirect power indices under all scenarios: Jagiellonian Compromise   70 Germany’s voting power in three voting systems according to the naive theory and classical theory   78 Parameters of winning and blocking power in EU15   82 The blocking structure of the Nice, double majority and Lisbon game 87 Voting weights in the EEC (1958)   93 Voting weights for the Council from 1995 to 2004   94 Some of the Banzhaf numbers for the Nice voting procedure (for 25 member states)   99 Comparison between power indices (EU27)   101 Comparison between power indices (for 27 member states) 105 Relative gains or losses of member states  106 EP fifth term (1999–2004)   127 EP sixth term (25 countries, distribution of seats and population at 2004)   128 EP sixth term (27 countries, distribution of seats at July 2007 and population at 2005)   129 Distribution of elected representatives by cells in the parliament of a federation   131 Strategic bloc formation under the same political affiliation 132 Strategic bloc formation under the same national affiliation 132 Countries’ representation (with countries ordered by seats/population ratio)   134 Electoral voting rights of citizens (EU15)   144 Electoral voting rights of citizens (EU25)   145 Electoral voting rights of citizens (EU27)   147 Distribution of voting weights, qualified majority and blocking minority thresholds in the Council, 1958–2004   154 The capacity of the Council to Act: Share of winning coalitions in all possible coalitions among member states, 1958–2004   156

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9.3 9.4

9.5

9.6

10.1 10.2 10.3 10.4 10.5 10.6 11.1 11.2 11.3 11.4 11.5 12.1 13.1 13.2 13.3 13.4 13.5 13.6 13.7

Institutional Design and Voting Power in the European Union

Overview of population size, voting weights in the Council, seats in the European Parliament and voting power in the framework of a hypothetical EU bicameral parliamentary system (mid-1990s)   The power of a collectivity to act for a hypothetical bicameral EU parliamentary structure: Share of winning coalitions in all possible coalitions among EU states (allocation of seats and votes 1995 to 2004)   The power of a collectivity to act for an hypothetical bicameral EU parliamentary structure: Share of winning coalitions in all possible coalitions among member states (allocation of seats and votes 1986– 1994)   The Council’s capacity to act for different population quotas between the simple majority clause and unanimity, Constitutional and Lisbon Treaties (27 states, second threshold – 55 per cent of member states – kept constant)   Pareto violation of amendment procedure   Pareto violation of the successive procedure   Pareto violation with high majority threshold   Ostrogorski’s paradox   Anscombe’s paradox   Paradox of multiple elections   Decision making by QMV in the Council in the years 2001–2008  Contested voting in the Council of Ministers five years immediately before the enlargement (10.1999–04.2004)   Contested voting in the Council of Ministers after enlargement (05.2004–11.2008)   Statements of the member states accompanying the voting records (legislative acts) after accession (2004–2008)   Contested voting in the Council of Ministers three years immediately after the enlargement (05.2004–04.2007) in 51 non-legislative trade measures (roll-calls made public)    Proposals decided upon in the Council 2004–2006   Two very different allocations meeting Lamassoure and Severin criterion   Inapplicable Lamassoure and Severin criterion (H=116)   Inapplicable Lamassoure and Severin criterion (H=255, Minimum = 2 or 3 or 4 or 5 or 6, Maximum = 70 or … or 96)   Parabolic allocation and Lisbon proposal for the EP   Parabolic allocation for EU28 (i.e. EU27+Croatia)   EP Composition in proportion to the square root of the population  (Im)balance of power in an EP distributed by the Square Root method  

159

160

162

164 175 176 176 178 179 179 185 187 189 192 193 203 217 218 219 223 226 230 231

List of Tables

14.1 Allocation of European Parliament seats to member states: Citizen-based apportionment method ‘Fix+Prop’ and negotiated ad hoc allocation ‘AFCO+1’   14.2 Qualified majority voting systems for the Council of Ministers: Citizen-based Jagiellonian Compromise ‘JC’ and negotiated ad hoc double majority ‘DM’   14.3 Allocation of European Parliament seats to member states: Apportionments of four variants ‘base + divide & round’ of the parabolic allotment, and of ‘AFCO+1’   15.1 Allocation of EP seats by means of the Balinski method for proportional allotments with restrictions   15.2 Ten proposed allocations for the EU of 27 member states   15.3 Summary of properties for several proposals of EP seats distribution  15.4 Allocations by ParF, FPuk and SplF methods for the 24 most populous EU states   16.1 Lower bound Smin and upper bound Smax for the number of seats in the European Parliament for each of 27 members of the European Union 16.2 Allocation of seats in the European Parliament according to several proposals   17.1 Share of votes from the EU6 (1958) to EU27 (2007)   17.2 Voting power according to QMV in the Constitutional Treaty and according to the square root system with different definition of the population applied    17.3 Equal influence system vs. Constitutional Treaty  

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247 248 250 257 262 263 264 273 277 285 290 291

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List of Abbreviations AFCO Committee for Constitutional Affairs CAP Common Agricultural Policy COREPER Committee of Permanent Representatives EC European Community EDD Europe of Democracies and Diversities EEC European Economic Community ELDR Liberal Democrat European Group EP European Parliament EU European Union GUE European United Left ITS Identity, Tradition, Sovereignty JC Jagiellonian Compromise IGC Inter-Governmental Conferences MEP Member of the European Parliament MMD mean majority deficit NI Non-attached Members PPE-DE European People’s Party and European Democrats PSE Party of European Socialists SEA Single European Act OPOV one-person-one-vote SMV simple majority vote SQL Square root law SQRR Square-Root Rule QMV qualified majority voting UEN Union for a Europe of Nations UN United Nations WVGs weighted voting games Verts/ALE The Greens/European Free Alliance

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Notes on Contributors HARIS AZIZ European Science Foundation postdoctoral research fellow based at Technische Universität München. Author of: (with D. Leech and M. Paterson) Combinatorial and computational aspects of multiple weighted voting games. The Warwick Economics Research Paper Series (TWERPS), University of Warwick, 2007. JESÚS MARIO BILBAO Professor of Applied Mathematics at Seville University, Spain and director of the research group Combinatorial and Algorithmic Methods in Game Theory. His recent publications include: (with C. Chacón, A. Jiménez Losada, and E. Lebrón) Values for interior operator games. Annals of Operations Research, 137, 2005; (with E. Algaba, and J.R. Fernández) The distribution of power in the European Constitution. European Journal of Operational Research, 176, 2007. MAREK A. CICHOCKI Programme director of Natolin European Centre in Warsaw, Poland and editorin-chief of the magazine New Europe. Natolin Review. He was Polish negotiator (sherpa) on the IGC mandate on the Lisbon Treaty (2007). Author of: Europe Kidnapped, Institute for Political Thought, 2004; Power and Remembrance, Institute for Political Thought 2006; The impact of accession: Old and new member states and the legacy of the past, in Apres Enlargment. Legal and Political Responses in Central and Eastern Europe, edited by W. Sadurski, J. Ziller, K. Zurek. Florence: EUI, 2006. DESMOND DINAN Professor of Public Policy and Jean Monnet Chair in the School of Public Policy, George Mason University, Virginia, USA. He is director of the MA program in International Commerce and Policy at George Mason University. His publications include: Europe Recast: A History of European Union, 2004: Ever Closer Union: An Introduction to European Integration, 3rd edition, 2005, and Origins and Evolution of the European Union, edited, 2006. SILVIA FEDELI Professor at Dipartimento di Economia Pubblica, Facolta’ di Economia, Universita’ di Roma “La Sapienza”, Italy. Author of (with F. Forte): Voting powers and the efficiency of the decision-making process in the European Council of Ministers. Journal European Journal of Law and Economics, 12(1), 2001; Measures of the

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amending power of government and parliament. The case of Italy 1988–2002. Economics of Governance, 8(4), 2007. FRANCESCO FORTE Professor emeritus at Dipartimento di Economia Pubblica, Facolta’ di Economia, Universita’ di Roma “La Sapienza”, Italy. Author of (with S. Fedeli): Voting powers and the efficiency of the decision-making process in the European Council of Ministers. Journal European Journal of Law and Economics, 12(1), 2001; Measures of the amending power of government and parliament. The case of Italy 1988–2002. Economics of Governance, 8(4), 2007. MADELEINE O. HOSLI Professor in International Relations and Jean Monnet Chair at the Leiden University, the Netherlands. Her recent publications: (with H. Nurmi) Which decision rule for the future Council? European Union Politics, 4(1), 2003; (with K. Benoit, M. Laver, C. Arnold and P. Pennings) Measuring national delegate positions at the Convention on the Future of Europe Using computerized wordscoring. European Union Politics, 6 (3), 2005; (with R. Thomson) Who has power in the EU? The Commission, Council and Parliament in legislative decision-making. Journal of Common Market Studies, 44(1), 2006. WERNER KIRSCH Professor at the Fakultät für Mathematik und Informatik, FernUniversität Hagen, Germany. Recently published works: (with P. Hislop and K. Maddaly) Random Schrodinger operators with wavelet interactions, in Wavelets and Allied Topics, edited by P.K. Jain et al. New Dehli: Narosa Publishing House, 2001; An invitation to Random Schrödinger operators: Proceedings of the summer school in Disordered Systems, Paris, 2003; Wahlverfahren, Evangelisches Staatslexikon, 2006. DENNIS LEECH Professor of Economics, Department of Economics, University of Warwick, UK; Director of the Voting Power and Procedures programme and an External Associate member of the Centre for the Philosophy of Natural and Social Science at LSE. Recent publications: The utility of the voting power approach. European Union Politics, 4(4), 2003; (with R. Leech) Voting power and voting blocs. Public Choice, 127, 2006; (with R. Leech) Voting power in the Bretton Woods institutions, in The IMF, World Bank and Policy Reform, edited by A. Paloni and M. Zanardi. Routledge, 2006. MOSHÉ MACHOVER Professor Emeritus at the Department of Philosophy, Kings College, London and Centre for the Philosophy of the Natural and Social Sciences Fellow, LSE. Among his publications are: (with Dan S. Felsenthal) The Measurement of Voting Power; Theory and Practice, Problems and Paradoxes, Edward Elgar Publishing, 1998;

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(with D.S. Felsenthal) Population and Votes in the Council of Ministers: Squaring the Circle, Issue Document No. 10, 2004, Challenge Europe 10, available at: www.theepc.be; (with M. Hosli) The Nice Treaty and voting rules in the Council: A reply to Moberg. Journal of Common Market Studies, 42, 2004. JOSÉ MARTÍNEZ AROZA Professor, Department of Applied Mathematics, University of Granada, Spain. Coauthor of: An analysis of edge detection by using the Jensen-Shannon divergence. Journal of Mathematical Imaging and Vision, 13(1), 2000; A measure of quality for evaluating methods of segmentation and edge detection. Pattern Recognition, 34(5), 2001. AXEL MOBERG In private capacity; former officer at the Swedish Ministry for Foreign Affairs. Author of: The Nice Treaty and voting rules in the Council. Journal of Common Market Studies. 40, 2002. HANNU NURMI Professor of Political Science at the Department of Political Science, University of Turku, Finland; Academy professor in the Academy of Finland, Director of Centre of Excellence in Public Choice Research. Author of: Models of Political Economy. London and New York: Routledge, 2006; (with J. Kacprzyk) Political representation: perspective from fuzzy systems theory. New Mathematics and Natural Computation, 3, 2007; Assessing Borda’s rule and its modifications, in Designing an All-Inclusive Democracy. Consensual Voting Procedures for Use in Parliaments, Councils and Committees, edited by P. Emerson. Berlin: Springer 2007. EWA OŚNIECKA-TAMECKA Vice Rector of the Natolin (Warsaw) campus of the College of Europe. She was Polish negotiator (sherpa) on the IGC mandate for the Lisbon Treaty (2007). In 2006 and 2007, she served as Secretary of State for European Affairs in the Government of the Republic of Poland. BĚLA PLECHANOVOVÁ Department of International Relations, Faculty of Social Sciences, Charles University Prague. Recently published: Draft Constitution and the DecisionMaking Rule for the Council of Ministers of the EU – Looking for Alternative Solution, European Integration online Papers (EIoP), 8(12), 2004; The Treaty of Nice and the Distribution of Votes in the Council – Voting Power Consequences for the EU after the Oncoming Enlargement, European Integration online Papers (EIoP), 7(6), 2003.

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FRIEDRICH PUKELSHEIM Professor Dr., Institut für Mathematik, Universität Augsburg. Recent publications include: (with B. Simeone) Mathematics and Democracy. Recent Advances in Voting Systems and Collective Choice. Springer, 2006; (with S. Maier) Bazi: A Free Computer Program for Proportional Representation Apportionment. Universität Augsburg, Institut für Mathematik, Preprint 42/2007; (with N. Gaffke) Vector and matrix apportionment problems and separable convex integer optimization. Mathematical Methods of Operations Research, 67(1), 2008. VICTORIANO RAMÍREZ GONZÁLEZ Professor of Mathematics, Institute of Mathematics, University of Granada, Spain. Author of the following articles: Some Guidelines for an Electoral European System: Workshop on Institutions and Voting Rules in the EC (Sevilla, 2004); The Parabolic Method for the Allotment of Seats in the European Parliament Among Member States of the European Union, Analysis no. 63, Real Instituto Elcano, 2007. WOJCIECH SŁOMCZYŃSKI Professor of Mathematics, Institute of Mathematics, Jagiellonian University, Poland. Author of: (with K. Życzkowski and T. Zastawniak) Physics for fairer voting. Physics World, 2006; (with K. Życzkowski) Kompromis Jagielloński – alternatywny system głosowania dla Rady Unii Europejskiej (Jagiellonian Compromise: an alternative voting system for the Council of the European Union). Międzynarodowy Przegląd Polityczny, 18, 2007; (with K. Życzkowski) From a toy model to the double square root voting system. Power Measures IV. Special Issue of Homo Oeconomicus, edited by G. Gambarelli, 2007. TADEUSZ SOZAŃSKI Doctor of Sociology; Assistant Professor, Institute of Philosophy and Sociology Pedagogical University, Poland. On the core of characteristic function games associated with exchange networks. Social Networks, 28, 2006; The Mathematics of Exchange Networks. Wydawnictwo Uniwersytetu Jagiellońskiego (forthcoming). RAFAŁ TRZASKOWSKI Member of the European Parliament. Doctor of Political Sciences; Research Fellow at Natolin European Centre and Senior Lecturer at Collegium Civitas and KSAP – National School of Public Administration, Warsaw. Former adviser to the Chairman of the Foreign Affairs Committee of the European Parliament, Dr. Jacek Saryusz-Wolski. Recently published: Poland and the assessment of the Treaty of Nice, in Towards a New Europe: Identity, Economics, Institutions. Different Experiences, edited by A. Tonini. University of Florence, 2006; Assessing the institutional provisions of the Constitutional Treaty: Exercise in ambiguity, in Apres Enlargement, Legal and Political Responses in Central and Eastern Europe,

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edited by W. Sadurski, J. Ziller, K. Zurek. Florence: Robert Schuman Center for Advanced Studies, 2006. KAROL ŻYCZKOWSKI Professor of Physics working at the Centre for Research on Complex Systems, Institute of Physics, Jagiellonian University and Centre for Theoretical Physics of the Polish Academy of Sciences, Poland. Recently published articles: (with W. Kirsch and W. Słomczyński) Getting the votes right. European Voice, 3–9 May 2007; (with W. Słomczyński) Kompromis Jagielloński – alternatywny system głosowania dla Rady Unii Europejskiej (Jagiellonian Compromise: an alternative voting system for the Council of the European Union). Międzynarodowy Przegląd Polityczny, 18, 2007; (with W. Słomczyński) From a toy model to the double square root voting system. Power Measures IV. Special Issue of Homo Oeconomicus, edited by G. Gambarelli, 2007.

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Preface Over the course of the last few years, the European integration processes were marked above all by EU institutional reforms. The failure of the Nice Treaty to provide a universally satisfactory solution became an impulse to begin work on a more integrated, treaty-based foundation for the EU, known as the Constitutional Treaty for Europe. This task was given to a European Convention, an innovation intended to ensure that the resulting document was more broadly representative. The Constitutional Treaty did not, however, win the backing of all member states. In 2005 it was rejected by the citizens of France and Holland in national referenda. After a period of reflection the work on reforming the treaties was resumed in 2007 but this time a completely different approach was chosen, one relying on intergovernmental negotiations steered by the German presidency in the spirit of confidential diplomacy. The result is the current Lisbon Treaty. The negotiation process lasted almost six years and was overshadowed by the biggest enlargement in EU integration history which resulted in the creation of an EU composed of 27 member states. In the whole treaty-based foundation reform process, the institutional reform drew the keenest attention of the member states’ governments. Meanwhile, the issue that became perhaps the most difficult politically, both during the deliberations of the European Convention and during the later efforts in 2007 and beyond, concerned the changes to the majority decisionmaking mechanism in the EU Council of Ministers. At its core, this problem came down to defining a new distribution of power between the member states in the EU composed of 27 or more members. Institutional Design and Voting Power in the European Union discusses the emotional and attention-evoking issue of decision-making in the EU Council of Ministers, and in particular the conditions relevant to the new majority decisionmaking formula known as the double majority. The book pertains also to the interrelated issue of allocation of seats in the European Parliament. The publication features an array of chapters by prominent scholars and experts, including Haris Aziz, Jesús Mario Bilbao, Desmond Dinan, Silvia Fedeli, Francesco Forte, Madeleine O. Hosli, Werner Kirsh, Dennis Leech, Moshé Machover, José MartinezAroza, Axel Moberg, Hannu Nurmi, Ewa Ośniecka-Tamecka, Běla Plechanovová, Friedrich Pukelsheim, Victoriano Ramirez González, Wojciech Słomczyński, Tadeusz Sozański, Rafał Trzaskowski and Karol Życzkowski. The reader may initially be surprised by the fact that political science papers on the double-majority voting instituted by the Lisbon Treaty and the composition of the European Parliament are accompanied by mathematical analyses of this issue. Indeed, this publication endeavors to show how both of these perspectives are intertwined and how the question of power in the EU and the theory behind

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it is at its core related to mathematics. The relationship between voting weights assigned to individual member states has, in the practice of European integration, been for a very long time determined by the parity principle as a negotiated political compromise. In the end, however, the enlarging EU acted as a force that necessitated seeking more objective criteria to divide the votes between the member states in the Council. And where would one expect to find an objective answer if not in mathematical theories? In reality, this is not about the numbers, however. Mathematics is merely a means which allows us to better understand the problem behind the decisionmaking process. For the problem lies in the very nature of the EU. Do objective criteria for decision-making in a group of dozens of states differing in size and potential even exist? How does one go about maintaining a sense of belonging in such a diverse community of states; a sense which is best expressed by the decision-making process? This book presents some models for resolving this issue in the context of the reforms proposed by the Lisbon Treaty. Marek A. Cichocki

Introduction Desmond Dinan

Supranationalism – the pooling and delegation of sovereignty by national governments – is the most distinctive feature of the European Union (EU) and qualified majority voting (QMV) is the most distinctive feature of supranationalism. National governments are notorious for guarding and preserving their countries’ sovereignty. The EU member states’ governments are unusual in that, for reasons of history, geography, political culture, and economic advantage, they have agreed to pool and delegate sovereignty in a wide range of policy areas that affect the everyday lives of their citizens. The Council of Ministers is the EU institution where national governments decide to pool sovereignty, either by unanimous agreement or by taking a vote. In the latter case, the rules have generally called for a super – or qualified – majority rather than a simple majority, hence the acronym QMV, one of the best known of the thousands of acronyms spawned in the course of 60 years of European integration. Qualified majority voting is not only one of the most distinctive but also one of the most divisive features of the EU. Ever since the negotiations that culminated in the founding of the European Economic Community (EEC), the forerunner of today’s EU, national governments have fought bruising battles over the modalities of QMV – either the weighting of votes for each member state and the threshold for a qualified majority or, more recently, the threshold for the double majority (member states and population) – as well as over the scope of its application to policies under the EU umbrella. Accession treaties for new member states and inter-governmental conferences for treaty reform have served as the major battlegrounds. Highlights of these QMV battles include the row between Britain and other member states over the threshold for a blocking minority following the 1995 enlargement, and the dispute that pitted Poland and Spain against France and Germany over the switch to the double majority system in the proposed Constitutional Treaty of 2004. Governments have also fought tenaciously over whether using QMV was appropriate even when provided for in the treaties. At the root of the Empty Chair Crisis of 1965–1966, the most serious political crisis in the history of the EU (at the time known as the EEC), was French insistence that, even when the rules allowed for QMV, decisions in the Council should be taken by unanimity if a government deemed that a ‘very important’ issue was at stake. The outcome of the crisis – the Luxembourg Compromise – preserved the treaty provisions on QMV but acknowledged a government’s right to insist on unanimity in defence of a



Institutional Design and Voting Power in the European Union

vital interest, thereby effectively instituting a national veto over Council decisionmaking. The Luxembourg Compromise cast a long shadow over the EU greatly inhibiting the use of QMV until it withered in the wake of the Single European Act, the first major treaty reform in EU history which called for the use of QMV in policy areas deemed essential for the establishment of the full single market. Why has QMV been so contentious in EU history? Because, as an instrument of supranationalism, it hits such sensitive national nerves as principle, prestige, parity, power (influence), domestic politics, and parliamentary prerogatives. Not all of these issues may be in play for each member state during any particular debate, but on each of the occasions when QMV triggered a confrontation in the EU several of these sensitive issues motivated at least one national government to take a stand. National Sensitivities All member states must accept the principle of supranationalism, the EU’s defining characteristic. Nevertheless, national governments’ commitment to this principle is not uniform. Occasionally the party or coalition of parties in power in individual member states is more nationalistic and sovereignty-conscious than its predecessor or successor. Member states themselves, by virtue of history, culture, and internal political structure, tend to vary widely in their enthusiasm for, or dislike of, supranationalism. Germany and Britain are two contrasting examples. Post-war and post-unification German identity and sovereignty are bound up in the country’s involvement in European integration. Germany has rehabilitated itself and allayed the security concerns of its neighbours through a wholehearted commitment to the EU. Moreover, as a compound polity – a full-fledged federation – Germany is at ease with the principle and practice of multi-level governance. By contrast, Britain has traditionally prided itself on being independent in international relations and chafed at the idea of sharing sovereignty. Britain’s experience in World War II contrasted sharply with that of most countries on the continent which were defeated and occupied at some stage of the conflict. Accordingly, the British government played down the supranational character of the European Community during the domestic debate on membership and has generally favoured the application of QMV only in specific policy areas. Moreover, as a traditionally centralised state, currently grappling with devolution of authority to its constituent parts, the United Kingdom is uncomfortable as part of a multi-levelled entity such as the EU. Countries, like people, are image conscious and seek to increase their prestige among their peers. All countries are equal, but some are more equal than others. That maxim is as true in the EU as it is in wider international relations. Population size matters in the EU as it affects each member state’s voting weight in the Council, whether under the pre- (weighted votes) or post- (double majority) Lisbon Treaty system, and the apportionment of seats in the European Parliament. Until 2004, size also mattered as regards the composition of the European Commission, with

Introduction



the big countries allowed to appoint two commissioners each while their smaller counterparts had to make do with only one commissioner each. Countries accept the rationale for unequal representation, but strive to maximise their voting power in the Council and the size of their national delegation in the Parliament in order to enhance their prestige. Parity is related to prestige. No two countries in the EU have exactly the same population, but many are close enough to be categorised comparably. The designation ‘big,’ although inherently imprecise, refers to member states with a population significantly larger than that of the other member states. Although Germany, France, Italy, Britain, Poland, and Spain vary considerably in population, Poland, the country with the smallest population among this group of countries, is considerably larger than the next most populous EU member state, i.e. Romania. The populations of Germany, France, Italy, and Britain are significantly larger that those of Poland and Spain; hence the larger allocation of votes to the four biggest countries. Countries within the same category tend to want to maintain parity with each other. French prestige and identity in the EU were long bound up with maintaining parity in institutional representation with Germany, a much more populous country. Given the history of Franco-German relations and the centrality of Franco-German reconciliation to the EU project, France understandably sought equality of institutional representation with its erstwhile enemy. Similarly, for reasons of friendly rivalry rather than former enmity, Belgium, although less populous than its neighbour to the north, traditionally insisted on parity in institutional representation with the Netherlands. Belgium reluctantly accepted a smaller weighting of Council votes in the Nice Treaty only after receiving a concession in the form of a promise that all regular meetings of the European Council would thereafter take place in Brussels. Prestige and parity, in turn, relate to power, the currency of international relations. Indeed, prestige and parity are soft manifestations of hard power. The EU is not a classic international organisation, but a multi-level polity whose internal operation resembles that of a confederal state. Nevertheless, the European Community emerged from an international negotiation; the EU consists of member states; and revisions of the treaties are the result of intergovernmental conferences. Given the unique character of the EU, member states generally behave differently within the framework of its institutions than they do in the wider global system or in classic international organisations. Thus, when the six founding countries negotiated the original modalities of QMV, they acknowledged the power differential among them by weighting votes according to each country’s population while at the same time recognising the novel nature of the Community system by giving the smaller member states (Belgium, Luxembourg, Netherlands) far more voting weight than the proportion of their population relative to the three big member states (France, Germany, Italy) would have implied. The greater voting weight of the smaller member states in turn allowed the bigger ones increased flexibility to form qualified majorities or blocking minorities. A quest for influence



Institutional Design and Voting Power in the European Union

rather than power is perhaps the best way to describe the behaviour of member states within the EU. Member states use their influence in the Council to enact measures that they consider advantageous and block measures they deem unfavourable, by building coalitions to form either qualified majorities or blocking minorities. Similarly, when deciding on the scope of QMV during intergovernmental conferences at various times in EU history, national governments have taken positions based on general policy preferences. In policy areas where they are reluctant to pool sovereignty, national governments have resisted instituting QMV whereas in policy areas where they are eager to advance integration, national governments have advocated decision-making by QMV. Governments’ preferences are a function of broad national characteristics and specific circumstances. Understandably, in democratic systems national preferences stimulate the government’s desire to satisfy domestic constituencies so as to maintain the popular support necessary to win the next election. Thus, a government’s assessment of what is advantageous or disadvantageous in deciding whether to vote for or against a particular Council measure depends to a large extent on domestic pressures and politics. Governments’ positions in negotiations on the modalities and especially the scope of QMV are also influenced by national politics and domestic conditions. Here again prestige plays a part. Sometimes governments want to be seen at home to be taking a strong position in Brussels, and strive to maximise their influence in the EU system partly to reassure domestic opinion or rally political support. Sensitivity to national parliamentary positions and prerogatives is part of the domestic political equation. The trend throughout EU history toward greater use of QMV has helped to undermine the authority of national parliaments and, in tandem with the co-decision procedure, enhance the power of the European Parliament. In cases where QMV prevails, national parliaments can no longer insist that their governments cast a veto. Increasingly, national parliaments believe that their position has weakened as a result of the concentration of policy-making capacity in Brussels. In national political systems where governments depend on parliamentary support in order to stay in office, the backlash against Brussels, often couched in terms of the democratic deficit, is a highly sensitive matter. Efforts to increase the involvement of national parliaments in the EU system, while not directly related to QMV, have made many governments more aware of and responsive to parliamentary concerns when voting in the Council or considering changes to the modalities and scope of QMV. An additional point about QMV is that people have invigorated politics and shaped EU institutions for the past 50 years. The most heated arguments over QMV have reached the highest levels of government, often pitting national and Commission leaders directly against each other. Deep personal differences between French President Charles de Gaulle and Commission President Walter Hallstein, as well as the pent-up frustration of other national leaders with de Gaulle’s highhanded behaviour, undoubtedly exacerbated the already profound differences of

Introduction



principle and policy during the Empty Chair Crisis. At the less exalted level of everyday decision-making, the conduct and outcome of Council voting owes much to the experience, skill, and personality of the officials involved, especially those representing the country in the Council Presidency and working in the Council Secretariat. Despite frequent complaints voiced in member states alleging that EU institutions are remote and technocratic, the Council, like other Brussels-based institutions, is staffed by people who are steeped in its culture, expert in its rules, and immersed in the game of legislative decision-making. For those people, QMV is not an abstract formula but a crucial mechanism for advancing national positions – as well as their own careers – ideally in the overall European interest. The following sections provide a brief overview of the interplay of principle, prestige, parity, power (influence), domestic politics, parliamentary prerogatives, and personality in the development of QMV. The first section covers the period from the early 1950s, when institutionalised European integration began with the Coal and Steel Community, to the Single European Act of 1986 which facilitated deeper European integration and heralded the birth of the European Union. The second section covers developments from the Single European Act to the Lisbon Treaty of 2007, which emerged after a lengthy period of constitutional reform. From Coal and Steel to the Single European Act The European Coal and Steel Community was significant for political rather than economic reasons. It symbolised Franco-German rapprochement and eased the entry of the new Federal Republic of Germany into the regional and global political system. A proposal to extend integration to European defence, prompted by the outbreak of the Korean War in 1950 and calls on the part of the US government for German rearmament, failed spectacularly in 1954. The legacy of the Coal and Steel Community and fallout from the collapse of the defence project provided the boost for the next initiative in institutionalised integration: the European Economic Community. Yet the EEC owed its existence largely to the desire shared by the core countries in the integration project (France, Germany, Italy, Belgium, the Netherlands, and Luxembourg) to build a far-reaching customs union and a common market, thereby liberalising cross-border transactions and maximising economic growth. Of the founding member states, France, traditionally protectionist and industrially weaker than Germany, was the most apprehensive about taking such bold steps. Only when assured that special provisions for agriculture and assistance to former colonies would be included in the treaty, and enticed with concessions for French industry during the transition to the customs union, did France acquiesce in the EEC project. The institutional architecture of the Coal and Steel Community – a High Authority, Council of Ministers, Common Assembly and a Court of Justice  

On the institutional and political history of the EU, see Dinan 2004.



Institutional Design and Voting Power in the European Union

– provided the blueprint for the organisational structure of the EEC. But the institutional arrangements of the latter differed from those of the former in a number of important respects. In particular, national governments were much more reluctant in the late 1950s to delegate sovereignty to a supranational institution, partly because of their previous experience with the High Authority and partly because of the much greater scope – and therefore higher political prominence – of the EEC compared to its predecessor. The governments’ caution was apparent in their decision to call the executive body of the EEC the Commission, not the High Authority, to delegate relatively little sovereign authority to it, and to vest most decision-making powers in the Council of Ministers, which in the Coal and Steel Community was merely an advisory body. How and in what areas would the Council decide? Unanimity – the requirement that every member agree with the decision being taken – is inherently difficult to achieve. Voting is much more efficient. National governments appreciated the efficiency implicit in decision-making by means of voting in the Council, but were reluctant to relinquish their traditional right in international organisations: veto power. Inevitably, the negotiations leading to the signing of the Rome Treaty were a series of compromises, which generally favoured unanimity over voting in Council decision-making. Thus, on crucial constitutional questions, such as membership (enlargement) and treaty change, the Council would decide by unanimity; likewise, unanimity would be relied on in most policy areas, although in some cases after a certain length of time the basis of decision-making would eventually switch to voting. Only a few provisions of the Rome Treaty called for voting in the Council immediately following the establishment of the EEC. Neither, in most cases where voting was permitted, would governments decide by a simple majority. The smaller member states would have been content with a rule based on one vote per member state, but their bigger counterparts, especially France, felt that their greater size warranted additional influence in the Council. The solution reached in the closing stages of the Rome Treaty negotiations – upon which the EEC was founded – was a system of weighted voting. Namely, between all member states there were 17 votes in total, with 12 (approximately 71 per cent) constituting a qualified majority and 6 a blocking minority. Of the 17 Council votes, France, Germany and Italy each had four, Belgium and the Netherlands each had two, and Luxembourg had one. Thus, a blocking minority would have to consist of at least two big member states. Despite the greater number of votes allocated to the big member states, the disparity in the Council-vote-to-population ratios – for instance, one vote to 13.5 million people in Germany and one to 0.3 million in Luxembourg – demonstrated the significant advantage that the smaller countries enjoyed. The tentative attitudes of the participating governments toward voting, both as regards the modalities and scope of QMV, reflected their reservations about undertaking such a novel international initiative and their awareness that it would take time to develop mutual trust. Even in those areas subject to QMV – whether from the beginning or only after a transition period – the six governments taciturnly

Introduction



agreed that they would not ignore the outright opposition of any one among them to a proposed measure. In other words, they would be mindful of each other’s concerns and operate as much as possible on the basis of consensus. Given the cautious, pragmatic nature of QMV, and the satisfactory experience with Council decision-making in the EEC’s early years, it seems surprising that the Empty Chair Crisis erupted in 1965. The proximate cause was a Commission proposal to link a new financial agreement for the Common Agricultural Policy to greater control over the budget for the Commission and the European Parliament. De Gaulle wanted the financial agreement, but not at the expense of empowering two institutions whose supranational character he disliked. Only after de Gaulle withdrew French participation from the Council (hence the empty chair – or chairs), did he reveal, at a press conference in September 1965, a more deeprooted cause behind the crisis. Under the terms of the EEC founding treaty, QMV rules were due to be extended in January 1966 to agricultural and trade policies, two areas of particular concern to France. Taking a principled stand against QMV, de Gaulle insisted that national governments should forever maintain the right of veto in Council decision-making. An avowed champion of intergovernmentalism and national sovereignty, de Gaulle had opposed the Rome Treaty while in political retirement in France, but accepted it once he returned to power in 1958. Clearly, his principles had not prevented him from accepting QMV until its impending application to agriculture and trade policies allegedly threatened to undermine important French interests. In fact, the transition to QMV in these policy areas would not necessarily have been detrimental to France. In the event of an unacceptable proposal, de Gaulle could have conveyed his concerns to the other national leaders, who, in keeping with the prevailing ethos of consensus, would probably have responded sympathetically. Instead, wrapping himself in the cloak of ideological purity and greatly irritated by the posturing of Commission president Walter Hallstein, de Gaulle chose to trigger the crisis. The outcome was as good as de Gaulle – who did not want to destroy the EEC – could have expected. The crisis inflicted a serious blow on the Commission, whose president Walter Hallstein retired soon after. As for the Council, while the other member states stood firm in defending the principle of QMV, they did accept de Gaulle’s contention that ‘when very important issues are at stake, discussions must be continued until unanimous agreement is reached.’ The transition to QMV for agriculture and trade policies did indeed take place, but votes were rarely called as the Luxembourg Compromise became a de facto veto. Although the Council did not stop functioning, there were few breakthroughs in new or difficult policy areas. De Gaulle’s insistence on the primacy of unanimity over majority voting heightened governments’ awareness of various special interests and increased

  There is a huge literature on the Empty Chair Crisis. One of the most recent and authoritative assessments of it is Palayret, and Wallace 2006.



Institutional Design and Voting Power in the European Union

their reluctance to call a vote even when no vital interest was at stake – whatever such an interest was understood to mean. The Luxembourg Compromise had another negative effect. Britain and Denmark, two countries that joined the EEC in 1973, were wary of supranationalism and seized on the Luxembourg Compromise as evidence that a national veto could override QMV. The combined legacy of the Empty Chair Crisis, British and Danish insistence on a right to veto, and the serious economic downturn of the 1970s, which made governments vulnerable to pressures from domestic interests apprehensive of economic integration, all but thwarted the use of QMV. The Commission was reluctant to introduce proposals that risked provoking strong national opposition for fear that they would become bogged down in the Council, whereas measures already in the Council decision-making process languished in the face of a real or anticipated national veto. Member states’ voting weights changed as a result of the 1973 enlargement, both numerically – namely France, Germany, Italy and the newly admitted Britain each got 10 votes; Belgium and the Netherlands five; new members Denmark and Ireland three; and Luxembourg two – and as a percentage of the total whereby the big countries’ share of the votes decreased from 23.5 per cent to 17.2 per cent. Of the 58 Council votes, 41 constituted a qualified majority and 18 a blocking minority. As in the past, a blocking minority would have to include at least two big member states. The decade from the mid-1970s, following the so-called ‘spirit of The Hague’ – a brief, post de-Gaulle revival of the EEC – until the acceleration of integration processes in the mid-1980s, is often portrayed as a period of stagnation. That description belies progress in a number of areas, notably global development (the 1975 Lomé Convention) and monetary policy (the establishment of the European Monetary System in 1979), as well as negates several important institutional changes, notably the creation of the European Council in 1975 and the inauguration of direct elections to the European Parliament in 1979. Yet, during this time of global downturn, the Community also experienced economic stagnation and failed to evolve much beyond a customs union. In particular, insidious non-tariff, behind-the-border barriers to intraCommunity trade remained stubbornly in place, frustrating completion of the single market. Regardless of the voting rules applicable in the Council for tackling nontariff barriers, the Luxembourg Compromise came to symbolise the Community’s inability to integrate further and pass measures necessary to facilitate the free movement of goods, services, capital, and people. A series of European Council conclusions (communiqués) and special, high-level reports on the Community’s future, published in the 1970s and early 1980s, singled out the Luxembourg Compromise – in effect, the national veto – as the culprit behind stalled European integration. Governments readily acknowledged the perniciousness of the national veto, while nonetheless clinging to it in the form of the infamous Compromise. Considering these circumstances, it is no wonder that a blow against the Luxembourg Compromise, struck by the Belgian presidency in May 1982, assumed

Introduction



great importance. When Britain cited the Luxembourg Compromise in an effort to prevent approval by the Council of an already agreed-upon annual agricultural price schedule unless member states supported Britain on an unrelated issue, the Belgian presidency nonetheless called for a Council vote. The presidency reasoned that, as Britain had already agreed to the annual prices, refusing to formally endorse them in the Council could not be justified as a defence of its national interest. Most other governments concurred and Britain was outvoted. Belgium, a strong advocate of QMV, had acted for reasons of principle and pragmatism. Personality was also a factor – other national leaders were deeply resentful of the heavy-handed manner in which British Prime Minister Margaret Thatcher was advocating Community budget revisions at the time (see Wall 2008, 8–17). Margaret Thatcher was also central to another decisive development in the saga of QMV – the single market project and the Single European Act. Pressure to complete the single market had built steadily since the early 1980s as a consequence of the obvious need to reinvigorate economic integration and boost the Community’s lagging performance in the face of intense American and Asian competition. Well before Jacques Delors became Commission President in January 1985, Margaret Thatcher and other national leaders, strongly supported by business executives, advocated greater liberalisation and integration of the European marketplace. The Rome Treaty provided the blueprint, but unanimity bedevilled decision-making in the Council. Margaret Thatcher’s views were distinctly opposite to those embraced by de Gaulle as regarded QMV but only as long as the majority voting mechanism remained limited to single market measures. Also, she did not see the need for treaty reform in order to ensure completion of the single market. Why not simply reach a political agreement among national leaders – sort of a reverse of the Luxembourg Compromise – whereby governments would renounce the national veto and promise to enact single market measures by QMV? However, the majority of other national leaders preferred to hold an inter-governmental conference to formally revise the Rome Treaty; the British Prime Minister was outvoted on this issue in June 1985, in the first vote ever taken by the European Council. French President François Mitterrand, German Chancellor Helmut Kohl and Commission President Jacques Delors dominated the ensuing inter-governmental conference, which produced the Single European Act, a treaty reform that extended Community competencies and changed its institutions in significant ways. The provisions on QMV were hard-fought. Despite the strong impetus for deeper integration, governments were reluctant to extend majority voting into sensitive policy areas, notably taxation. As a result, the Single European Act provided for QMV in only about 60 per cent of the nearly 300 measures in the Commission’s White Paper (policy design) for the single market project (Moravcsik 1991).

10

Institutional Design and Voting Power in the European Union

From the Single European Act to the Lisbon Treaty The signing of the Single European Act and the inception of the single market program in the late 1980s were landmark events in the history of the EU. Prior to that, the Community was limited in policy scope and public impact. Thereafter, it was subsumed into the EU, whose scope extended from collaboration on justice and home affairs to co-operation on foreign policy, security and defence, and to monetary union. The geographic as well as the policy reach of the new EU grew dramatically. The Community had increased from nine members after the first enlargement to 10 in 1980 (when Greece joined) and to 12 in 1986 (when Portugal and Spain joined). The end of the Cold War, which coincided with the acceleration of European integration in the late 1980s, created the opportunity for a further, large-scale enlargement as, firstly, traditionally neutral or non-aligned countries applied for membership and, secondly, newly-independent countries in Central and Eastern Europe sought to join. Cyprus and Turkey applied as well. The EU’s greater policy scope and geographical reach had a profound effect on public opinion. Hitherto, most Europeans knew little and cared less about the Community. With the inception of the single market program, however, the Community began to touch the everyday lives of an increased number of people in a greater number of ways. At first, the public reaction seemed positive; European integration has never been more popular than in the late 1980s and early 1990s, at the height of the single market program. That changed with the dramatic extension of Community competencies under the Maastricht Treaty coupled with uncertainty about the new EU’s ability to handle bewildering geo-political and economic change, epitomised by the end of the Cold War and the onset of globalisation. The narrow rejection of the Maastricht Treaty by the Danish electorate was a harbinger of public discontent with the EU, epitomised in the term ‘democratic deficit.’ A vague but palpable sense of alienation from the EU, not least the result of unfamiliarity with its institutions and decision-making mechanisms, overcame the member states’ citizens. Popular discontent was strongest in traditionally Eurosceptical countries such as Britain, Denmark, and Sweden; however, there was considerable popular dissatisfaction even in traditionally EU-friendly countries. The evidence of this phenomenon was provided during the treaty reform debacle of 2005–2008, when the French and the Dutch voters rejected the Constitutional Treaty while the Irish voters rejected the successor Lisbon Treaty. Clearly, the series of major treaty reform negotiations in the post-Maastricht era, culminating in the Amsterdam Treaty (1997), the Nice Treaty (2000), the Constitutional Treaty (2004), and the Lisbon Treaty (2007), stoked public unease with the policies and practices of the EU. The primary purpose of the Amsterdam Treaty was to revise the Common Foreign and Security Policy, first introduced in the Maastricht Treaty. However, in anticipation of the eventual accession of numerous Central and Eastern European countries, institutional issues came to dominate the inter-governmental conference instead. The most contentious of them concerned QMV. With the number of small countries hoping to join the EU

Introduction

11

greatly outweighing the number of big candidates, the balance of influence in Council decision-making would tilt further away from the existing big member states. Hence their efforts in the Amsterdam negotiations to win agreement to a reweighting of Council votes, in return for their willingness to appoint only one commissioner – a step necessary in any case to keep the enlarging Commission to a manageable size – and to reconsider the allocation of seats in the European Parliament. Failure to reach agreement during highly contentious negotiations in the closing hours of the Amsterdam summit demonstrated the apparent intractability of these issues. Enlargement on the one hand and the EU’s greater policy scope on the other had raised the political stakes surrounding QMV, much as the related phenomenon of growing public unease about deeper European integration had previously done. A bitter dispute among member states in the run-up to the EU’s first post-Cold War enlargement – which took place in 1995 and included Austria, Finland, and Sweden – further illustrated the political sensitivity of QMV. As with previous enlargements, the acceding countries received a number of Council votes that was roughly proportionate to their populations, and the existing member states recalculated the number of votes needed for a qualified majority (which remained at about 71 per cent of the total as had previously been the case). However this time, motivated by principle and presumed national interest, and because of intense pressure from Eurosceptical Conservative back-benchers, the British government (with Spanish support) demanded that the number of votes needed for a blocking minority be kept at the pre-enlargement number of 23 instead of accepting the new post-enlargement number, i.e. 26. After heated negotiations, governments thrashed out the Ioannina Compromise, whereby ‘if members of the Council representing a total of 23 to 25 votes indicate their intention to oppose the adoption by the Council of a decision by a qualified majority, the Council will do all within its power to reach, within a reasonable time … a satisfactory solution that can be adopted by at least 65 votes’, i.e. Britain’s preferred qualified majority. For all intents and purposes, the Ioannina Compromise was mostly a facesaving device for Britain and had little practical effect on EU decision-making (see Hayes-Renshaw and Wallace 2006, 271–3). Instead, its real significance lay in highlighting the political prominence of QMV and the institutional challenges linked to enlargement. Undoubtedly, Britain’s government at the time was obstructionist and Eurosceptical. That changed when Labour won the general election in May 1997. Nevertheless, the new British government, as well as the governments of other big member states, grew increasingly concerned about the impact on their decision-making power of the likely accession, sometime after 2000, of numerous small member states (ranging in size from Cyprus to Hungary), and only one big member state (Poland). Although the Amsterdam Treaty did not address their concerns, it stipulated that Council votes would have to be reweighted during the next round of treaty reform. That set the stage for another inter-governmental conference, this time dealing with the so-called Amsterdam leftovers (Council votes, Commission size, and European Parliament seats).

12

Institutional Design and Voting Power in the European Union

The 2000 inter-governmental conference, resulting in the Nice Treaty, was the most limited in duration and scope of all the inter-governmental conferences that have taken place since the mid-1980s (Laursen 2006; Usher 2003). It dealt almost exclusively with institutional issues decided mostly between EU leaders during the acrimonious Nice summit. Prominent on the agenda was the issue of the future institutional representation of all twelve prospective member states (10 Central and Eastern European countries plus Cyprus and Malta). As expected, given the pressure from the big member states, the ensuing Nice Treaty radically reweighted the number of votes for each existing member state while allocating votes to the prospective member states. The total number of Council votes would increase from 87 before enlargement to 321 subsequently once the Nice Treaty took effect in November 2004. Under its provisions the four biggest member states would maintain parity, with 29 votes each, while Poland and Spain would also be on a par with an astounding 27 votes each, only two fewer than the biggest member states. This was an extraordinary diplomatic victory for the latter two countries, scored against a French presidency preoccupied with upholding French representational interests in the face of Germany. In addition to amending the total number of votes, the Nice Treaty introduced two criteria for a qualified majority: at least half (and in some cases two-thirds) of the member states comprising at least 62 per cent of the total EU population (should a member state seek such confirmation). The apparent complexity of the Nice arrangements, and the acrimony surrounding the summit, brought the Council voting system and the procedure for treaty change into public disrepute. Yet few people understand voting systems in most legislative arenas and the Nice system has actually proved remarkably efficient. Far from paralyzing Council decisionmaking, implementation of the Nice arrangements in the enlarged EU has not had a detrimental impact on the Council’s legislative output (Hagemann and De Clerck-Sachsse 2007). Nevertheless, political pressure to simplify the voting system by moving to a double majority of member states and population intensified in the aftermath of the Nice negotiations. Reflections on Council voting became bound up in the much broader debate on the Future of Europe, launched by the German Foreign Minister Joschka Fischer in May 2000 and eagerly seized on by other national leaders. This was the prelude to yet another round of treaty reform. In view of widespread disappointment with the Nice Treaty and disillusionment with the inter-governmental conference that produced it, the European Council agreed in December 2001 both to widen the agenda of the next round of treaty reform and to prepare for it by calling a convention representing national governments and parliaments of existing as well as prospective member states, the European Commission, and the European Parliament. QMV was one of the many institutional

Introduction

13

issues considered by the Convention on the Future of Europe, which produced a Draft Constitutional Treaty in June 2003. The paradox of the Constitutional Convention was that while it sought to democratise and legitimise the process and product of treaty change in the EU, under existing EU rules such change could only happen as a result of an intergovernmental conference. Accordingly, the Draft Treaty was subject to review and possible revision by national governments during a follow-up inter-governmental conference (hence the qualifier ‘draft’). Understandably, national governments used this opportunity to try to change parts of the Draft Treaty which they saw as detrimental to their interests. The most controversial issue, which caused a fierce argument at the 2003–2004 inter-governmental conference and flared up again in 2007 during the short inter-governmental conference that preceded the signing of the Lisbon Treaty, was QMV (Dinan 2005 and Dinan 2008). At issue was the effort by Poland and Spain to maintain the huge advantage in voting weight that they had won in the Nice Treaty. Why should Spain surrender an advantage to which the other governments had agreed in the hard-fought Nice negotiations? Meanwhile, Poland’s justification was that, having recently won a referendum on its EU membership terms, it would be wrong (not to mention politically risky) to renounce the prize of a voting weight nearly equivalent with that of France and Germany. For their part, France and Germany were determined to preserve the proposed new double majority system in the Constitutional Treaty, which would give them, being the most populous member states, an obvious advantage. Revisiting the Convention’s institutional proposals was akin to opening Pandora’s Box. Indeed, as member states had their heels dug in not only on QMV but also on the size of the Commission, a renegotiation of institutional arrangements could not be avoided. Ultimately, the stalemate between France and Spain on the question of Council voting led to a breakdown of negotiations in December 2003. Threats by France and Germany, the chief proponents of the double majority system, to link the outcome of the inter-governmental conference to the upcoming budget negotiations (by implication threatening EU funding for Poland and Spain), and to forge ahead with a ‘core’ or ‘pioneer’ group of like-minded member states, exacerbated the situation. The incoming Irish presidency urged restraint and managed to get the negotiations restarted. Meanwhile, leadership changes in Poland and Spain (for reasons unrelated to the inter-governmental conference) improved the chances of agreement. Consistent with the newly accommodating attitudes to their EU partners, the two countries’ governments were now willing to work toward a compromise on the proposed new arrangements for Council voting. Although other sensitive issues remained open, resolution of the QMV question paved the way for a successful conclusion of the inter-governmental conference in June 2004, in the form of the Constitutional Treaty.   On the Constitutional Convention and the Constitutional Treaty, see Laursen 2008 and Normal 2005.

14

Institutional Design and Voting Power in the European Union

Reflecting not only Spanish and Polish concerns but also the misgivings of the smaller member states, the provisions on Council voting in the final Constitutional Treaty differed appreciably from those contained in the Convention’s Draft Treaty. Whereas the Draft Treaty had provided for a double majority consisting of at least 50 per cent of the member states and at least 60 per cent of the total population, in the Constitutional Treaty this was changed to at least 55 per cent of the member states and at least 65 per cent of the total population, with an additional stipulation that a qualified majority would have to consist of at least 15 member states and a blocking minority of at least four member states. These changes meant that the provisions for Council voting in the Constitutional Treaty were less congenial to the most populous member states, and also more complicated, than the original proposal. On the one hand, it would be harder for the most populous member states to form winning coalitions; on the other, it would be easier for them to form blocking minorities. Yet compared to the traditional system of weighted votes, the four most populous member states (France, Germany, Britain, and Italy) would clearly be better off. The Constitutional Treaty provisions for Council voting were not an issue in the French and Dutch referenda of 2005. Nevertheless, the Polish government used the rejection of the Constitutional Treaty in France and Holland as a pretext to revisit the question of QMV during the negotiations that transformed the Constitutional Treaty into what most national governments hoped would be the politically more acceptable Lisbon Treaty. After some particularly sharp exchanges between the Polish President Lech Kaczyński and the Prime Minister Jarosław Kaczyński on one side and the French President Nicolas Sarkozy and the German Chancellor Angela Merkel on the other, Poland won a delay in the entry into force of the double majority system and an agreement on a new iteration of the Ioannina Compromise. As in the previous disputes over QMV, this one combined elements of principle, policy, politics, and personality. Conclusion The seemingly endless series of inter-governmental conferences and treaty changes from the mid-1980s to the mid-2000s greatly changed the character and scope of QMV. The national governments’ agreement, embodied in the Single European Act, to make greater use of QMV in Council decision-making effectively put an end to the Luxembourg Compromise. Subsequent practice confirmed that countries were indeed willing to play by the new rules and risk being outvoted on a wide range of issues. A decade after the Single European Act, however, a mechanism similar to the Luxembourg Compromise found its way into the Amsterdam Treaty as regarded closer co-operation (flexible integration) among member states. According to the new provision, a government could, ‘for important and stated reasons of national policy,’ prevent a vote being taken in the Council on whether to allow closer cooperation to take place. The inclusion of a quasi-veto with respect to flexibility,

Introduction

15

and elsewhere in the treaty with respect to ‘constructive abstention’ in foreign and security policy decision-making, demonstrated the supreme sensitivity of these issues for most member states. Similarly, the Constitutional Treaty (and later the Lisbon Treaty) included so-called ‘emergency brakes’ that governments could rely on in case of alleged endangerment of the national interest in certain policy areas. The spectre of the Luxembourg Compromise hovering over the contemporary EU, as well as the revival of the Ioannina Compromise, illustrates the old adage that plus ça change, plus c’est la même chose. Ironically, the far greater applicability of voting rules since the Single European Act does not necessarily mean that an increased number of agenda items are put to a vote. Since the late 1980s there has been greater use of QMV in principle rather than in practice. National governments are willing to abide by qualified majority decisions but, ever cognizant of each other’s political sensitivities and imbued with a deep-rooted culture of consensus, which soon pervades the new member states, they usually prefer that a formal vote not take place. The presidency may call for a vote, but voting does not always follow. Instead, the country or countries in the minority often accept the inevitable and acquiesce in the majority’s position. Undoubtedly QMV is important in facilitating decisionmaking, but not necessarily because of actual voting (see Heisenberg 2005, 65–90; Hayes-Renshaw and Wallace 2006, 277–97; Naurin and Wallace, 23–80) There is little reason to think that things will change dramatically in this respect following implementation of the Lisbon Treaty. References Andenas, M., Usher, J. A. 2003. The Treaty of Nice and Beyond: Enlargement and Constitutional Reform. Portland: Hart Publishing. Dinan, D. 2004. Europe Recast: A History of European Union. Basingstoke: Palgrave Macmillan. Dinan, D. 2005. Governance and Institutions: A New Constitution and a New Commission, Journal of Common Market Studies, 43, s1, 37–54. Dinan, D. 2008. Governance and Institutional Developments: Ending the Constitutional Impasse, Journal of Common Market Studies, 46, s1, 71–90. Hagemann, S., De Clerck-Sachsse, J. 2007. Decision-Making in the Enlarged Council of Ministers: Evaluating the Facts. CEPS Policy Brief Number 119, Brussels: CEPS. Hayes-Renshaw, F., Wallace, H. 2006. The Council of Ministers. 2nd Edition. Basingstoke: Palgrave Macmillan. Heisenberg, D. 2005. The Institution of ‘Consensus’ in the European Union: Formal Versus Informal Decision-Making in the Council. European Journal of Political Research, 44:1, 65–90. Laursen, F. (ed.). 2006. The Treaty of Nice: Actor Preferences, Bargaining and Institutional Choice. Leiden: Brill.

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Laursen, F. (ed.). 2008. The Rise and Fall of the EU’s Constitutional Treaty. Leiden: Brill. Moravcsik, A. 1992. Negotiating the Single European Act: National Interests and Conventional Statecraft in the European Community. International Organization, 45:1, 19–56. Naurin, D., Wallace, H. (eds). 2006. Unveiling the Council of the European Union: Games Governments Play in Brussels. Basingstoke: Palgrave Macmillan. Norman, P. 2005. Accidental Constitution: The Making of Europe’s Constitutional Treaty. 2nd Edition. Brussels: EuroComment. Palayret, J.M. and Wallace, H. 2006. Visions, Votes and Vetoes: The Empty Chair Crisis and the Luxembourg Compromise Forty Years On. Brussels: Peter Lang Publishers. Usher, J.A. 2003. Assessment of the Treaty of Nice – Goals and Institutional Reform, in The Treaty of Nice and Beoynd, edited by M. Andenas and J.A. Usher. Oregon: Hart Publishing, 183–206. Wall, S. 2008. A Stranger in Europe: Britain and the EU from Thatcher to Blair. Oxford: Oxford University Press.

Part I Voting System for the Council of European Union

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Chapter 1

Is the Double Majority Really Double? The Voting Rules in the Lisbon Treaty Axel Moberg

A Long and Winding Road Since the establishment of the European Economic Community (EEC) in 1958, decisions by qualified majority voting (QMV) in the Council have been based on a system of weighted votes, with over-representation of medium-sized and small states (‘degressive proportionality’). The voting rules have been under constant negotiation, together with other institutional issues, over the past 15 years, in the light of successive EU enlargements, particularly at the Inter-Governmental Conferences (IGC) on treaty changes held at Amsterdam (1997) and Nice (2000). The voting rules were the most controversial issue in these negotiations. On the eve of enlargement of the EU to Central and Eastern European countries, an agreement was reached at Nice on the institutional changes that were necessary for enlargement. The voting rules consist of qualified majorities of the weighted votes and the population and a majority of member states. So far the principle of degressivity was not questioned. The new weights were integrated into the Accession Treaty, agreed in Copenhagen in December 2002, and after a provisional arrangement during the first months after the enlargement, began to apply on 1 November 2004. At the EU summit at Laeken in December 2004, the member states decided to call a ‘convention for the future of Europe’, in order to prepare yet another treaty. In July 2003 the Convention proposed a draft Constitutional Treaty in which the weighted votes were replaced by a double majority of member states and population. In the following IGC, in particular Spain and some medium-sized states initially resisted the double majority, but an agreement including the double   This is an updated, revised and shortened version of a working paper published on the website of Real Instituto Elcano, Madrid, No 290, 31 May 2007. Available at: http://www. realinstitutoelcano.org/wps/portal/rielcano_eng/Content?WCM_GLOBAL_CONTEXT=/ Elcano_in/Zonas_in/Europe/DT+23-2007. The views expressed are the author’s alone, and not those of any government or public institution. The author would like thank a great many colleagues and researchers for useful advice and interesting discussions, in particular M. Hosli, M. Machover, I. Paterson, M. Albert, H. Wallace, W. Słomczyński, K. Życzkowski, A. Laruelle and J.-E. Lane.

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majority, with higher percentages for qualified majority, was finally reached in June 2004. The ratification procedure then stalled after the referenda in France and the Netherlands. Double majority was undoubtedly the driving force in the efforts to save parts of the treaty. The German Presidency succeeded in pushing through an agreement on all political issues, including the double majority, at the summit in June 2007, so that the next IGC was merely a technical exercise. The Lisbon, or Reform Treaty was signed in Lisbon in December 2007, but was again put in limbo by the results of a referendum held in Ireland in June 2008. Enlargement, Balance of Power and ‘Legitimacy’ The discussion of voting rules in the EU must be seen in terms of the balance of power between member states. Some of the large member states have been seriously concerned that their share of the votes has decreased through the admission of new members (as would happen in any club), and wish to restore the situation. In absolute terms the share of, say, France, has fallen from almost 25 per cent in the original EC6 to about 8.4 per cent in EU27. The under-representation of the large states has also increased moderately, with the increased number of small and over-represented member states. Spain has also been concerned about the balance after the 1995 ‘northern’ enlargement. The code words for these demands have often been ‘democratic legitimacy’ or ‘efficient institutions’. However, the share of each of the smaller countries has also fallen by the same percentage, the over-representation of all smaller countries has also decreased proportionally, and the proportions between a given large country and a given small one did not change until Nice (Moberg 1998, 2002). The voting rules of the Nice Treaty, as well as other parts, have been increasingly criticised in the public debate, not least by the governments – France and Germany – that once designed them. It has been argued that the rules are extremely complicated and difficult to apply, that Spain and Poland obtained too much weight compared with the big four, and that the high thresholds (required share of votes) for a qualified majority would lead to paralysis in decision-making. The latter fear is largely inspired by academic studies on voting power (Baldwin et al. 2001, Felsenthal and Machover 2001). There are several explanations for the criticism of the Nice rules. There was obviously some confusion at Nice and important points had to be straightened out afterwards. Many in the public debate had not understood, or accepted, the limited mandate of the Nice IGC. More important, the large countries had been hoping to get more. Some medium-sized and small member states may have hoped to get away without any substantial re-weighting, despite commitments they had   Germany to Italy. Spain and Poland are a group to themselves. The medium-sized are the Netherlands to Bulgaria. Small refers to the rest. Cf. Table 1.1.

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made at Amsterdam. Germany had insisted on a greater weight to reflect its larger population after its reunification. France had resisted, insisting on the historical ‘parity’. The Netherlands and Belgium had a similar dispute, and others were also uneasy about the weight of neighbouring countries. The alleged ‘inefficiency’ of the system also played a role. Excursus: What is ‘Democratic Legitimacy’? This chapter does not intend to solve the question of what a voting system ‘should’ look like. However, as a background it is necessary to point out that authors have widely diverging views of what ‘democratic legitimacy’ means in the EU context, and whether it is at all possible or desirable, in the same sense as in member states. On one end of the spectrum is the traditional, and legally indisputable, view that it is the governments of member states that are represented in the Council. The Council shall consist of a representative of each Member State at ministerial level, who may/authorised to commit the government of that Member State...

The Council is not meant to be like the US Congress, where the entire population is represented at the federal level, bypassing the states. A priori, this could provide good arguments for using the traditional inter-governmental principle, one state/ one vote, but this is utterly unrealistic. The weighted votes have existed since 1958, and the large member states insist on a greater weight. On the other end of the spectrum there is the principle of one man/one vote and the view that weights should be proportional to population. The double majority is often presented as if this were the purpose, and it is often forgotten that the majority was meant to be ‘double’, with a state component. It should be recalled that proportionality is not always observed within the constitutional systems of many member states where, for instance, rural regions are sometimes favoured, as in the French Senate, or small states in federal systems as in the German Bundesrat. The main emphasis in academic studies on the subject since the mid-1990s has been voting power, i.e., a country’s ability to tip the balance, based on Penrose’s theories. His rather cautious conclusion was that governments of small nations are more representative than governments of large states. Therefore each voter would have the same possibility of indirectly deciding the outcome, if voting power were almost proportional to the square root of the number of voters. Some of his later followers see this as the ‘correct implementation of the one person, one vote principle’. The Constitutional Treaty introduced a new principle, according to which the Union is based on both member states and citizens. This was probably a way of preparing the ground for the Presidium’s proposal on the double majority and a

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greater weight for the large countries. In any case it is doubtful that this principle is at all relevant for decision-making in the Council, where governments are represented. The author is not very convinced by any of these views. What a voting system ‘should’ be is a political choice. A degressive voting system, such as the pre-Nice system, can be seen as a compromise between opposite interests, which takes account of both states and population at the same time, and could help to make EU decisions more acceptable. It should be noted that a double majority, or a triple one like Nice, are not compromises. Each criterion can be used independently with its full weight for blocking decisions. Decision Making in the EU Member states pursue national interests, but are also driven by a common wish to move forward and to stay in the mainstream. It has been described as ‘decisions in the shadow of a vote’. The votes are only potential weapons. The threat of a majority decision is a powerful instrument to bring about consensus. So far, a vast majority has been required for a decision. Blocking minorities are a powerful instrument to obtain concessions. They can be seen as the key to decision making. Maintaining blocking possibilities has been the underlying leitmotif in past negotiations on voting rules. Declaration 21 of the Nice Treaty actually defines the qualified majority in EU27 through the blocking minority. Blocking minorities are a dynamic element in the process. They do not stop decision-making. If a decision is blocked, it only means there are continued negotiations until a solution – acceptable to at least a majority – is reached. The Presidency determines whether there is support for the proposal, mostly without a vote. Member states normally only vote openly against, if they want to show domestic opinion that they fought to the end. The important thing is whether anyone actively objects to the Presidency’s conclusion. If no one does, a decision can actually be taken with the support of a smaller majority than QMV. If it is a matter for qualified majority, there will be an agreement sooner or later. There is hardly any evidence that more than a few decisions on QMV issues have ever been blocked indefinitely by a minority. The weights and thresholds determine the bargaining strength of member states. They do not decide whether there will be a decision, but rather which decision it will be. Voting Power Voting power studies calculate the power, by computing in how many of the theoretically possible coalitions a state can decide the outcome, by casting its vote for or against a proposal. Most studies are based on the a priori assumption that

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any state can take any position on an issue, or remain indifferent, and that all coalitions are equally probable, they thus assume an impartial coalition culture. Garrett and Tsebelis (1999) have criticised voting power methods for disregarding the spatial distribution of a member states’ positions, and the effects of the institutional setting. Albert (2003) has criticised them for not being based on any relevant ‘political’ science, and for disregarding existing knowledge of how member states actually behave. The author’s most important objection is that the very concept of power as a member state’s ability to tip the balance is dubious. As Laruelle, Martinez and Valenciano (2006) have pointed out, what member states are concerned with is the result of the decision-making process, they also care about being on the winning side in a majority or a blocking minority along with other like-minded countries. The formal weight is what counts when member states try to piece together a blocking minority, or a majority. In negotiations about voting rules, member states look at the effect they would have for themselves and expected allies on predictable issues. Moreover, simple mechanical counting of the number of coalitions, without weighting them by the importance of the issue, is a blunt instrument. In the end, voting potential must be seen in the light of member states’ own perception of their priorities and predictable allies. This chapter only touches upon a few concrete possible coalitions (large states, net contributors or beneficiaries, old and new members, friends and opponents of CAP reform, free trade, etc.). Furthermore, voting power studies do not analyse the effects of each of the components of the voting rules, or put them in the political context. As a consequence, important aspects and the reasons why the rules were designed the way they were are often overlooked. This is the case with the effects of the population criterion under Nice, the role of the ‘state component’ and the disappearance of the threshold for the weighted votes. Finally, combinatorical effects should become less interesting as the number of theoretically possible coalitions increase from just 64 originally, to 135 million in EU27, and voting power should go in roughly the same direction as weights. To summarise, voting power calculations may be logical and relevant to groups with a small number of actors, such as parties in a parliament, and in case of clearcut issues. But it is doubtful that they are really suited to the highly consensusdriven decision making in the EU, with a large number of members. Therefore this chapter does not make use of voting power calculations. The calculations of ‘power’ will be based instead on the member states’ share of the weighted votes and on their share of the necessary blocking minority, or qualified majority, with different voting rules in EU27. To avoid confusion with voting power terminology the latter shares are referred to as a state’s voting/blocking ‘potential’. The ratio between a country’s share of the votes and its share of the population is used as a simple measure of its over-/under-representation. Unlike other measures used at the IGCs, it offers a point of equilibrium.

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Bargaining, not Bingo Game Many studies (Baldwin et al. 2001, Felsenthal and Machover 2001, Lane and Maeland 2002), also use voting power methods to calculate the probability that the Union will reach a decision. They claim that the ‘effectiveness’ of decision-making decreases dramatically with higher thresholds, and with the number of member states at the same threshold as in successive probability calculations. Hosli and Machover (2004) claim that the ‘chances’ of a decision being made have already declined, since 1981, from 6:1 to 12:1, but also point to contrary findings. The author’s greatest objection to calculations of ‘effectiveness’ is that such an approach treats decision making in the EU as a bingo game, where member states all cast their votes on one occasion, independently of each other, and this results in a decision or no decision. The crucial mistake is that decision making in the EU it is not a bingo game, where probabilities decide the outcome, but a bargaining process. Even if decision making has reached deeper down into sensitive matters and moved into new areas, working methods have changed and the involvement of parliament has increased, it is doubtful that there has been a significant, if any, slow-down in recent years. It may even be the other way around. To conclude, calculations of ‘effectiveness’ have little to do with reality and are rather misleading. The Nice Rules are Not All That Complicated The Nice/Copenhagen rules consist of three elements: 1. Weighted votes with degressive proportionality, as in the old system. The weighting was changed moderately in favour of the large countries. The threshold for a qualified majority was increased from the traditional level of about 71 per cent to 73.91 per cent in EU27. 2. A majority of member states. The old provision – that two-thirds of member states are needed when the Council is not acting on a Commission proposal – was maintained. 3. A possibility for member states to demand that member states representing 62 per cent of the population support a given decision. For all practical purposes the only important factors are the weighted votes and the 62 per cent population criterion. The population criterion only has one effect. It gives Germany substantially greater blocking potential than its 29 votes, and thereby greater weight than the other large countries (without being so visible). Germany alone has almost half of a blocking minority. This blocking potential can only be used in coalitions with other large countries. In this way, three of the

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large states can maintain a blocking majority in EU27, provided that Germany is among them. This was the declared objective of at least the UK. Even if this does not give the whole picture of the larger states’ interest, and it is highly unlikely that these states would be alone in opposing a proposal, it is a good yardstick for judging the effects of different rules. The population criterion is only relevant when Germany is against a proposal, and can be disregarded in all other situations in EU27. The reason why this criterion was introduced was in all likelihood to accommodate German demands for a greater weight. It was not to guarantee that decisions are backed by a certain share of the total population. The weighted votes alone guaranteed at least 58.4 per cent. The majority of member states is symbolically important, because it would otherwise be theoretically possible, from EU25, to reach a qualified majority against a majority of member states. But in practice it could only decide an issue if the majority of member states are standing against a group that already commands a qualified majority of votes, and 62 per cent of the population. Simple simulations show that this can only happen if almost all the large states are against a coalition consisting of almost all the small member states. Such highly polarised situations have hardly ever occurred. A point in the Nice rules that has been heavily criticised is that there is hardly any difference in votes, 27 against 29, between Spain or Poland and Germany, which has twice the population of either Spain or Poland. The population criterion largely compensates Germany for this. If it is translated into votes with the same effect, the proportions between Spain’s and Germany’s blocking potentials are more like 27 to 41, which is not unreasonable in a degressive system. On the other hand, the disproportion between the weight of Spain and Poland, and that of the UK, France and Italy, with a population up to 50 per cent greater, is evident. The population criterion is only of marginal use to the latter. And, in comparison to medium-sized and small countries, Spain’s and Poland’s weight is not unreasonable. The Double Majority is Not Really Double It can be debated whether the institutional issues in the Nice Treaty, that had just been settled in view of the coming enlargement, were at all covered by the Convention’s mandate. None of the issues was directly related to enlargement, even if the media and politicians rarely made that distinction. There was a very general wording about greater democratic legitimacy and transparency, but none of the 57 specific questions in the document concerned the Nice issues, and it was only halfway through the Convention that it became clear that they would be on the agenda.

  These and other calculations can easily be made with the author’s calculation tool, which can be downloaded from the website cited in note 1 above.

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Since these issues are extremely sensitive there has always been little open analysis of them at the IGCs, and consequently delegations have not always been fully aware of the effects of the options. At the Convention, which was otherwise a step forward when it comes to transparency, there was rather less analysis of this issue. The Presidium did not appoint a special working group for this, as for many other matters, and it was only discussed in a few plenary debates at the end. The Convention model is often referred to as ‘the double majority’. However, it is just one version of a double majority, i.e., of population and member states, which was not discussed much in the Amsterdam and Nice IGCs. At that time, Germany and several other countries were pursuing a different version, with weighted votes and population, which was basically integrated into the Nice deal. The double majority abolishes the weighted votes, (1) above, and the overrepresentation of smaller countries. Only the two other criteria remain: (2) a majority of member states in the Convention proposal, and in the 2004 IGC deal, 55 per cent, but at least 15 states, which is automatically reached in EU27; and, finally, (3) a requirement that it represents 60 per cent of the population in the convention proposal, and 65 per cent in the IGC deal. Unlike Nice, the population criterion is now a compulsory element. With this double majority there is no need to modify the rules before the future enlargements, or in view of the dramatic demographic changes that are to be expected. Again, the majority of member states criterion will hardly ever play a role, at least with thresholds at this level. It can only do that if the group can outweigh member states with 65 per cent of the population. Simulations show that it could only happen if the majority is against a coalition including three of the large states. In practice, only criterion (3) counts. Therefore the weight of member states is, for all practical purposes, directly proportional to the size of their population. In the 2004 IGC deal there were a few additions that marred the original beauty of the formula. In the cases where the Council is not acting on a Commission proposal, the threshold is raised to 72 per cent of member states (which means that, theoretically, a minority of eight states representing 3 per cent of the population could block a decision, against 5 per cent under Nice). There is also a ‘double key’ according to which at least four states are required for a blocking minority. This means that the large states, in principle, gave up the blocking minority of three of them, although any country, however small, would do as a nominal fourth partner. On the other hand, a special check for ‘almost blocking’ minorities, reminiscent of the ‘Ioannina compromise’ was introduced. This compromise was made in 1994 on the eve of the EFTA enlargement. The gist of it is that member states that constituted a blocking minority before that enlargement, but not after the accession of the new states, would still have a kind of ‘suspensive veto’. The compromise was linked to the pre-Nice voting rules, and has thus ceased with the Nice rules. It was re-introduced, for an undefined period, in the Constitutional Treaty and

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made permanent in the Lisbon Treaty. If countries representing three-quarters of a blocking minority in the Constitutional Treaty, or 55 per cent of a double majority in the Lisbon Treaty (i.e., 19.25 per cent of the population or eight member states), oppose a decision, the presidency shall try to find a satisfactory solution within ‘a reasonable time’. The period can be ended by a simple majority decision. The Ioannina formula hardly played a role in decision-making before Nice. It remains to be seen whether it will with the new treaty. If it does, it would mean a ‘hidden increase’ in the threshold, and would theoretically give small minorities even greater possibilities to block – although temporarily – than the much criticised Nice rules. Why the Balance Changes Weights The changes in weights are simple and straightforward. The weighted votes in the Nice Treaty disappear, and are replaced by the member states’ share of the population. There is no longer any degressivity. The overall effects can be seen in Table 1.1 Member states’ gains and losses in weight, compared with Nice, are the inverted value of their former over- or underrepresentation. The combined weight of the four largest states increases from 34 per cent of the votes to 54 per cent of the population. The weight of Germany doubles and that of most large countries increases by around 40 to 50 per cent. The weights of Spain and Poland only change marginally, but with the disappearance of degressivity, the gap to the large countries increases even beyond the pre-Nice situation, which is a blow to their old ambition of being considered members of that club. The weight of the medium-sized countries is reduced to around 60 per cent, and that of the smallest member states much more. The combined effect of losses and gains is that the weight of the large states increases on average around 2.5 times against the others. For example, the proportions between Belgium and France change from around 1:2.4 to almost 1:6. Medium-sized countries gain in relation to even smaller ones, etc. All in all, the double majority eliminates the effects of the last enlargements and restores the large countries’ shares to around what they were in EU12. (One caveat is necessary. If the population criterion becomes the dominating feature under the Nice rules, it could be argued that the balance hardly changes at all.)

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Table 1.1

Institutional Design and Voting Power in the European Union

Changes in voting weight and blocking potential

EU27

QMV BM Germany France UK Italy Spain Poland Romania Netherlands Greece Portugal Belgium Czech Republic Hungary Sweden Austria Bulgaria Denmark Slovakia Finland Ireland Lithuania Latvia Slovenia Estonia Cyprus Luxembourg Malta

Weight Population % Votes % Nice (,000)

82,438 62,886 60,422 58,752 43,758 38,157 21,610 16,334 11,125 10,570 10,511 10,251 10,077 9,048 8,266 7,719 5,428 5,389 5,256 4,209 3,403 2,295 2,003 1,345 0,766 0,459 0,404 492,881

16.7 12.8 12.3 11.9 8.9 7.7 4.4 3.3 2.3 2.1 2.1 2.1 2.0 1.8 1.7 1.6 1.1 1.1 1.1 0.9 0.7 0.5 0.4 0.3 0.2 0.1 0.1

Share of BM % over- Change Nice by DM Change rep. in DM Vote Pop. Pop.

255 73.91 91 26.38 29 8.41 0.50 29 8.41 0.66 29 8.41 0.69 29 8.41 0.71 27 7.83 0.88 27 7.83 1.01 14 4.06 0.93 13 3.77 1.14 12 3.48 1.54 12 3.48 1.62 12 3.48 1.63 12 3.48 1.67 12 3.48 1.70 10 2.90 1.58 10 2.90 1.73 10 2.90 1.85 7 2.03 1.84 7 2.03 1.86 7 2.03 1.90 7 2.03 2.38 7 2.03 2.94 4 1.16 2.49 4 1.16 2.85 4 1.16 4.25 4 1.16 7.46 4 1.16 12.5 3 0.87 10.6 345

2.0 1.52 1.46 1.42 1.13 0.99 1.08 0.88 0.65 0.62 0.61 0.60 0.59 0.63 0.58 0.54 0.54 0.54 0.53 0.42 0.34 0.40 0.35 0.24 0.13 0.08 0.09

31.9 31.9 31.9 31.9 29.7 29.7 15.4 14.3 13.2 13.2 13.2 13.2 13.2 11.0 11.0 11.0 7.7 7.7 7.7 7.7 7.7 4.4 4.4 4.4 4.4 4.4 3.3

62 38 44.0 33.6 32.3 31.4 23.4 20.4 11.5 8.7 5.9 5.6 5.6 5.5 5.4 4.8 4.4 4.1 2.9 2.9 2.8 2.2 1.8 1.2 1.1 0.7 0.4 0.2 0.2

65 35 47.8 36.5 35.0 34.1 25.4 22.1 12.5 9.5 6.4 6.1 6.1 5.9 5.8 5.2 4.8 4.5 3.1 3.1 3.0 2.4 2.0 1.3 1.2 0.8 0.4 0.3 0.2

1.09 1.09 1.09 1.07 0.85 0.75 0.81 0.66 0.49 0.46 0.46 0.45 0.44 0.48 0.44 0.41 0.41 0.41 0.40 0.32 0.26 0.30 0.26 0.18 0.10 0.06 0.07

Note: Population figures for 2007

Blocking Minorities The blocking potential is also affected by the lowered threshold and the need for greater blocking minorities. The situation does not change dramatically for the

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large states. Already under Nice their strongest card was the population criterion, in particular Germany’s population, and the threshold population was even raised slightly in the Lisbon Treaty. By comparison, the Commission proposal in the Nice negotiations of a ‘double single majority’ with 50 per cent of states and of the population, which was unearthed at the Convention, would actually have reduced the blocking potential of the large states (and of all other states in the same proportion). In absolute terms each of the large states, with the exception of Germany, would even have had slightly less blocking potential than if the original pre-Nice system had been continued, and three large states would no longer have a blocking minority in EU27. The limit for this is around 59 per cent. This is, in all likelihood, why the Convention proposed 60 per cent. However, the balance of power is relatively precarious: the blocking potential of three large member states could also be maintained after an enlargement with the remaining countries in Western Europe and the Balkans, or with Turkey, but not both. The medium-sized and small countries are in a different situation. Not only do they lose in weight, but the relatively high threshold for the weighted votes, which was their strongest card, also disappears and the necessary blocking minority increases. Therefore they lose another 25 per cent of their blocking potential. Spain and Poland’s loss in blocking potential, despite a slight increase in weight, is an effect of this phenomenon. The combined effect of eliminated degressivity and the lowering of the threshold is that the medium-sized states’ blocking potential falls to less than half, compared with Nice, and to even less for the smallest member states. Majorities In building majorities, the lowering of the threshold plays the other way, and increases each state’s voting potential. Germany’s share more than doubles and that of the other large states increases by about two-thirds, and it mitigates the loss in weight of the other member states. One aspect of the double majority is that it might shift the focus of member states somewhat, from the possibilities of blocking decisions to the relatively increased possibilities of reaching a majority. Six countries are sufficient to reach 65 per cent of the population, and then all that is needed is nine more states, out of 21 possible. Any member states would do; the votes of medium-sized states would not be so essential any more. Thresholds Do Not Change the Balance Under the double majority, changes in the threshold for population only increase or decrease the blocking potential of all member states by the same percentage. A raised threshold for states has only marginal effects. Furthermore, if the population

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threshold is raised, the majority of member states can only be decisive if there is an even greater polarisation between large and small countries. However, the absolute level of the threshold determines whether some coalitions can block or not. This is largely what the negotiations in the 2003–2004 IGC were about. A higher threshold increases the blocking potential for a given coalition. But it also increases the potential of other coalitions with opposite interests. The blocking potential through the weighted votes cannot be directly translated into the population criterion. To take Spain as an example, in some cases its potential allies are large states, for example, concerning agriculture or fisheries, and then only a low threshold is needed. In other cases, the natural allies are among smaller countries, for example, countries receiving cohesion funds, and then a very high threshold would be necessary. At 65 per cent, Spain could block with two large countries and one medium-sized country, at 67 per cent with two large and Lithuania as under the Nice rules, and at 68 per cent with two large member states and Malta. Were Any Other Options Possible? A few other models have figured in the debate. Some of them could once have provided simple and balanced solutions, if the large countries had accepted a differentiation between Germany and the others. More Votes to Large States Technically it is quite easy to find a compromise, under Nice, by adding some more votes to the large states an idea the Italian presidency floated in 2003. Four more votes to Germany, would be enough to ensure that the blocking minority of three large is maintained, and that a majority of the votes represents at least 62 per cent of the population. The population criterion then becomes superfluous. However, if Germany were given full compensation for the population criterion, 12 more votes, the lack of degressivity would create dramatic discrepancies to the other large states Why the Square Root Wouldn’t Fly The realism of Penrose’s theories, and proposals based on the square root of the population, have already been discussed. The square root would, however, ensure consistent and equal degressivity throughout the system. In the Nice negotiations the Swedish delegation made a proposal based on the square root. This was not founded on Penrose’s theories, but was just meant as a practical compromise (Moberg 2002). At some point many delegations were prepared to accept it, whether for genuine agreement or tactical reasons. The model was not accepted at Nice, probably because some of the large member states were hoping to get more,

Is the Double Majority Really Double? The Voting Rules in the Lisbon Treaty

31

and because of their qualms about a greater weight for Germany. Eventually some large states gained one vote more. The Nice allocation is, actually, quite close to the square root in absolute numbers. Poland gained four votes that Germany would have had, if the Nice votes had been distributed by the square root, while Spain gained three, mainly from Romania. Otherwise the difference is just about plus/minus one vote for a handful of countries. The square-root formula has been overtaken by events. Many scientists have suggested models based on the square root with a substantially lower threshold, the Polish government at 62 per cent. This makes the proposals even less realistic, because it would decrease the blocking potential of the large countries dramatically. With the square root and the Nice threshold, three large states, including Germany, would have 99 per cent of a blocking minority, with the proposed threshold just 67 per cent. But the Curve Could be Made Steeper It is also possible to make the curve more proportional to population than the square root, but still keep it strictly degressive. The ‘H-method’, as it will be called here, after Anders Hagelberg who pointed out this possibility to the author, gives a whole range of options at different levels of proportionality (the ‘alpha proportionality’ used by Felderer, Paterson and Silárszky (2003) is basically the same idea). In principle the only points to negotiate would then be the slope of the curve and the threshold. The mathematical formula is quite simple. The square root can be defined as (weight in proportion to) the population, raised to the power of 0.5. In principle any figure for power can be substituted. In popular terms one could say that this figure (multiplied by 100) represents a percentage of proportionality; 0 per cent is the same weight for all member states, 50 per cent the square root, 59 per cent closest to the maximum blocking potential of all countries under Nice, and 100 per cent is full proportionality, as in the double majority. A few examples, with one member state per cluster, and the 345 Nice votes redistributed with different slopes, are given in Table 1.2. Levels of 60 per cent or more would automatically ensure that all decisions are backed by member states representing at least 65 per cent of the population (with the Nice thresholds), and they would largely maintain the Nice clusters. At about 70 per cent, the large states would have about the same degree of under-representation they had in the original EEC6. This method could also be used to obtain a consistent allocation of seats in the Parliament, which according to the Lisbon Treaty is to be ‘degressive’ in an undefined way. ‘Depopulation’ In the preludes to the summit in June 2007, and with the Polish demands for a radically different model, some actors were reportedly toying with the idea of

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putting a ‘ceiling’ on the population of Germany, or possibly all the large states. The population would then not be taken into account, or only partially, above a certain level. This would narrow the gap between the large countries and Spain/ Poland and could re-introduce some amount of degressivity, in a crude way, without jeopardising at least the blocking potential that the large states have under Nice. The idea was dismissed by the German Presidency. The Easiest Way: States and Ppopulation in the Same Bag. ‘Overpopulation’ Another simple way would be to give member states a weight, which is the sum of a fixed number of votes to all states, irrespective of size, and then more votes in proportion to their population (Moberg 1998). This would actually do what the double majority claims to do, i.e., take both member states and population into account at the same time. Unlike the state leg in the double majority the fixed number would give small states some real weight. The easiest way to achieve this model, is to keep the double majority, and then just increase the the population of each country by X fictitious millions. Table 1.2

Votes in Nice and with equal degressivity

EU27 Nice

Germany France Spain Romania Netherlands Belgium Sweden Denmark Ireland Latvia Luxembourg

29 29 27 14 13 12 10 7 7 4 4

Votes 345 votes redistributed at different degrees of full proportionality 50% 60% 65% 70% 80% 90% 100%= DM =sqrt 33 38 40 42 48 53 58 29 32 34 35 38 41 44 24 26 26 27 29 30 31 17 17 17 17 16 16 15 15 14 14 14 13 12 11 12 11 10 10 9 8 7 11 10 10 9 8 7 6 8 7 7 6 5 5 4 7 6 6 5 4 4 3 5 4 4 3 3 2 2 2 2 1 1 1 0 0

Is the Double Majority Really Double? The Voting Rules in the Lisbon Treaty

33

Conclusions The main driving force behind the voting rules proposed by the Convention was the large member states’ wish to maintain their position, and in particular blocking power, after enlargement. Those member states that initially opposed the double majority had different agendas. The main objective of the more vociferous, Spain and Poland, was to remain among the large countries, and to maintain their blocking potential. The medium-sized and small countries, which had more to lose, kept a lower profile. Most of these did not seriously pursue the Nice model, but eventually accepted the double majority, and some even pursued it actively. It may be that some did not realise the effects of the double majority. It may have seemed easier to present it to domestic opinion, as losses of weight and differences from neighbouring states are not so evident. Furthermore, many sincerely believed in the allegations of ‘ineffectiveness’ in the Nice system. Some may have found other issues more important. Finally, no country wanted to be the one that torpedoed the new treaty. The two main voting rule concepts in the 2003–2004 IGC were, in fact, incompatible, as Nice was based on degressivity, and the double majority was not. Once the choice of a double majority of states and population had been made, a genuine compromise was no longer possible. A compromise on the degree of degressivity could only be found in a different framework. When double majority is accepted, the balance of power between member states is determined by the relative size of their population alone. The ‘state’ component is hardly ever decisive. For all practical purposes the double majority is not double. The introduction of double majority entails a substantial shift in the balance of power. The long discussion about the threshold for states and population was basically a battle with windmills. The percentage of the population does not change the proportions between member states in terms of weight. However, the percentage of population is critical for the potential of some coalitions to block. The negotiations at the 2003–2004 IGC focused on finding a solution that would be acceptable to Spain. The Spanish objective to maintain its blocking potential was largely achieved in the end, through an increase of the threshold for population, and possibly the provision that four states were necessary to form a blocking minority. The motives for the Polish resistance to the double majority up to the summit in June 2007 were probably similar. What it achieved was a postponement of the double majority and the lowering of the threshold for the ‘Ioannina mechanism’. Time will show whether the latter will have any practical effect. Even if the double majority enters into force, it is an open question whether it would eventually stand the test of further enlargements. An accession of Turkey around 2015 would, according to population forecasts, mean that this country would soon become the largest member state and the gap with other large states would continue to grow. This would change the balance of power with any set of voting rules, but the effects would inevitably be greatest under the double

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majority. The question is whether the present member states are prepared to accept this, or whether there would be attempts to move back to a system based on some degressivity. References Albert, M. 2003. The voting power approach: Measurement without theory. European Union Politics, 4(3), 351–66. Baldwin, R., Berglöf, E., Giavazzi F., Widgrén, M. 2001. Nice try: Should the Treaty of Nice be ratified? Centre for European Policy Research paper MEI, 11. Felderer, B., Paterson, I. and Silárszky, P. 2003. Draft Constitution and the IGC: Voting can be Simple and Efficient – Without Introducing the Massive Transfer of Power Implied by the Convention’s Double Majority Proposal. Vienna: Institute for Advanced Studies. Felsenthal, D. and Machover, M. 2001. The Treaty of Nice and Qualified Majority Voting, revised [Online: Voting Powers and Procedures Project, Centre for the Philosophy of the Natural and Social Sciences, London School of Economics]. Available at: http://lse.ac.uk/votingpower [accessed: 21 November 2007]. Garrett, G. and Tsebelis, G. 1999. Why resist the temptation to apply power indices to the European Union. Journal of Theoretical Politics, 11(3), 291–308. Hayes-Renshaw, F. and Wallace, H. 2006. The Council of Ministers. 2nd edition. Basingstoke: Palgrave MacMillan. Hosli, M. and Machover, M. 2004. The Nice Treaty and voting rules in the Council: A reply to Moberg. Journal of Common Market Studies, 42(3), 497–521. Lane, J.-E. and Maeland, R. 2002. Note on Nice. Journal of Theoretical Politics, 14(1), 123–8. Laruelle, A., Martinez, R. and Valenciano, F. 2006. Success versus decisiveness. Conceptual discussion and case study. Journal of Theoretical Politics, 18(2), 185–205. Mattila, M. 2004. Contested decisions: Empirical analysis of voting in the European Union Council of Ministers. European Journal of Political Research, 43(1), 29–50. Moberg, A. 1998. The voting system in the Council of the European Union. The balance between large and small countries. Scandinavian Political Studies, 21(4), 347–65. Moberg, A. 2002. The Nice Treaty and voting rules in the Council. Journal of Common Market Studies, 40(2), 259–82.

Chapter 2

Penrose’s Square-Root Rule and the EU Council of Ministers: Significance of the Quota Moshé Machover

Introduction In 1946, Lionel S. Penrose proposed his Square-Root Rule (SQRR) for the General Assembly of the UN (Penrose 1946: 53–7, 1952). Like many people at that time, he looked forward to the UN evolving into a kind of federal world government. That hope was soon abandoned with the onset of the cold war; and the SQRR – along with the rest of Penrose’s scientific theory of voting power – was ignored and forgotten by mainstream social-choice research. In 1965, John F. Banzhaf – who re-invented the basic idea of that scientific theory (Banzhaf 1965: 317–43) – proposed the SQRR should be applied the following year in connection with US local (county) government (Banzhaf 1966: 1309–38); and in 1968 he discussed the SQRR in connection with the Electoral College used for the (indirect) election of the US President. By then the EU had come into being: the Treaty of Rome, establishing what was then called the European Economic Community, was signed in 1957 and came into force on 1 January 1958. Although the logic of the SQRR is clearly applicable to the EU’s main decision-making body, the Council of Ministers, it took quite a long time for this to be seriously considered and proposed. As far as I know, the first paper to propose this in an academic journal was published just over 10 years ago, in 1997, by Dan Felsenthal and myself (Felsenthal and Machover 1997: 33–47). This was soon followed by others, and since then the idea of applying the SQRR to the main decision rule of the Council has been urged by many academic experts. However, EU practitioners – politicians and civil servants – have on the whole shown little enthusiasm for applying the SQRR to decision-making in the Council. During preparatory discussions before the Nice Conference of December 2000, Sweden proposed something that looked similar to the SQRR: a weighted   Banzhaf’s discussion of the SQRR is somewhat roundabout: he presents what amounts to a proof of the rule, but does not actually state the rule itself, see Banzhaf 1968: 304–32.

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rule in which the weight of every member state was approximately proportional to the square root of its population size. This scheme was not really conceived as an implementation of the SQRR, but as a convenient way of implementing the principle of so-called ‘degressive’ allocation of voting weights, which had hitherto been practised by the EU. Indeed, the actual effect of the Swedish scheme would have been only a rather rough and imperfect approximation to the SQRR. The main reason for this is that the quota proposed by Sweden, 71.57 per cent of the total weight, was – as I shall show – too high for close proportionality between voting weights and voting powers. In any case, the Swedish scheme did not win much support. Instead, the Nice Treaty adopted by the Nice conference (Conference of the Representatives of the Governments of the Member States 2001), prescribes for the Council a decision rule modelled roughly on the degressive weighted rules used in previous phases of the EU, but with a couple of ‘epicycles’ added on to it as extra complications. More recently, at the European Council held in Brussels in June 2007, Poland argued very insistently for adopting a decision rule for the Council based explicitly on the SQRR in the form known as the ‘Jagiellonian Compromise’ devised by Wojciech Słomczyński and Karol Życzkowski (2007: 381–99). However, Poland won little support for this position and remained virtually isolated. Instead, the decision rule adopted at that meeting for inclusion in the forthcoming Reform Treaty (Council of the EU 2007) – which is the same rule as that contained in the failed EU Constitution – is much further away from the SQRR than is the Nice rule (or, for that matter, the weighted rules used by the Council during earlier phases of the EU). In view of this past experience, as an advocate of the SQRR, I feel there is not much ground for optimism. The experience of the United States also does not bode well. Circumstances may change, of course, and encourage greater political receptiveness for the SQRR. However, it would be naive to expect that our task will be easy. In the present chapter I am not going to present any new mathematical result or analysis. My aim here is to propose a politically flexible tactic in our advocacy of the SQRR. Briefly, I argue that we lose little and may well gain by not insisting   The Swedish scheme, along with other schemes that were discussed at the time, was analysed in Felsenthal and Machover 2000. The Swedish scheme is labelled there as ‘Proposal D’. Another reason for the not-so-good fit between this scheme and the SQRR is that in the former even the weights were only roughly proportional to population square roots.   For an account of the US experience concerning the SQRR, see Felsenthal and Machover 1998: Chapter 4.   This could be brought about by a coalition of all the middle-sized EU memberstates, who would gain by adopting a decision rule based on the SQRR instead of the one prescribed by the Reform Treaty. In fact, the greatest gain would be made by those whose population is about 11 million; Greece, Portugal and Belgium. See Felsenthal and Machover 2007.

Penrose’s Square-Root Rule

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on a too-precisely determined quota. There are various considerations that have been or may be used in determining the quota; and they do not necessarily lead to exactly the same conclusion. It may therefore be easier to gain acceptance for the SQRR if we do not insist on packaging it together with a specific formula for the quota. In other words, the argument in favour of the SQRR should be separated from arguments in favour of this or that quota. Various Effects of the Quota As is well known, the set of all simple voting games with a given set of voters is finite. The same applies a fortiori to the set of proper weighted voting games (WVGs) with a given set of voters. However, if the number (n) of voters is sufficiently large (say n > 15) then these WVGs are rather densely distributed in the appropriate n-dimensional space. What this means is that for given q ∈ [ 1/2, 1] and non-negative β1, . . ., βn such that β1 + … + βn = 1, it is possible to find nonnegative weights w1, . . ., wn such that w1 + … + wn = 1, and in the WVG [q; w1, . . ., wn] the relative powers (the values of the relative Banzhaf index) of the voters are quite close to the respective βi. Dennis Leech has written an algorithm that performs this ‘inverse computation’. We used it in our 2003 paper (Leech and Machover 2003: 127–43), where we took the βi to be proportional to the square root of the respective populations of the 27 present member states of the EU. For each value of q under consideration, we obtained a system of weights w1(q), …,w27(q), which we called ‘equitable weights’ – a terminology which I will also use here – because the WVG [q; w1(q), …,w27(q)] produced the desired relative voting powers (values of the Banzhaf index) β1, . . ., β27 to an excellent approximation. Thus, for any quota q ∈ [ 1/2, 1], the SQRR can be implemented in the Council by using the WVG [q; w1(q), …,w27(q)] as a decision rule. The required equitable weights can be readily computed. In other words, the WVGs that would implement the SQRR in the Council – and so would result in what we regard as an equitable distribution of voting power – constitute a one-parameter family, with the quota q as a parameter whose value can be chosen freely from a purely mathematical viewpoint. The question I wish to address here is what considerations may – or should – be used in making the choice.   Of course, a given WVG has infinitely many different representations by means of a system of weights and quota, and this is still the case for normalized representations, in which the weights are non-negative and add up to one. For convenience I shall only consider weighting systems that are normalized in this sense.   At that time 12 of them were of course only prospective members.   In fact we did the computation for values of q from 0.51 to 0.99 at 0.01 intervals.   The same can be done for a future somewhat enlarged EU.

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Transparency Strong heuristic arguments put forward by Słomczyński and Życzkowski (this volume) show that for WVGs [q; w1, . . ., wn] with sufficiently many voters (say n > 15), the relative voting powers of the voters tend to be most closely proportional to their respective weights when the quota q has an ‘optimal’ value that, to a very good approximation, is given by q := {1 + √(w12 + … +wn2)}/2

(1)

This is also confirmed by quite extensive simulations (Chang, Chua and Machover 2006: 90–106). Thus, equitable weights for the Council can be obtained directly from population data, by taking weights wi proportional to the square root of the respective population size of the member states – provided q is then determined by (1). For the present 27-member EU, using the most recent (2006) population data provided by Eurostat, we obtain q = 61.57 per cent (Felsenthal and Machover 2007). This recipe for implementing the SQRR is known as the ‘Jagiellonian Compromise’. As a mathematician, I find the elegance of this scheme extremely appealing. It is – in a somewhat loose, but nonetheless obvious, sense – a fixed-point solution, which is always an admirable thing. Moreover, the actual value of q that it determines is in my opinion very reasonable by various substantive yardsticks, which I shall mention later on. The main advantage of the Jagiellonian Compromise, however, is its transparency: the relative ease of explaining it to those who are not mathematically minded – which includes the vast majority of the general public, as well as most EU practitioners. Most people can easily understand the concept of voting weight, but are baffled by the scientific concept of voting power, and by the distinction between these two concepts. In the Jagiellonian scheme, the weights are calculated directly, in a fairly simple way, from population figures, while the concept of voting power is, as it were, hidden behind the scenes and does not enter explicitly into the calculation. To follow the calculation, you only need to know the definition of square root, which most people can recall (possibly with a bit of help to jog their memory) from their school days. Of course, most people will be puzzled as to why weights are allocated in proportion not to population size but to its square root, but they may accept it as a reasonable application of the degressive allocation of weights, which has been EU practice hitherto. (Recall that this was how it was justified by Sweden before the Nice conference.) Personally, I regard the Jagiellonian scheme as ideal; and I know that many, probably most, votingpower experts share this view.

  The mapping of which it is a fixed, or almost fixed, point is of course the one that maps weighting systems to distributions of voting power.

Penrose’s Square-Root Rule

39

However, the determination of the quota in this scheme is by no means transparent. In order to justify Equation (1) one must make use of sophisticated mathematical concepts and results from the theory of voting power, which the vast majority of people (including EU practitioners) certainly find totally opaque. This surely constitutes a serious obstacle to the acceptance of the Jagiellonian Compromise – in addition, of course, to the general reluctance to adopt the principle of the SQRR as such. It is not just a matter of failure to understand the justification for Equation (1), however. The point is that there are various independent considerations, some of which I shall now discuss, that may be applied in determining the quota, and they may conflict to a lesser or greater extent with one another and with the value determined by the Jagiellonian scheme. All the WVGs considered below are assumed to be equitable as decision rules for the Council – in other words, they implement the SQRR – but with various values of the quota. In particular, I will use the WVGs [q; w1(q), …,w27(q)] computed in the paper of Leech and Machover (2003) mentioned above, and I will draw heavily on the results reported there. Sensivity, Mean Majority Deficit and Efficiency Equitability is a democratic desideratum of the two-tier decision-making structure in which the European citizens are the indirect voters at the lower tier, acting through their representatives at the Council, which constitutes the upper tier. It is desirable because it equalises the (indirect) voting powers of the citizens, thus implementing the democratic principle of equal suffrage, encapsulated in the slogan ‘one person, one vote’. Equitability is not the only democratic desideratum, however. Two other principles are empowerment of the people (‘power to the people’) and majoritarianism (‘majority rule’). In the present context, empowerment of the people means that the (indirect) voting power of the citizens should be as great as possible. Obviously, I am referring here to absolute voting power, which we quantify by the Penrose measure. The sensitivity of the EU two-tier structure is the sum of the indirect voting powers of all EU citizens.10 Majoritarianism prescribes that majority deficits should be minimised. A majority deficit occurs when a decision taken at the upper tier (the Council) is opposed by a majority at the lower tier (the citizens of the EU at large). Actually, these two desiderata are equivalent, because the mean majority deficit (MMD) of a decision-making structure (the a priori expected value of the size of 10  This should not be confused with the sensitivity of the Council considered as a stand-alone decision-making body, which is the sum of the direct absolute voting powers of its members.

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the majority deficit, regarded as a random variable) is a negative linear function of its sensitivity (For details, see Felsenthal and Machover 1998: 60–61). Now, as can be seen from Figure 3 and the last column of Table 1 in the paper of Leech and Machover (2003), the MMD is a monotone non-decreasing function of q. For the present 27-member EU, the MMD first increases quite rapidly with q, but remains constant from about q = 77 per cent on. The democratic desideratum of majoritarianism (as well as the equivalent one of empowering the citizens) would suggest choosing a very low value of q. Another consideration that points in the same direction is that of efficiency. This is an attribute of the Council as a stand-alone decision-making body (rather than as the upper tier of a two-tier structure). This is conveniently measured by Coleman’s index A (‘the power of a collectivity to act’), which is defined as the a priori probability that a proposed bill will be adopted (as opposed to blocked) by the Council. As we can see from Figure 1 and the penultimate column of Table 1 in Leech and Machover (2003), A is a monotone non-increasing function of q. For the present 27-member EU, it decreases rapidly as q increases from 51 per cent, and becomes dangerously small once q reaches about 73 per cent. Stability and Blocking Power There are of course other considerations, pointing in the opposite direction and suggesting a high value of the quota. These have to do with political stability and the member states’ interest in blocking power. For obvious reasons of political stability, the status quo should arguably be given a privileged position, and changing it should not be made too easy. This argument has special force because the EU is supposed to be not only a union of Europe’s people but also a union of states. This is why certain issues are decided by the Council by the unanimity rule, which is extremely inefficient – so inefficient that it threatens paralysis. The danger of this is generally recognised. But it would be quite reasonable if some issues of special importance were to be decided by a quota of two-thirds, say q = 67 per cent. Blocking power of individual member states is another important issue. From a detached scientific viewpoint, there is complete symmetry between both components of absolute voting power: the positive power to help getting a resolution adopted, and the negative power to help getting it blocked – Coleman’s ‘power to initiate action’ and ‘power to prevent action’, respectively. Indeed, Penrose’s measure of voting power is a harmonic mean of these two Coleman measures. For wellknown political reasons, however, member states are considerably more interested in the negative component of voting power. (The fact that most practitioners do not know how to quantify blocking power does not reduce their motivation to secure it for their respective governments.) Assuming an equitable weighted decision rule, the only way to increase the blocking powers of the individual member states is to

Penrose’s Square-Root Rule

41

increase the quota.11 For the interesting behaviour of blocking powers as functions of q, see Figures 4a and 4b in Leech and Machover (2003). There is also a special insistence on the part of the present four largest member states to fix the quota at a level that would make the four of them a blocking coalition. Assuming an equitable weighting system, this would imply a quota of about 67 per cent for the present 27-member Council. Room for Flexibility In the end, the ‘right’ value of the quota must be determined by political considerations, balancing between the various arguments – some of which conflict with others. Although I believe that the quota proposed by the Jagiellonian scheme is ideal or near-ideal, I think it would be counter-productive to insist on it as an inseparable part of the SQRR. Fortunately, the behaviour of the equitable weights wi(q) leaves considerable room for flexibility. This is so because although the Jagiellonian quota is indeed optimal in securing proportionality between voting weights and relative voting powers, this optimality is by no means ‘sharp’. As can be seen from Figures 2a–2e in Leech and Machover (2003), the wi(q) vary very little indeed – their graphs are very nearly flat – as q varies from 51 per cent to about 70 per cent. Thereafter they begin to vary quite rapidly, and from about q = 76 per cent onwards they vary as steep (and very nearly linear) functions of q. What this means is that if q is chosen anywhere within a reasonable interval, say between 55 per cent and 69 per cent, the resulting equitable weights will not differ very significantly from the transparent weighting of the Jagiellonian scheme. Alternatively, if the weights will be fixed exactly as in the Jagiellonian scheme – that is, proportional to population square root – and the quota chosen anywhere in that reasonable interval, then the resulting decision rule will be almost as equitable as the Jagiellonian scheme in terms of Penrose’s SQRR. References Banzhaf, J.F. 1965. Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Review, 19(2), 317–43. Banzhaf, J.F. 1966. Multi-member electoral districts – do they violate the ‘one man, one vote’ principle? Yale Law Journal, 75(8), 1309–38. Banzhaf, J.F. 1968. One man, 3.312 votes: a mathematical analysis of the Electoral College. Villanova Law Review, 13, 304–32. 11  This is true more generally, for any weighted rule in which the weights are a nondecreasing function of population size. It was this fact that led to fixing the quota at a dangerously high value in the Nice Treaty.

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Chang, P., Chua, V.C.H. and Machover, M. 2006. L.S. Penrose’s limit theorem: Tests by simulation. Mathematical Social Sciences, 51(1), 90–106. Also available at: http://eprints.lse.ac.uk/535/. Conference of the Representatives of the Governments of the Member States. 2001. Treaty of Nice Amending the Treaty on European Union, the Treaties Establishing the European Communities and Certain Related Acts. CONFER 4820/00, Brussels, 28 February 2001. Available at: http://register.consilium. europa.eu/pdf/en/00/st04/04820en0.pdf [accessed: 3 Febuary 2009]. Council of the European Union. Brussels European Council 21/22 June 2007. Presidency Conclusions. 11177/1/07 REV 1, Brussels, 20 July 2007. Eurostat, http://europa.eu.int/comm/eurostat/. Felsenthal, D.S. and Machover, M. 1997. The weighted voting rule in the EU’s Council of Ministers, 1958–95: intentions and outcomes. Electoral Studies, 16(1), 33–47. Felsenthal, D.S. and Machover, M. 1998. The Measurement of Voting Power: Theory and Practice, Problems and Paradoxes. Cheltenham: Edward Elgar. Felsenthal, D.S. and Machover, M. 2000. Enlargement of the EU and Weighted Voting in its Council of Ministers (VPP 01/00), London: London School of Economics and Political Science, Centre for Philosophy of Natural and Social Science. Available at: http://eprints.lse.ac.uk/407/. Felsenthal, D.S. and Machover, M. 2007. Analysis of QM Rule Adopted by the Council of the European Union, Brussels, 23 June 2007, Project Report, London: London School of Economics and Political Science. Available at: http://eprints.lse.ac.uk/archive/2531/. Leech, D. and Machover, M. 2003. Qualified majority voting: The effect of the quota, in European Governance. Jahrbuch für Neue Politische Ökonomie, Vol. 22, edited by M.J. Holler et al. Tübingen: Mohr Siebeck, 127–43. Also available at: http://eprints.lse.ac.uk/archive/435/. Penrose, L.S. 1946. The elementary statistics of majority voting. Journal of the Royal Statistical Society, 109(1), 53–7. Penrose, L.S. 1952. On the Objective Study of Crowd Behaviour. London: H.K. Lewis and Co. Słomczyński, W. and Życzkowski, K. 2007. From a toy model to the double square root voting system. Homo Oeconomicus, 24(3/4), 381–99. Available at: http:// arxiv.org/abs/physics/0701338.

Chapter 3

Jagiellonian Compromise – An Alternative Voting System for the Council of the European Union Wojciech Słomczyński and Karol Życzkowski ‘I cannot conceive of the Community without total parity.’ Konrad Adenauer to Jean Monnet at a meeting held in Bonn on 4 April 1951 during the preparations for the signing of the Treaty Establishing the European Coal and Steel Community.

Voting Weights, Powers and Indices Voting rules implemented by various political or economic bodies may be studied with the help of tools that have been developed over many decades in game theory (Felsenthal and Machover 1998). A mathematical theory of indirect voting was devised after World War II by a British psychiatrist and mathematician, Lionel S. Penrose, in the context of a hypothetical distribution of votes in the United Nations General Assembly (Penrose 1946). He introduced the concept of a priori voting power, a quantity measuring the ability of a participant of the voting body to influence the decisions taken. This notion may be also used for analysing rules governing decision taking in the Council of the European Union (EU). It is important to differentiate clearly here between the voting weight of a given country and its potential voting power, the latter reflecting the extent to which it may influence decisions taken by the Council when all possible coalitions between different countries are taken into consideration. To illustrate the difference with just a simple example: a shareholder with 51 per cent of stocks of a company has only 51 per cent of all votes (voting weight) at the shareholders’ assembly, but he takes 100 per cent of the voting power if the assembly takes decisions by a simple majority vote. In other words, ‘a member state’s power is defined as its capacity to affect EU Council decisions and not merely to affect Council votes. In this perspective, when a member state’s vote does not affect the decision, it is not considered an expression of its relative power’ (Bobay 2001). Clearly, with 27 member states and potentially complicated voting procedures, it is a non-trivial task to analyse the distribution of power in the Council since one has to consider more than 134 million possible coalitions. To quantify the notion  

Jean Monnet, Mémoires, Paris: Fayard, 1976.

44

Institutional Design and Voting Power in the European Union

of voting power, mathematicians introduced the concept of power index which measures the potential voting power of each member of the voting body. Although the current scientific literature contains several competing definitions of power indices, the original concept of Penrose is often used. In his approach, the a priori voting power of a country is proportional to the probability that its vote will be decisive in a hypothetical ballot: should this country decide to change its vote, the winning coalition would fail to satisfy the qualified majority condition. Without any further information about the voting body it is natural to assume that all potential coalitions are equally likely. This very assumption leads to the concept of the Penrose-Banzhaf index (PBI, or simply the Banzhaf index) named after John Banzhaf, an American attorney who introduced this index independently in 1965. For convenience Banzhaf indices are often normalised in such a way that their sum is equal to unity. It is easy to show that the voting power held by a given country depends not only on its voting weight but also on the distribution of the weights among all the remaining member states of the European Union. Note that this approach is purely normative, not descriptive: we are interested in the potential voting power arising from the voting procedure itself. Although in the mathematical model it is assumed that all the coalitions are equally likely, in reality some coalitions are a priori more probable than others. Thus, the actual voting power depends on the polarisation of opinion in the voting body and may change from voting to voting. Dennis Leech referred to this problem in the following terms: An understanding of where power lies requires us to take account of many relevant factors: the political complexions of governments, the Paris-Bonn axis, the commonality among the Benelux countries, the Nordic or Mediterranean members, the small states versus the large states, new Europe versus old Europe, the Eurozone, etc. etc. … But from the point of view of the design of the formal voting system in a union that is expanding with the admission of new members being quite a normal process, it would clearly be inappropriate to base constitutional parameters like voting weights on such considerations. … That would appear arbitrary and would fail to provide a guide for what the votes of new entrants should be. Far better to allocate the voting weights on the basis of general philosophical principles that can be seen to apply equally to all countries and citizens, to new members as well as old ones. A priori power indices are useful in this. (Leech 2003).

Definitely, the model of the calculation of voting power based on the counting of majority coalitions is applicable while analysing institutions in which alliances are not permanent, but change depending upon the nature of the matter under consideration. The Council of the European Union constitutes just such a body. The meaning of voting power is not purely theoretical. In a series of papers, the Finnish scholars Mika Widgrén and Heikki Kauppi investigate the relationship between the Council voting rules and EU budget transfers by using a power

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politics model (Kauppi and Widgrén 2004, 2007, Widgrén 2006. See also Baldwin 2007). The main claim of the authors is that the distribution of voting power in the Council alone is sufficient to explain most of budget allocation: … quantitative power indices stemming from voting theory provide a good description of the actual distribution of power among EU members. Of course, we cannot directly verify the accuracy of such indices since it is impossible to measure power directly. Instead, we evaluate whether these power measures explain a quantifiable manifestation of the exercise of power, namely members’ shares of EU budget allocation … when we apply specific voting power measures that allow correlated preferences and cooperative voting patterns between the member states, our estimates indicate that the power politics view can explain as much as 90 per cent of the budget shares. We conclude that power politics can explain a major part of the Council decisions. (Kauppi and Widgrén 2007).

Two Voting Systems: Nice vs. Constitution Pursuant to the Treaty of Nice (2001) each member state is assigned a voting weight which to some degree reflects its population. The Council adopts a piece of legislation if: (a) the sum of the weights of the member states voting in favour is at least 255 (with the sum of the weights of all 27 member states being 345) which is approximately 73.9 per cent; (b) a majority of member states (that is at least 14 out of 27) vote in favour; and (c) the member states forming the qualified majority represent at least 62 per cent of the overall population of the European Union. For a proposal to pass, all three of these conditions must be satisfied, and so the system should therefore be thought of as one requiring a ‘triple majority’. However, as the mathematical analysis has shown, condition (a) is the most significant one, since the probability of forming a coalition which would meet only this condition and fail to meet one of the other two is extremely low (Felsenthal and Machover 2001). According to the agreement reached in Brussels in June 2004 and signed in Rome in October 2004, the Council of Ministers of the European Union acting on a proposal from the Commission or from the Union Minister for Foreign Affairs takes its decisions if two criteria (‘double majority’) are simultaneously satisfied: (b) at least 55 per cent of member states vote in favour; (c) these member states comprise at least 65 per cent of the overall population of the European Union. Additionally: (d) a blocking minority must include at least four Council members, failing which the qualified majority shall be deemed attained. The same rules apply to the European Council when it is acting by a qualified majority. As can be seen, the Constitutional Treaty removes condition (a), the voting weights of the member states. To put it differently, the weights applied are directly proportional to the population of each individual member state.

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Institutional Design and Voting Power in the European Union

The majority of experts agree that both the voting system established by the Treaty of Nice (2001) and the Treaty Establishing a Constitution for Europe (2004) have obvious drawbacks. It seems that the basic defect of the Nice voting rules lies in the low decision-making efficiency of the system. This quantity, also called the Coleman power of a collectivity to act, is measured as the probability that the Council would approve a randomly selected issue and it equals the proportion of winning coalitions assuming that all coalitions are equally likely. Whereas, in the case of the rules laid down in the Constitutional Treaty, approximately 12.9 per cent of possible coalitions lead to approving a randomly selected issue, for the Treaty of Nice this index is equal to only 2.1 per cent. However, according to the recent analysis by Sebastian Kurpas and Justus Schönlau, from the Centre for European Policy Studies in Brussels, this deficiency has only theoretical meaning: Innovations affecting the Council are the ones cited most frequently when arguments in favour of the Constitutional Treaty are made. One central element was supposed to be the new rules for the weighting of member states’ votes under qualified majority voting, which were designed to reduce the danger of blockage in a more diverse Union. Calculations have proved that the introduction of the ‘double majority system’ would indeed make it much easier to avoid the formation of blocking minorities with 25 member states. So far, however, figures on the voting reality do not confirm the widespread fear of deadlock after enlargement while the Nice system of weighting votes is still in place. (Kurpas and Schönlau 2006. See also Hagemann and De Clerck-Sachsse 2007, Trzaskowski 2007 and this volume).

On the other hand, it is possible to show that, with no fundamental change in the voting power of each particular member state, the Nice system may be modified so that its formal effectiveness increases significantly (see Baldwin, Berglöf, Giavazzi and Widgrén 2000, Baldwin and Widgrén 2004). Another defect of the Nice system lies in the necessity to apply three criteria simultaneously in the calculation of the qualified majority. However, the studies conducted by Dan S. Felsenthal and Moshé Machover have shown that, with a slight correction of the weights assigned to each country, one can achieve a system almost equivalent to the Nice one but much simpler, as it is based on the weight criterion alone (Felsenthal and Machover 2001). Therefore, the rules underlying the Nice system may be cut ruthlessly with Ockham’s razor, as the mechanism based on the three criteria is needlessly complex and difficult to comprehend by the average citizen of the Union. Although the proposal contained in the Constitutional Treaty does away with the voting weights, which have no objective basis, and constitutes a more efficient voting system, it has serious flaws of its own. Many authors have pointed out that it is favourable to the countries with the largest and the smallest populations at the expense of all medium-sized states. For instance, Richard Baldwin and Mika

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Widgrén summarised their analysis of the Constitutional Treaty voting rules in the following words: The Constitutional Treaty rules will break the traditional French-German power equality making France the junior partner in the Franco-German alliance. Spain and Poland will lose the Near-Big status they won in the Nice Treaty. The biggest losers are the Mediums [about 10 million citizens]. The chief winners are the Big-4; Germany alone wins more than the other Big-4 combined. (Baldwin and Widgrén 2004).

In fact, all voting systems in the decision-making bodies of the European Union, and formerly of the European Communities, have been based on a compromise between two principles – the equality of member states and the equality of citizens – and the ‘double majority’ system apparently reflects these principles. However, in this system large states would gain a lot from the direct link to population, while small countries would derive disproportionate power from the increase in the number of states needed to support a proposal. The combined effect would sap influence away from medium-sized countries. Ironically, a similar conclusion follows from a book written 50 years earlier by Lionel Penrose, who discovered this drawback of a ‘double majority’ system: If two votings were required for every decision, one on a per capita basis and the other upon the basis of a single vote for each country, this system would be inaccurate in that it would tend to favour large countries. (Penrose 1952).

This passage may be interpreted as a prophetic and critical opinion on the arrangements laid down in the Constitutional Treaty, formulated 50 years before their adoption by the Intergovernmental Conference of the European Union in Brussels in 2004. Besides, we shall see that the arrangements adopted at Nice distribute the influence upon the decision-making process in the Council among all the citizens of the Union more evenly than those proposed in the Constitution. The fact that the Constitutional Treaty makes use of only two criteria does not remedy another of its basic defects: the system is not transparent since an average citizen has no simple way of calculating the potential voting power held by each member state under this system. This requires mathematical calculations that are equally complex as under the Nice system. Such calculations show that the basic democratic principle, that the vote of any citizen of any member state is of equal worth, is violated in both systems, though not in equal degree.

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Institutional Design and Voting Power in the European Union

Jagiellonian Compromise Square Root Weights Is it possible to design objectively a voting system in which each citizen of each member state would have the same power to influence the decisions made on his or her behalf? Can it be done in a way that is transparent, easy to implement, efficient to use, and will readily accommodate any future extensions of the EU? We believe that the answer is ‘yes’. A partial response to this question was already given by Penrose who deliberated principles of an ideal representative voting system in which each citizen of each country has the same potential voting power. First consider direct elections of the government (which nominates the minister voting on behalf of the entire country in the Council) in a state with population N. It is easy to imagine that an average German citizen has smaller influence on the election of the government than, for example, a citizen of the neighbouring Luxembourg. Penrose proved, under some natural assumption, that in such elections the voting power of a single citizen decays as one over the square root of N. Thus, the system of indirect voting applied to the Council is representative in the above sense, if the voting power of each country behaves proportionally to the square root of N, so that both factors cancel out. This statement is known in the literature as the Penrose square-root law. Kauppi and Widgrén express this claim in the following words: …although using a square-rooted population as the basis for a voting scheme might sound mysterious, it can also be justified from the point of view of fairness. It can be shown that in a two-tier decision-making system (e.g. the member states at the lower level and the EU at the upper) the square-root rule guarantees under certain circumstances that each citizen is equally represented in the Council regardless of his/her home country. This proposal obtained considerable support from academics. (Kauppi and Widgrén 2007).

Some people may find this counter-intuitive and think that the weights (or powers) should be directly proportional to population. However, as it was observed by Edward Best, of the European Institute of Public Administration in Maastricht: It has never been the case that the principle underlying the representation of states in the EU system qua states is that of direct proportionality … the ‘Founding Fathers’ of Europe explicitly rejected ‘objective’ keys and population, in favour of a distribution of votes reflecting a balancing act between states. This balance was conceived in terms of clusters of states and responded to a general principle of ‘degressive proportionality’ [which figures explicitly in the text of the draft Constitution with regard to the European Parliament] by which the larger units are under-represented compared to the smaller ones. (Best 2004).

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Figure 3.1 The weights attributed to the member states

Note: Weights are represented; proportionally to population (squares), proportionally to the square root of population (circles), and uniformly (triangles).

The idea of dividing votes proportionally to the square root of population not only has a special position in the mathematical theory of voting, but is in fact the simplest mathematical implementation of the principle of degressive proportionality and lies exactly between two extremes: ‘one country-one vote’ (as if the European Union were a loose association of states) and votes proportional to population (as if the European Union were a single state). Note that a similar degressive system is also used in the German Bundesrat to assign the number of representatives to each Land. A voting system based on the Penrose square-root law was first proposed for the Council of Ministers in 1996 by Annick Laruelle and Mika Widgrén (although they did not refer to Penrose) and, independently, by Dan Felsenthal and Moshé Machover in 1997. Since then it has been analysed by many authors from different countries. Such voting procedures have also been used in practice in several international institutions. Prior to the European Union summit in Brussels in June 2004, an open letter in support of square-root voting weights in the Council of Ministers, endorsed by more than 40 scientists from 10 European countries, had been sent to EU institutions and the governments of the member states. On the other hand, the square-root voting system was proposed independently in the EU context without any relation to the Penrose square-root law by several authors; Schmitter and Torreblanca (1997) (termed ‘proportional proportionality’), Moberg (1998), Bovens and Hartmann (2002), Mabille (2003), and Beisbart, Bovens and Hartmann (2004). When a system based on the square-root weights was put forward by the Swedish government in 2000, Sweden’s then Prime Minister Göran Persson said: Our formula has the advantage of being easy to understand by public opinion and practical to use in an enlarged Europe … it is transparent, logical and loyal.

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Figure 3.2

Institutional Design and Voting Power in the European Union

The ‘square root’ weights attributed to member states

Note: The square-root weights are proportional to the sides of the squares representing their populations. The figure presents exemplary data for seven selected countries of different size.

The assertion that ‘the voting power of each country should be proportional to the square root of its population’ does not entirely solve the problem. Werner Kirsch explained this as follows: The square root law tells us how the power should be distributed among the countries. It is, however, not clear at first glance how to implement it in terms of voting weights, as the voting weights do not give the power indices immediately (Kirsch 2004). Accordingly, the question arises of how to allocate weights and how to set a quota or threshold for qualified majority (the Council reaches a decision when the sum of the weights of the member states voting in favour exceeds that threshold) to obtain required distribution of power. The answer we have proposed is surprisingly simple: one should choose the weights to be proportional to the square root of the population and then find such an optimal quota that would produce the maximally transparent system, that is, a system under which the voting power of each member state would be approximately equal to its voting weight (Życzkowski and Słomczyński 2004). Optimal Quota for Qualified Majority The choice of an appropriate decision-taking quota (threshold) affects both the distribution of voting power in the Council (and thus also the representativeness of the system) and the voting system’s effectiveness and transparency. Different authors have proposed different quotas for square-root voting systems, usually varying from 60 per cent to 74 per cent. In a series of papers we have shown that it is possible to find the optimal quota enabling the computed voting power of each country to be practically equal to the attributed voting weight, and so to be proportional to the square root of the population (Życzkowski, Słomczyński and Zastawniak 2006, Życzkowski and Słomczyński 2006, 2007. See also Feix, Lepelley, Merlin and Rouet 2007). Then the Penrose law is practically fulfilled, and the potential influence of every citizen of each member state on the decisions taken in the Council is the same (representativeness). Such a voting system is not only representative but also transparent: the voting powers are proportional to the voting weights. Furthermore,

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the system is simple (one criterion only) and objective: it does not a priori favour nor handicap any European country. It has been dubbed the ‘Jagiellonian Compromise’ by the media. For the Council of Ministers of EU27 the optimal quota equals 61.6 per cent (it was 62 per cent for EU25). For an arbitrary voting body, the optimal quota q can be approximated by a simple mathematical formula: N 1 + ... + N M 1 q = 1 + 2  N 1 + ... + N M

   

(Q)

where Ni stands for the population of the i-th country. Since the number of member states is not going to be explicitly provided in the text of the European Constitution, defining a specific threshold for the qualified majority should be avoided. In the system under consideration, the optimal quota depends on the number of members of the voting body and their size, so there should be a possibility to adjust it in future without modifying the European Constitution. Due to the above formula the system proposed is easily extendible. The detailed calculation shows that the optimal quota decreases with the size of the voting body. This choice of the quota guarantees that the system is moderately efficient, with the efficiency always larger than 15.9 per cent, which is even more than in the Constitutional Treaty, not to mention the Nice system. Besides, the efficiency of the system we propose does not decrease with increasing number of member states, whereas the efficiency of the ‘double majority’ system does. The representative voting system based on the Penrose square-root law and the appropriate choice of optimal quota may be used as a reference point while analysing the rules established by politicians. Table 3.1 and Figure 3.3 present a comparison of the voting power (measured by the PBI) of EU members according to the voting system established by the Treaty of Nice, that proposed in the Constitutional Treaty, and the ‘Jagiellonian Compromise’ (square-root weights plus the optimal quota equalling 61.6 per cent). The ‘Jagiellonian Compromise’, which allocates voting power according to the square root of population, restores some of the power to medium-sized countries (from Spain to Ireland) that would be taken away by the Constitution. It is also apparent why it is called a compromise. Germany, for example, would gain considerable power under the new system compared with the Treaty of Nice, but not as much as it would if the proposals in the Constitution were adopted. It is important to stress that similar conclusions can be achieved by examining how other indices of the potential voting power change. There has been a long tradition of weighted voting in the Council of the European Union (and earlier in the Council of the European Communities). As politicians have agreed in the past to voting weights allotted somewhat arbitrarily, they could find even more acceptable the voting weights allotted according to an explicit rule based on clear principles.

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Figure 3.3

Institutional Design and Voting Power in the European Union

Jagiellonian Compromise compared with the Treaty of Nice and with the Constitution proposals

Note: If the ‘Jagiellonian Compromise’ was adopted, the voting power for each of the 27 EU states would change. The figure shows the difference relative to the existing system: (a) in the Treaty of Nice and (b) in the Constitution proposal.

  The calculations are based on data from: G. Lanzieri, Population in Europe 2005: First Results. EUROSTAT. Statistics in focus. Population and social conditions 2006, 16: 1–12.

Jagiellonian Compromise

Table 3.1

53

Comparison of voting power of EU27 member states Jagiellonian Compromise for EU27: q = 61.6%

Member state

Population (in millions)

Voting power (Constitution)

Voting weight (JC)

Voting power (JC)

Germany

82.44

11.66

9.47

9.45

France

62.89

9.02

8.27

8.27

UK

60.39

8.69

8.10

8.10

Italy

58.75

8.49

7.99

7.99

Spain

43.76

6.55

6.90

6.91

Poland

38.16

5.71

6.44

6.45

Romania

21.61

4.15

4.85

4.85

Netherlands

16.33

3.50

4.21

4.21

Greece

11.13

2.88

3.48

3.48

Portugal

10.57

2.80

3.39

3.39

Belgium

10.51

2.80

3.38

3.38

Czech Republic

10.25

2.77

3.34

3.34

Hungary

10.08

2.74

3.31

3.31

Sweden

9.05

2.63

3.14

3.14

Austria

8.27

2.53

3.00

3.00

Bulgaria

7.72

2.47

2.90

2.90

Denmark

5.43

2.19

2.43

2.43

Slovakia

5.39

2.18

2.42

2.42

Finland

5.26

2.17

2.39

2.39

Ireland

4.21

2.04

2.14

2.14

Lithuania

3.40

1.95

1.92

1.92

Latvia

2.29

1.81

1.58

1.58

Slovenia

2.00

1.78

1.48

1.48

Estonia

1.34

1.69

1.21

1.21

Cyprus

0.77

1.63

0.91

0.91

Luxembourg

0.46

1.59

0.71

0.71

Malta

0.40

1.58

0.66

0.66

Note: Comparison of voting power of EU27 member states: population; voting power measured by PBI in the system of the European Constitution; voting weights and voting power measured by PBI in the proposed solution (‘Jagiellonian Compromise’) based on the Penrose law with the 61.6 per cent threshold.

Institutional Design and Voting Power in the European Union

54

Conclusions We shall conclude this chapter by proposing a complete voting system based on the Penrose square-root law. The system consists of a single criterion only and is determined by the following two rules: A. The voting weight attributed to each member state is proportional to the square root of its population. B. The decision of the voting body is taken if the sum of the weights of members of a coalition exceeds the 61.6 per cent quota. In each case of future extension of the Union the value of the quota is adjusted according to the formula (Q). We would like to emphasise the following advantages of the proposed voting system: • • • • • • •

It is extremely simple since it is based on a single criterion, and thus it could be called a ‘single majority’ system; It is objective (no arbitrary weights or thresholds), hence it cannot a priori favour or handicap any member of the European Union; It is representative: every citizen of each member state has the same potential voting power; It is transparent: the voting power of each member state is (approximately) proportional to its voting weight; It is easily extendible: if the number of member states changes, all that needs to be done is to set the voting weights according to the square-root law and adjust the quota accordingly; It is moderately efficient: as the number of member states grows, the efficiency of the system does not decrease; It is also moderately conservative, that is, it does not lead to a dramatic transfer of voting power relative to the existing arrangements.

Of course, this compromise solution may be also combined with a simple majority of states (Kirsch, Słomczyński and Życzkowski 2007). Such a ‘modified double majority’ voting system based on the Penrose square-root law is determined by the following two rules: the rule A (same as above) and the modified rule B*: B*. The decision of the voting body is taken if the sum of the weights of members of a coalition exceeds the 61.6 per cent quota. In each case of a future extension of the Union the value of the quota is adjusted according to the formula (Q); the coalition consists of at least 50 per cent of member states (that is 14 for EU27).

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Quantitative analysis shows that the second criterion does not introduce a considerable shift of power, nor does it reduce the advantages of the single criterion Penrose system. From a pragmatic point of view, the square-root system proposed here is as easy to use as the double majority system, for which fulfilment of the population criterion during a given voting will in practice be confirmed with the help of a calculator. Moreover, the system based on the idea of weighted votes has worked in Europe for more than a half a century. After small modifications of this system (a single weights criterion with a minor shift of the number of votes allotted in the Treaty of Nice combined with the optimal quota for qualified majority), it would be consistent with the representative square-root voting system of Penrose. In our opinion, such a voting system for use in the Council of Ministers of EU is likely to be treated as a model solution to be used later while designing voting rules for other international institutions. Epilogue Before the IGC in Brussels (21–22 June 2007) Poland was ‘arguing strongly for a revision of the EU voting rule that allocates votes to each member according to the square root of their population’ (Baldwin and Widgrén 2007. See also Gros, Kurpas and Widgrén 2007). In fact, the official Polish proposal was based on the ‘Jagiellonian Compromise’ system described in this chapter. However, European leaders decided in Brussels that, from 1 November 2014, qualified majority voting will be based on the principle of the double majority. (The rules of the Nice Treaty will apply until 2014. In addition, during a transitional period ending on 31 March 2017, a Council member can still request that a decision be taken in accordance with the rules of the Nice Treaty.) Is this the end of the square root? It was General de Gaulle who said, ‘Treaties are like roses and young girls. They last while they last.’ The future will show whether the system of double majority will be in use after the next decade. The European Union is known to be eager to foster modern technology and promote scientific research. Therefore, while designing future European treaties it would be natural to make use of the results of the game theory and operation research conducted in Europe in the last 50 years. References Baldwin, R., Berglöf, E., Giavazzi, F. and Widgrén, M. 2000. EU reforms for tomorrow’s Europe. CEPR Discussion Paper No. 2623. Available at: http:// www.cepr.org/pubs/dps/DP2623.asp [accessed 1 August 2010].  According to Time, 12 July 1963.

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Baldwin, R. and Widgrén, M. 2004. Winners and losers under various dual majority rules for the EU Council of Ministers. CEPR Discussion Paper No. 4450. Available at: http://www.cepr.org/pubs/dps/DP4450.asp [accessed 1 August 2010]. Baldwin, R. 2007. Poland’s fight on voting rules matters for EU budget allocations. VoxEU.org (website), 18 June 2007. Available at: http://www.voxeu.org/index. php?q=node/279 [accessed 1 August 2010]. Baldwin, R. and Widgrén, M. 2007. Poland’s square-root-ness. VoxEU. org (website), 15 June 2007. Available at: http://www.voxeu.org/index. php?q=node/262 [accessed 1 August 2010]. Banhazaf III, J.F. 1965. Weighted voting does not work: A mathematical analysis. Rutgers Law Review, 19(2), 317–43. Best, E. 2004. What is really at stake in the debate over votes? EIPAScope, 1, 1423. Bobay, F. 2001. Political economy of the Nice Treaty: Rebalancing the EU Council. Centre for European Integration Studies (Bonn) Policy Paper, B 28. Available at: www.cepii.fr/anglaisgraph/communications/pdf/2001/ffa25260601/bobay. pdf [accessed 1 August 2010]. Feix, M., Lepelley, D., Merlin, V. and Rouet, J.-L. 2007. On the voting power of an alliance and the subsequent power of its members. Social Choice and Welfare 28(2), 181–207. Felsenthal, D.S. and Machover, M. 1997. The weighted voting rule in the EU’s Council of Ministers, 1958–95: Intentions and outcomes. Electoral Studies, 16(1), 33–47. Felsenthal, D.S. and Machover, M. 1998. Measurement of Voting Power: Theory and Practice, Problems and Paradoxes. Cheltenham: Edward Elgar. Felsenthal, D.S. and Machover, M. 2001. Treaty of Nice and qualified majority voting, Social Choice and Welfare, 18(3), 431–64. Gros, D., Kurpas, S. and Widgrén, M. 2007. Weighting votes in the Council: towards a ‘Warsaw compromise’? VoxEU.org (website), 20 June 2007. Available at: http://www.voxeu.org/index.php?q=node/291 [accessed 1 August 2010]. Hagemann, S. and De Clerck-Sachsse, J. 2007. Decision making in the enlarged Council of Ministers: Evaluating the facts. CEPR Policy Brief No. 119. Kauppi, H. and Widgrén, M. 2004. What determines EU decision making? Needs, power or both? Economic Policy, 19(39), 221–66. Kauppi, H. and Widgrén, M. 2007. Voting rules and budget allocation in the enlarged EU. European Journal of Political Economy, 23(3), 693–706. Kirsch, W. 2004. The new Qualified Majority in the Council of the EU. Some comments on the decisions of the Brussels Summit. Preprint. Available at: http://www.ruhr-uni-bochum.de/mathphys/politik/eu/Brussels.pdf [accessed 1 August 2010]. Kirsch, W., Życzkowski K. and Słomczyński, W. 2007. Getting the votes right. European Voice, 13(17), 12.

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Kurpas, S. and Schönlau, J. 2006. Thinking ahead for Europe. Deadlock avoided, but sense of mission lost? The enlarged EU and its uncertain Constitution. CEPR Policy Brief No. 92. Laruelle, A. and Widgrén, M. 1998. Is the allocation of voting power among EU states fair? Public Choice, 94(3), 317–39; earlier version of this paper: Is the Allocation of Voting Power Among the EU States Fair? CEPR Discussion Paper No. 1402, 1996. Leech, D. 2003. The utility of the voting power approach. European Union Politics, 4(4), 234–42. Penrose, L.S. 1946. The elementary statistics of majority voting. Journal of the Royal Statistical Society, 109 (1), 53–7. Penrose, L.S. 1952. On the Objective Study of Crowd Behaviour. London: H.K. Lewis. Słomczyński, W. and Życzkowski, K. 2006. Penrose voting system and optimal quota. Acta Physica Polonica. B37 (11), 3133–43. Słomczyński, W. and Życzkowski, K. 2007. From a toy model to the double square root voting system. Homo Oeconomicus, 24(3/4), 381–99. Trzaskowski, R. 2007. Can the Council function on the basis of the Nice Treaty? European Policy Centre Issue Paper 16, 43–9. Widgrén, M. 2006. Budget allocation in an expanding EU – A power politics view. Swedish Institute for European Policy Studies SIEPS, 11. Available at: http:// www.sieps.se/en/publications/rapporter/budget-allocation-in-an-expandingeu.html [accessed 1 August 2010]. Życzkowski, K. and Słomczyński, W. 2004. Voting in the European Union: The Square Root System of Penrose and a Critical Point. Preprint condmat.0405396. Available at: http://arxiv.org/abs/cond-mat/0405396 [accessed 1 August 2010]. Życzkowski, K., Słomczyński, W. and Zastawniak, T. 2006. Physics for fairer voting. Physics World, 19, 35–7.

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Chapter 4

The Double Majority Voting Rule of the EU Reform Treaty as a Democratic Ideal for an Enlarging Union: An Appraisal Using Voting Power Analysis Dennis Leech and Haris Aziz

Qualified Majority Voting and Future EU Enlargement The Council of Ministers, the senior legislature of the EU, is an intergovernmental body in which some matters are decided by unanimity but the most important voting rule is qualified majority voting (QMV), which is being used for an increasing number of decisions. Under QMV each country has a certain number of votes it can cast that is related in some way to its size. Under the Reform Treaty’s proposals, the number of votes will be strictly proportional to population sizes but, under the system determined by the Nice Treaty and under the previous system, the voting weights were not directly based on populations in a transparently mathematical way. The problem of the determination of the voting weights is an important one because under the rules of the Council each country must cast its votes as a bloc. A country is not permitted to divide its votes for any reason, as it might, for example, in order to reflect a division of domestic public opinion. Alternatively if, instead of a single representative with many votes, the country’s representation was by a number of elected individuals who voted individually as representatives or delegates rather than as a national group acting en bloc, as for example members of the European Parliament are able to do, the problem addressed in this chapter would not exist. In that case the voting power of the citizens of each country would be approximately the same. However in a body that uses weighted voting, there is not a simple relation between weight and voting power and each case must be considered on its merits by considering the possible outcomes of the voting process, making a voting power analysis. The proposed new double majority rule is that a decision taken by QMV should require the support of 55 per cent of the member countries whose combined populations are at least 65 per cent of the total population of the EU. This contrasts with the system currently in use (the Nice system) under which each country has a given number of weighted votes, all of which were laid down in the Nice Treaty.

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Specifically the Nice system is a triple-majority rule that works as follows. For a vote to lead to a decision, three requirements must be met: (i) the countries voting in favour must constitute a majority of members; (ii) they must contain at least 62 per cent of the population of the union; and (iii) their combined weighted votes must exceed the specified threshold. The Nice Treaty specified a threshold that depended on the size of the membership: for the union of 15 countries it was about 71 per cent of the total of the weighted votes, increasing gradually with enlargement to its present level, with 27 members, to almost 74 per cent. Studies using voting power analysis have concluded that the Nice system is broadly equitable in the sense that the resulting powers of individual countries are fair in relative terms (in an appropriately defined sense), with one or two exceptions, but that the threshold was set much too high for the Council to be able to deal with a greater range of decisions by qualified majority voting in an efficient manner (Felsenthal and Machover 2001, Leech 2002). Advocates of the double majority rule argue, first, that it would be much simpler to understand than the Nice system (which has been described as ‘fiendishly complex’) which is lacking in transparency because of its use of artificially constructed voting weights. The Nice weights are criticised because they are not, even approximately, directly proportional to populations. The countries with larger populations are assigned larger weights than the smaller ones but the difference does not fully reflect relative populations. Superficially it appears that larger states are underrepresented, although it can be argued that such weights, in actual fact, may be consistent with a reasonable degree of fairness in the distribution of voting power. This argument by itself, however, would not be decisive in favour of change given that the Nice system is already in place. A second criticism of the Nice system is that the threshold is set too high, and moreover, increasing it as the membership increases makes decisions harder by requiring a larger qualified majority, or makes it easier for a blocking minority to form. Studies of the formal a priori decisiveness of the system have shown that the probability of a qualified majority emerging could be extremely small (Felsenthal and Machover 2001). However, despite these fears, recent studies have found little evidence in practice of the sclerosis that was feared, and qualified majority voting appears to be working quite well (Wallace and Hayes-Renshaw 2006). The third argument for change is that the Nice system was designed for certain specified anticipated enlargements of the Union, which have now all occurred. It provided for a union of up to 27 members – the 15 members at the time of the treaty, plus the 10 countries that acceded in May 2004 followed by Bulgaria and Romania which joined in January 2007 – and further enlargement beyond that is therefore outside its scope. The formal position is that the accession of a new country would require a new treaty that included amendments to the system of qualified majority voting. However there are further candidates, including Turkey   Germany was deliberately underrepresented relative to its population and it turned out that Spain and Poland were overrepresented.

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and the former republics of Yugoslavia, and there is also the remote possibility of further former Soviet Union countries, and perhaps also other European countries joining. It would clearly be impossibly inefficient to hold an Intergovernmental Conference every time further enlargement took place. Hence there is need for a system that embodies a principle that can be applied in a more or less routine manner each time a new member accedes. An example of such a voting system is the double majority rule in the Reform Treaty. It is this administrative simplicity that makes the double majority voting rule most attractive. It enables us to know immediately how many votes a new member will have and in what ways the operation of qualified majority voting will be affected. All that it is necessary to know is the country’s population. Appraisal of Voting Rules by Power Analysis It does not follow that we understand all the consequences of enlargement for the fairness and efficiency of the voting system. It has been claimed that a weighted voting rule based directly on populations will implement a desirable democratic principle of equality: that each country will have a voting power proportionate to its population. That is undoubtedly a major factor in the thinking behind the proposal. However, it is a serious mistake because in a weighted voting body like the Council, where members cast all their votes as a single bloc, power in the sense of the ability to influence decisions is not related straightforwardly to weight. It is possible, for example, for a country to have voting weight that is not translated into actual voting power. It is therefore necessary to make a voting power analysis to establish the properties of this system and in particular the powers of the members. In this chapter we do this by considering voting in the Council of Ministers as a formal two-stage democratic decision process that allows us to compare the voting power of citizens of different countries. It is a fundamental principle of the EU that all citizens should have equal rights, whatever country they happen to live in. This provides a natural criterion on which to judge the adequacy of the voting system, a benchmark against which to compare the fairness of the distribution of voting power. We use voting power analysis to do this, following the approach of Penrose (1946 and 1952), treating the Council of Ministers as a delegate body on which individual citizens are represented by government ministers elected by them.

  Luxembourg, in the original EEC of six members, is a case in point. It had one vote while France, West Germany and Italy each had four votes, the Netherlands and Belgium two each. Luxembourg did not have one-quarter the voting power of France, as these figures suggest, but precisely zero, because the decision threshold was set at 12, and therefore in order that its vote could make a difference, the combined votes of the others would have to come to 11, which was impossible. See Leech (2003).

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The voting power of a citizen is derived from two components: (i) power of his or her country in the Council (a property of the system of weighted QMV in the Council), and (ii) the power of the citizen in a popular election within the country. A citizen’s voting power, as a structural property of the voting system, is measured by his or her Penrose power index, which is the product of these two voting power indices. We make two analyses. First we compare the double majority rule with the Nice system for the current EU of 27 countries. Secondly we investigate various scenarios for further enlargement. These begin with the expected accession of the known candidate countries and then become more and more speculative as further new members are considered. Our primary purpose is to test the claim that the Reform Treaty proposals are simple and transparent in the face of further enlargement. We also investigate the alternative voting rule that has recently been proposed, known as the Jagiellonian Compromise, and find it remarkably equitable (Słomczyński and Życzkowski in this volume). We report analyses of the following Scenarios for possible future enlargement of the EU: •

• • • • • •

O  EU27: the current union. Member countries: Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, United Kingdom. I  EU29: as above plus Croatia, Macedonia. II  EU30: with Turkey. III  EU34: with Albania, Bosnia, Montenegro, Serbia. IV  EU37: with Norway, Iceland, Switzerland. V  EU40: with Belarus, Moldova, Ukraine. VI  EU41: with Russia.

In the next section we describe the mathematics of the voting power approach that we employ to analyse these scenarios. The Penrose Power Index Approach The EU Council of Ministers at any given time is assumed to consist of n member countries, represented by a set N={1,2,. . ., n}, where each country is labelled   Obviously, since the analysis is theoretical, we could have done this using hypothetical countries with assumed or randomly generated populations; but it is of considerable intrinsic interest to use real countries.   We do not include any microstates with populations under 100,000, such as Lichtenstein, Andorra, Monaco or San Marino, in any future enlargements.

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by an integer i = 1 to n. Each country has a population (which we take, as a first approximation, to be the same as its electorate), represented for country i by mi . The total population of the EU is m = ∑ j ∈N m j . Under the Reform Treaty, any normal decision requires a double majority in favour of the proposal: at least 55 per cent of member countries whose combined populations are at least 65 per cent of the total population. Suppose that in any vote concerning such a decision there are s countries in favour, represented by a set S, a subset of N. Then the decision is taken if: (i) s > 0.55n ; and (ii)

∑

j ∈S

m j ≥ 0.65m 

(1)

Let us denote the number of such subsets that satisfy condition (1.) by ω; that is, ω is the number of possible outcomes of votes among the countries in the Council of Ministers that lead to a decision. The number ω reflects the general capacity of the body to act (a measure of its decisiveness). The appropriate measure of a priori voting power for each country can now be defined in terms of its ability to influence decisions taken by this rule, strictly by its being able to swing a decision by adding its vote to those of the other members. A swing is defined for member i as a subset S which does not contain i such that: it is just losing and becomes winning with the addition of member i. Formally, the two conditions for a swing are: (i )

0.55n - 1 ≤ s < 0.55n,

and

(2)

(ii ) 0.65m - mi ≤ ∑ m j < 0.65m , for any S ⊆ N , i ∉ S . j ∈S

The number of possible swings, S, taking account of all possible voting outcomes among the n-1 members other than i, that is the number of subsets of N\{i}, is 2n-1. If the number of swings for country i is denoted by hi, then the (modified) Penrose index for the Council of Ministers is defined as PiC : PiC =

ηi , 2n -1

for i = 1, 2,..., n. 

(3)

The basic interpretation of expression (3) is the proportion of all possible voting outcomes that are swings for country i. It is usually given a probabilistic interpretation by assuming that all possible voting outcomes are equally likely.   We also assume this to be the number of electors who participate in elections. We make no allowance for possible variations in voter turnout.   The index is modified because we are considering a double majority rule rather than the conventional single rule. The difference is conceptually trivial although important computationally.

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Computation of the indices PiC is a substantial problem especially when the number of countries is large, because the direct evaluation of expression (3) requires a search over all 2n possible voting outcomes. Such a computation becomes prohibitively slow even when n is relatively small and therefore alternative approaches have to be found. The method used in this study is a modification of the method of generating functions first defined by Brams and Affuso (1976) and extended to multiple decision rules by Algaba et al. (2003). The method of generating functions is very rapid even for very large voting bodies and therefore is suitable for the present analysis of a Union with an expanding membership. This great speed comes at a cost, however, in terms of space complexity which limits the sizes of the weights with which the method of generating functions can cope. The method of generating functions is described and full details of computation are given in Aziz, Paterson and Leech (2007). The Penrose index (3) is a measure of absolute voting power in the sense of meaning the country’s likelihood of being decisive when all voting outcomes are considered on an equal basis. A measure of the decisiveness of the Council, its Power to Act, AC, is a measure of its ability to make decisions defined on the same basis. The power to act is the number of subsets of all n countries that would lead to a decision (Coleman 1971): AC =

ω . 2n

(4)

The power of an individual citizen is defined formally by idealising the Council as a representative body in which the determination of how a country will cast its weighted votes follows a simple majority vote among its citizens. This requires finding a measure of the power of a single citizen within the country. The Penrose power index of a citizen, assuming a one-person-one-vote electoral system, is the likelihood of his or her being able to swing the national election. This is the binomial probability of his or her being the swing voter, considering all possible voting outcomes among the other voters to be equally likely. For country i, with mi voters, it is the probability that the number of votes cast by the mi-1 voters other than the single citizen under consideration are precisely one vote short of a majority. Denote this power index for the single vote of any citizen in country i by Pi S . Then, if mi is even, mi - 1  mi  m -1 S Pi = Pr [combined votes of mi-1 voters = ] =  mi  (0.5) i (5)  2   2 

  What Penrose called the power of a single vote. For simplicity this is modelled as a stylised plebiscite. More complex arrangements corresponding more closely to real world electoral systems await further research.   We disregard the possibility of a tie to save space. It does not affect the analysis when mi is large and (7) still holds.

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or, if mi is odd,

 mi - 1   mi - 1 m -1 Pi = Pr [combined votes of mi-1 voters = ] =  mi - 1 (0.5) i (6)   2  2  S

When mi is large, as is well known, (5) and (6) can be approximated very accurately by Stirling’s formula, which gives Pi S a very simple form, Pi S

=

2 0.79788 =  πmi mi

(7)

We can evaluate the indirect power index for a citizen of country i as the product of (7) and (3). Let us denote this composed power index Pi. Therefore we can write, for the indirect power of a citizen of country i,

Pi = PiC PiS 

(8)

The numerical value of Pi is of course rather small because Pi S is small. However its value can vary enormously between countries, over changes in the membership of the EU and changes in the voting system. Expression (8) provides a yardstick or benchmark to use in the evaluation of the weighted voting system on a consistent basis of democratic legitimacy. Comparisons can be made using relative voting power indices to compare countries and therefore to test the extent to which the voting system is egalitarian. Expression (8) can be used as the basis of the Penrose Square Root rule for equalising voting power in all countries. The rule is that weighted voting be adopted in the Council with a decision rule and weights chosen such that (8) is constant for all i. The power indices PiC therefore should be proportional to the square roots of the populations. This can be a decision rule with a single majority. An approximation to this that will be sufficient in many cases is to choose the weights themselves in proportion to population square roots. This has been applied recently in the so-called Jagiellonian Compromise in which also the decision threshold is also adjusted to improve the approximation (Słomczyński and Życzkowski 2007). We have investigated the performance of this proposed voting rule in equality of voting power and find it works very well indeed.

  Penrose (1946: 53, 1952: 11). See also, for example, Feller (1968: 50–53).

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Analysis: Voting Power in the EU27 We compared the three voting systems for the present-day union, EU27. The results are given in Table 4.110 in which the countries are in order of size. The Penrose indices agree very closely with those of Felsenthal and Machover (2007), with slight differences being due to the use of different weights. The method of generating functions requires that the weights be integers that are not too large. This necessitates, in practice, replacing the population figures, which are mostly in millions and numbers too large to be used as weights, by much smaller integers that are manageable computationally.11 The table also gives the quota in terms of the weights. Besides the Penrose index for each country, PiC, Table 4.1 also shows the indirect citizen power indices, Pi , defined in (8). These are presented in two ways, as absolute values and relative to the power of a citizen of Germany. (In all our results the relative voting power of a German citizen is taken as equal to 1.) The absolute citizen voting power indices are of course very small in all countries. Under the Reform Treaty, that for Germany is equal to 1.76×10-5, that is, 0.0000176, while that for the smallest member, Malta, is 3.41×10-5. The relative voting power indices show the inequity inherent in the voting rule, with all but those for the smallest group of countries being less than 1. The effect is biggest for the medium-sized countries, especially Belgium, with 0.673, and Greece, 0.671. The conclusion is that the double majority system would create large disparities in voting power in different countries. Inequality is measured by the Gini coefficient of citizen voting power for the whole Union.12 Table 4.1 shows how much more unequal the proposed voting system would be compared with the existing Nice system, under which citizens of every country (with the exception of Latvia, to a minor extent) have slightly greater voting power than those of Germany. This result is due to the fact that Germany has no greater weight than France, Italy and the UK despite its much larger population. The Gini coefficient for Nice is 0.059, that for the Reform Treaty is 0.080.

10  A spreadsheet containing the detailed calculations is available from the authors. The power indices for the Nice system have previously been published in Leech (2002) and Felsenthal and Machover (2001). Indices for the double majority rule and Jagiellonian Compromise have been published by Felsenthal and Machover (2007). 11  For the case of EU27 we have also done these computations using direct enumeration, that is by searching over all voting outcomes and using expression (3) directly, which does not require us to use this fudge, and the results are the same to a very close approximation. This exact method was not available to use for the larger enlargement scenarios, of course, and therefore we have used generating functions throughout. 12  The Gini coefficients have been calculated by treating all citizens from all countries as a single group.

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Table 4.1

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Voting power analysis of the EU27

We have also reported the power to act of the Council of Ministers, AC, which shows that the Reform Treaty voting rule is a very much more decisive voting rule than Nice13, with a power to act of 0.129 compared with a very low value of 0.02. The results for the Jagiellonian Compromise are quite impressive in showing that this method would lead to the equalisation of voting power throughout the Union of 27 countries.14 There is almost no variation in the relative citizen voting power indices across countries, which indicates how good an approximation to the Penrose square root rule is obtained by using population square roots as weights. Analysis: Enlargement Scenarios Table 4.2 presents the results for the enlargement scenarios I to VI. They are presented diagrammatically for existing members in Figures 4.1 to 4.3. We also present a parallel analysis for the Jagiellonian Compromise in Table 4.3. In all scenarios the same population figures have been used, the 2006 estimates taken from Eurostat.15

13  The powers to act have been reported in Felsenthal and Machover (2007). 14  We found that we could compute these power indices to full accuracy using weights that are the square roots of the populations without adjustment. 15  It would be an interesting analysis to allow for future population growth. That would suggest important new scenarios which did not necessarily involve new members.

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They show that the inequality in citizen voting power under the double majority rule persists although there are sharp changes in relative voting power following changes in the membership. On the other hand, the Jagiellonian system turns out to be remarkably successful in creating a very equal distribution of citizen power in all scenarios, and to be quite robust to membership changes. The use of square root weights and adjustment of the quota gives an extremely good approximation to the Penrose square root rule. The results for the Reform Treaty voting rule in Table 4.2 show that citizen voting power is relatively unequal under all scenarios. The Gini coefficient for Scenario VI (41 countries including Russia) is the same as in Scenario O (EU27) although it falls below this in some scenarios. Citizen voting power is most equal following the accession of Turkey, Gini = 0.059, Scenario II, which may be largely Table 4.2

Citizen indirect power indices under all scenarios: Reform Treaty

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due to the similarity in population of the two largest members, Germany and Turkey. Whereas having one country that is much larger than all the others creates an unequal power distribution, where there are two members with very large weight, a bipolar voting structure, there is a tendency for them to counteract one another. Thus the presence of Turkey would reduce Germany’s power and increase the power of other members, making the distribution more equal. The accession of Turkey would substantially increase the voting power of citizens of Poland and Spain, from 0.718 and 0.772 to 0.822 and 0.815. There is a similar effect for medium-sized countries, but their relative voting power remains much lower: for example, the index for Belgium goes from 0.661 to 0.760. The effects for small countries, whose citizen voting powers are already much larger than Germany’s, are quite large – for example, Malta’s goes from 1.859 to 2.442. The power of the Council to act, AC, declines more or less steadily as the Union enlarges, from 12.9 per cent for O (EU27) to 9.3 per cent in VI, although it is always much greater than under the current system. Our overall conclusion is that the Reform Treaty’s double majority rule falls a long way short of the democratic ideal of ensuring that the votes of all members of the community are of equal value in whatever country they are cast. It is an endemic feature that citizens of middle-sized countries have considerably less voting power than those in either large or small countries. This pattern persists under all the enlargement scenarios we have looked at. Table 4.3 shows the results for the Jagiellonian Compromise under the same scenarios. For each scenario the weights, which are the population square roots, √mi, are shown in the first column, and the quota is equal to: n  1 q =  m + ∑ mi   2  i =1

There is almost no variation in the relative citizen voting powers either between countries or over scenarios. We conclude that the method is therefore found to be extremely successful in equalising voting power in a wide range of circumstances.

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Table 4.3

Citizen indirect power indices under all scenarios: Jagiellonian Compromise

Figure 4.1

Relative citizen power: large countries

The Double Majority Voting Rule

Figure 4.2

Relative citizen voting power: middle-sized countries

Figure 4.3

Relative citizen voting power: small countries

71

Conclusions We have tested the suitability of the proposed double majority rule in the EU Reform Treaty by looking at its implications for voting power under various enlargement scenarios, some of which are realistic prospects, while some are no more than speculations. Our scenarios include the possibility of virtually all European countries, up to and even including Russia, acceding to membership. We have also tested the performance of the Jagiellonian Compromise based on the Penrose Square Root rule whereby voting weights are determined by a simple formula as proportional to population square roots. In judging the voting rule we

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looked at two criteria: (i) equality of voting power as measured by the Penrose power index at the level of the citizen, assuming one-person-one-vote in national elections, and (ii) decisiveness of the Council of Ministers, as measured by the Coleman power to act. We found that for the present Union of 27, the Reform Treaty voting rule gives a much more unequal distribution of citizen voting power than the existing voting rule, although it leads to the Council of Ministers being more decisive. The Jagiellonian Compromise leads to the equalisation of citizen voting power in all countries. In considering enlargement scenarios, the inequality of citizen voting power persists with each enlargement. The common pattern is for citizens of the smallest countries to have the greatest voting power, sometimes by a factor of as much as two or three times those of other countries, such as in the cases of Malta and Luxembourg. The medium-sized countries have the smallest citizen voting power. That for the Netherlands, for example, varies from about two-thirds that of Germany in EU27 to about four-fifths of it following the accession of Russia. Our conclusion is that the Reform Treaty voting system is a flawed proposal that fails to reach the democratic ideal of equality of voting power of all citizens in the European Union. This ideal is reached, however, by the Jagiellonian Compromise. References Algaba, E., Bilbao, J.M., Fernandez, J.R. and Lopez, J.J. 2003. Computing power indices in weighted multiple majority games. Mathematical Social Sciences, 46, 63–80. Aziz, H., Paterson, M. and Leech, D. 2007. Combinatorial and computational aspects of multiple weighted voting games. University of Warwick, Warwick Economic Research Papers, 823. Brams, S.J., Affuso, P.J. 1976. Power and size: a new paradox. Theory and Decision, 7, 29–56. Coleman, J.S. 1971. Control of collectivities and the power of a collectivity to act, in Social Choice, edited by B. Lieberman. New York: Gordon and Breach, 277–87. Dubey, P. and Shapley, L.S. 1979. The mathematical properties of the Banzhaf Index. Mathematics of Operations Research, 4(2), 99–131. European Union. Treaty of Nice Amending the Treaty of the European Union, the Treaties Establishing the European Communities and Certain Related Acts 2001. EU Document CONFER 4820/00, 28 February. Feller, W. 1968. An Introduction to Probability Theory and its Applications Vol. 1. 3rd edn. New York: Wiley.

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Felsenthal, D.S. and Machover, M. 1998. The Measurement of Voting Power: Theory and Practice, Problems and Paradoxes. Cheltenham UK: Edward Elgar. Felsenthal, D.S. and Machover, M. 2001. The Treaty of Nice and qualified majority voting. Social Choice and Welfare, 18, 431–64. Felsenthal, D.S. and Machover, M. 2007. Analysis of QM Rule adopted by the Council of The European Union, 23 June 2007. Voting Power and Procedures Project, CPNSS, London School of Economics. Leech, D. 2002. Designing the voting system for the Council of the European Union. Public Choice, 113(3–4), 437–64. Leech, D. 2003. The utility of voting power analysis. European Union Politics, 4(4), 479–86. Leech, D. and Leech, R. 2004. Algorithms for Computing Voting Power Indices. Available at: www.warwick.ac.uk/~ecaae/. Penrose, L.S. 1946. The elementary statistics of majority voting. Journal of the Royal Statistical Society, 109, 53–7. Penrose, L.S. 1952. On the Objective Study of Crowd Behaviour. London: H.K. Lewis. Wallace, H. and Hayes-Renshaw, F. 2006. The Council of Ministers. Basingstoke: Palgrave Macmillan.

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Chapter 5

The Blocking Power in Voting Systems Tadeusz Sozański

Constructing Voting Systems: Theory and Practice When the opportunity arises to modify electoral law based on the principle of proportional representation by changing a method of allocating seats in the parliament, the range of available methods is known to political actors, and their conflicting preferences are transparent for themselves and political scientists. Each party will opt for the method bringing it the largest number of seats under the expected support from the electorate. Can one interpret in this way the disputes over the choice of a voting system for the Council of Ministers? Unfortunately, not. First, the EU leaders have always preferred their own amateurish creativity to selecting solutions from a menu offered by the specialists in voting theory. Secondly, even though in negotiations every country has always cared about its own voting power, it has hardly ever been clear what is the quantity everyone would like to maximise. The voting power of a member of a decision-making assembly can be defined informally as the ability to influence group decisions that is granted to the actor solely by virtue of the voting rules. That is all that one can say without a theory giving a quantitative meaning to this concept. No politician can do without theorising, no matter whether they choose to theorise by themselves or seek help from mathematicians or mathematical political scientists studying voting systems. Mathematicians investigate the structural properties of well defined mathematical objects they call voting games. In particular, they have analysed voting games which are mathematical models of voting systems constructed by the politicians. A model is obtained by translating given voting rules from the legal language used by the politicians into the set-theoretical language of mathematics. For example, Article 16(4) of the Lisbon Treaty provides: As from 1 November 2014, qualified majority shall be defined as at least 55 per cent of the members of the Council, comprising at least fifteen of them and representing Member States comprising at least 65 per cent of the population of the Union. A blocking minority must include at least four Council members, failing which the qualified majority shall be deemed attained.

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The voting game that is a mathematical counterpart model of this definition has the form (H1∩ H2)∪H3, where H1, H2 and H3 are three weighted voting games with the same set of 27 voters. H1 is a weighted voting game with relative population weights which add up to 1,000 and a quota q1=650. H2 and H3 are two one-voterone-vote games with quotas q2=15 and q3=24. Leaving for later an explanation of the above formal description, let us remark that this example shows that the politicians like to construct voting systems with pretty complex structures. To examine the structure of a voting game, one cannot rely on lawyers whose educational background comprises at best a course of elementary logic. One needs the help of a full-fledged mathematician. Mathematicians have devised a number of indices of voting power, each providing a particular operational definition of this concept. Since theorists also have their own preferences as to which measure is best, say, the Banzhaf index or the Shapley-Shubik index, the abundance of measures may produce some confusion and discourage potential users of the theory. Nevertheless, there do exist certain tools which could be used by the politicians if they made an effort to become acquainted with the available formal theory which, as it were, has to a greater or lesser degree been inspired by political practice. Why has the ‘scientific’ concept of voting power developed by men and women of knowledge so far held little appeal for men and women of power? An answer is offered in this chapter, written to help the two ‘tribes’, speaking different languages, to communicate with each other. Naive Theorising and the Classical Mathematical Theory of Voting Power The scope of the most popular way of theorising is limited to voting systems which are defined by assigning weights (number of nominal votes, share of the total population, etc.) to voters and setting a quota, q, or a fixed threshold that must be attained by the total weight of a set of voters in order that such a qualified majority may be entitled to pass any bill. Under the naive approach, the power of a voter is equated with the voter’s weight or relative weight. The power distribution does not depend on the choice of quota, the role of the latter being reduced to determining the range of qualified majorities, which has to do with the efficiency of the voting system – the more majorities can be formed the easier it is to take group decisions. The classical theory of voting power arose from seminal papers by Penrose (1946), Shapley (1962), Banzhaf (1965) and Coleman (1971). The theory’s key concept is critical membership in a winning coalition. Let N denote the set of voters (actors/players) and W the set of winning coalitions. Let w=|W| denote the number of all winning coalitions (the number of elements of a finite set Z will be noted |Z|). To simplify notation, we put N={1, ... ,n}. A subset C of N is a winning coalition if the support of all members of C suffices – by virtue of certain rules – to pass any bill. Given the assignment of

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weights p1,..,pn and a quota q, the simplest rule is defined by the condition: C∈W if and only if p(C)≥q where p(C) is the sum of pi over all i∈C. Definition 1: Voter i is said to be a critical (decisive/pivotal/swing) member of a winning coalition C if i∈C (i is a member of C) and C-{i}∉W (C-{i} is not a winning coalition). That is, if a member i of a winning coalition C fails to vote for a bill, the votes of the remaining members of C will no longer suffice for passing it. Under the classical approach, the voting power of an actor i is directly proportional to the number wc(i) of winning coalitions containing voter i as a critical member. The number w(i) of all winning coalitions containing i can also be applied to measure voting power because it is related to wc(i) through the formula w(i)=2(wc(i)+w) discovered by Dubey and Shapley (1979). The most widely used normalised (with values in the [0,1] interval) coefficient of voting power is the Banzhaf index, β(i). It is obtained by dividing wc(i) by the sum of wc(j) over j=1, ... ,n. The Banzhaf index is a measure of relative power, which means that its values over the set of voters add up to 1. Let pi and pj be the weights of players i and j. If pi>pj, then w(i)≥w(j), which implies in turn that wc(i)≥wc(j) and β(i)≥β(j). Thus, the order of players with respect to weight and their order with respect to the Banzhaf index value always agree with each other (however, it is possible that pi>pj and w(i)=w(j)). Słomczyński and Życzkowski (2006) proposed to calculate a quota from the weights in such a way that the relative weight pi/p(N) of each voter and the respective value of the Banzhaf index are approximately equal. The use of ‘optimal’ quota may help political users reconcile their naive approach to voting power with the classical conception. However, the success of this strategy of promoting the classical theory of voting power depends on whether the politicians agree to apply it in practice. A scholar can do nothing to gain acceptance for a given approach when he or she hears from a politician: ‘I’m sorry, but your way of measuring voting power differs greatly from mine’. Nevertheless, the classical theory is not doomed to remain ‘academic’, as it has often been used in the USA (Felsenthal and Machover 1998). If a choice between two or more voting systems has to be made by those who are going to be the future players of the chosen voting game, then an actor’s evaluation of each system in terms of the strength of his position in it depends on the measure of power used. If a player’s ‘strength’ is quantified by two different measures, such as relative weight and the Banzhaf index, then the consistency of the orderings generated by them need not suffice to find a compromise solution of the problem of which game to choose. The example given below provides a plausible explanation of why Germany refused to accept the Jagiellonian voting system (Słomczyński and Życzkowski 2006) in which the weight of each member of EU27 is defined as the square root of its population and the relative quota equals 61.6 per cent.

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Let us compare the Jagiellonian system with two other voting systems for the EU27 so differently evaluated by Poland and Germany, the Nice system and the Lisbon system. Under the naive approach, the Nice ‘triple majority system’ is usually identified with its main component: the system with ‘political weights’ (nominal votes) and quota of 255. Table 5.1

Germany’s voting power in three voting systems according to the naive theory and classical theory

Voting system Power measure Integer weight

Nice

Jagiellonian

Lisbon

29

33

58

Relative weight

.0841

.0957

.1673

Banzhaf index

.0778

.0955

.1164

If one computes the mean of the Banzhaf index values for the Nice game and the Lisbon game, the result is 0.0971, which slightly differs from the respective value for the Jagiellonian game. Thus, the latter game can in fact be regarded as a compromise solution according to the classical theory. Relying on the naive approach, however, and taking into account relative weight or absolute integer weight (calculated so as to imitate the Nice nominal votes which add up to 345), one will arrive at a different conclusion: the ‘Jagiellonian system’ by no means lies in the middle between two systems that Germany considered best and worst. The values of the Shapley-Shubik index (the second most popular classical power coefficient), which in the three games are equal to 0.0874, 0.1001 and 0.1592 for Germany, also show that the Jagiellonian game is closer to the Nice game than to the Lisbon game. Mathematical Theory of Blocking Power The third approach to voting power shares the basic concepts of the classical theory, yet its most fundamental term is blocking coalition (blocking minority in EU documents). Definition 2: C is called a blocking coalition if (i) N-C∉W and (ii) C∉W. That is, neither non-members nor members of C form a winning coalition. Condition (i) means that coalition C can prevent any bill from being passed. If all members of C refuse to vote for a bill, then it will not be passed, even if all remaining voters, or members of N-C, vote for it. Since condition (i) is satisfied by all winning coalitions (because C and N-C cannot both be

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winning), condition (ii) must be added in order to distinguish between winning and blocking coalitions. Condition (ii) implies that if all members of C vote for a bill, but all other voters fail to vote for it, then the bill will not be passed. Blocking coalitions are less powerful than winning coalitions; the latter can both block initiatives of non-members and push through their own initiatives. Definition 2 brings back to life the original sense that was given to the term blocking coalition by Lloyd Shapley (1962). That sense, according to Felsenthal and Machover (1998: 23), ‘agrees with common political parlance, in which the term is used to refer to a coalition that is able to stop a bill being passed but cannot force one through. However, subsequent usage in the voting-power literature has shifted to the broader sense of blocking, which we adopt here.’ The sense which actually prevails in the literature is obtained by defining a blocking coalition as any subset C of N such that N-C is not winning. The theory of blocking power I am going to develop in this chapter breaks with this tradition and builds on the following general heuristic principles: (i) blocking power should be distinguished from winning power; (ii) blocking power should be measured with the use of blocking coalitions; (iii) blocking coalition should be defined in agreement with political practice, that is, according to Definition 2. The classical theory of voting power, which does not distinguish between winning power and blocking power, offers the ratio wc(i)/w as a measure of ‘preventive power’. This coefficient, defined by James Coleman (1971), however it is based on counting winning coalitions, has in fact to do with blocking power because it assumes the maximum value of 1 for a voter i if and only if i is a vetoer (that is, by definition, {i} is a blocking coalition) or a dictator (that is, {i}∈W). Dictatorship and the right of veto are extreme cases of winning and blocking power, respectively. While there can be only one dictator, maximal blocking power can be granted to all members of an assembly, as is the case with the consensus game having only one winning coalition made up of all players. Abstract Voting Games In order not to lose non-mathematical readers, who usually abhor excessively abstract discourse, I have not yet explicitly distinguished between the terms ‘winning coalition’ and ‘qualified majority’, the latter being used by those who are accustomed to defining decision rules in the language of law. However, not all voting systems known from history have been designed solely by assigning weights to voters and setting a quota. Therefore, for the sake of generality, I must now introduce the theory of voting games as an abstract axiomatic mathematical theory. A voting game is a mathematical object of the form (N,W), where N is a finite set of voters, and W is a collection of subsets of N called winning coalitions. The distinction between N and N in notation is to show the reader that the set which is referred to as the assembly N of voters (N is the base set of the mathematical

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object (N,W) with structure W) is also a subset N of N, then being referred to as the grand coalition. The starting point for building the mathematical theory of voting games is not concrete ‘voting rules’ but axioms imposed on W, the only primitive term of the theory. The following axioms are most convenient insofar as one needs a formal theory suitable for typical political applications: A1 A2 A3

W≠Ø (there exists at least one winning coalition); If C∈W and C⊂D⊂N , then D∈W (any set of players containing a winning coalition is also a winning coalition); If C∈W , then N-C∉W (the non-members of a winning coalition do not form a winning coalition).

Many mathematicians love general concepts and general theorems. Thus, even those willing to attract non-mathematical readers (Felsenthal and Machover 1998, Straffin 1993) begin theory building from defining a simple voting game as a mathematical object which meets only two axioms: A1 and A2 (A1 is usually replaced by B1: N∈W, which under our axiomatics follows from A1 and A2). Axiom A3 is then used to define a particular class of simple voting games, referred to as proper simple voting games. In this chapter, I use the term voting game as shorthand for proper simple voting game ­– the special case corresponding to the political rule that two contradictory bills, one supported by C and the other supported by N-C, may not be passed simultaneously, which could be happen if Axiom A3 did not hold. A weighted voting game is obtained by assigning to voters any positive numbers p1, ... ,pn, setting a number q≤p(N)=p1+ ... +pn, and putting W={C⊂N: p(C)≥q}. In order to make sure that A3 holds, one must assume that q>½p(N). A coalition C is called losing if its complement N-C is winning. Note that the term ‘losing’ is used in classical theory as a synonym for ‘not winning’. The axioms imply that C is losing if and only if N-C is winning. Hence |W|=|L| where L stands for the set of losing coalitions. The remaining subsets of N are blocking coalitions. Let B denote their set. We have 2w+b=2n where b=|B|. The Measurement of Blocking Power Is it possible to measure blocking power in the same way as winning power? Once w(i) measures winning power, can b(i), or the number of blocking coalitions containing actor i, be used to construct an index of blocking power? The answer is negative due to the following:

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Proposition 1: b(i)=2n-1 – w To prove it, notice that the mapping C→N-C of the set of all coalitions onto itself establishes a 1:1 correspondence between B(i)={C∈B: i∈C}, B*(i)={C∈B: i∉C}, two disjoint sets which make up B. Therefore, b(i)=½b, but b=2n-2w. Thus, since b(i) unlike w(i) assumes the same value for all voters, my first attempt to measure blocking power by analogy with winning power turned out a fiasco. I considered in turn the analogue of wc(i), or the parameter bc(i)=|Bc(i)| where Bc(i)={C∈B(i): C-{i}∉B} is the set of blocking coalitions containing voter i as a critical member, where ‘critical’ now means that if actor i leaves a blocking coalition C, then C-{i} is no longer a blocking coalition (so it must be losing). Proposition 2: bc(i)≤wc(i); bc(i)=wc(i) if and only if, for any C∈Wc(i), C-{i}∈B The proof of this fact is not complicated. Consider the mapping C→(N-C)∪{i} which assigns different sets to different sets. To conclude that bc(i)≤wc(i), we need only show that C∈Bc(i) implies that (N-C)∪{i}∈Wc(i). If C∈Bc(i), then C-{i}∉B and consequently C-{i}∈L, which implies that N-(C-{i})=(N-C)∪{i}∈W, but N-C∈B because C∈B, so that (N-C)∪{i}∈Wc(i). The condition given in Proposition 2 states that the defection of a coalition member can never result in a direct transition from winning to losing coalition. Since this condition holds true in most known weighted voting games, my second idea to quantify blocking power by defining the Banzhaf-like index of blocking power based on bc(i) has also turned out to be of little practical value, as blocking power would almost always be equal to winning power. Minimal Winning and Minimal Blocking Coalitions As Deegan and Packel (1979) and Holler (1982) have shown, voting power can also be operationally defined by means of the number of minimal winning coalitions containing a voter i. Definition 3: A winning (blocking) coalition C is called minimal if no proper subset of C is winning (blocking). Formally, C∈W (C∈B) is minimal if for any D such that D⊂C and D≠C, D∉W (D∉B). Equivalently, a coalition C of either type is minimal if every member of it is critical, that is, C has no redundant members whose defection would not change the coalition type. Let wm and bm denote, respectively, the number of minimal winning and minimal blocking coalitions. Like w and b, wm and bm characterise a voting game as a whole. The number wm,k=|{C∈Wm: |C|=k}| of minimal winning coalitions of size k, and bm,k defined similarly are also global structural parameters of a voting

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game (N,W). We define in turn the respective local structural parameters which enable comparing voters. Let bm(i)=|{C∈Bm: i∈C}| and bm,k(i)=|{C∈Bm: |C|=k, i∈C}| stand for the number of all minimal blocking coalitions containing voter i and the number of minimal blocking coalitions a voter i can form with k-1 other voters. Table 5.2

Parameters of winning and blocking power in EU15

EU15 member states 1. Germany 2. France 3. UK 4. Italy 5. Spain 6. Netherlands 7. Greece 8. Portugal 9. Belgium 10. Sweden 11. Austria 12. Denmark 13. Finland 14. Ireland 15. Luxembourg

pi

wc(i) bc(i)

wm(i)

10 10 10 10 8 5 5 5 5 4 4 3 3 3 2

1849 1849 1849 1849 1531 973 973 973 973 793 793 595 595 595 375

674 674 674 674 619 542 542 542 542 511 511 485 485 485 375

wm,k(i)

k=8 16 16 16 16 16 9 9 9 9 6 6 0 0 0 0

k=9 147 147 147 147 115 70 70 70 70 64 64 61 61 61 47

bm(i) 324 324 324 324 334 489 489 489 489 494 494 485 485 485 375

bm,k(i) k=3 k=4 6 153 6 153 6 153 6 153 6 108 0 86 0 86 0 86 0 86 0 74 0 74 0 64 0 64 0 64 0 36

All parameters are illustrated by the data displayed in Table 5.2 The sum of weights assigned to the Fifteen equals 87. The constructors of this game set the quota at 62, so that all coalitions with a total weight less than or equal to 87-62 = 25 are losing. Since the largest weight equals 10, any winning coalition C may lose at most 10 votes when its strongest member i leaves it. When this happens and D=C-{i} is not in W, its total weight may not drop below 62-10 = 52>25, so that D is a blocking coalition. As a consequence, the condition given in Proposition 2 is met and bc(i)=wc(i) for any i=1,..,15. Notice that in Table 5.2 wm(i) decreases with decreasing pi, but bm(i) behaves otherwise. Small countries surpass large countries in the number of minimal blocking coalitions because they can form many such coalitions among themselves. However, since these coalitions must have many members, their formation may turn out to be more difficult than the formation of smaller size coalitions in which strong players ally with weaker players.

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Measuring Blocking Power with the Use of Small Minimal Blocking Coalitions The above reasoning leads to the idea that the blocking power of a voter should depend on the smallest size of a minimal blocking coalition the voter can form with other voters and on the number of possible small minimal blocking coalitions containing the voter. What size of minimal blocking coalition, besides kmin = min {k: bm,k>0}, should be considered small? Such a question should be asked of the users of a given voting system. Every player i would probably agree that any minimal blocking coalition of the size kmin(i)= min{k: bm,k(i)>0} is small, as for that player it is the smallest possible size. If bm(i)=0 (that is, bm,k(i)=0 for any k), we put kmin(i)=0. The Case of Minimum Winning and Blocking Power. If wm(i)=0, a voter i is said to be a dummy (the case of Luxembourg in the Six is the most famous example). It is not difficult to show that wm(i)=0 if and only if wc(i)=0. Suppose that wm(i)=0 and wc(i)>0, that is, i is a critical member of at least one winning coalition C. If C is minimal, then wm(i)>0, if C is not minimal, then C contains a minimal winning coalition D. i must be a member of D because otherwise the coalition obtained from C by removing i would contain D and thus would be winning. We can now prove the following proposition, which means that any voter having no winning power does not have blocking power either. Proposition 3: If wm(i)=0, then bm(i)=0 If wm(i)=0, then wc(i)=0, but then bc(i)=0 in virtue of Proposition 2. Since bm(i)≤bc(i), we get bm(i)=0, which completes the proof of Proposition 3. Does bm(i)=0 imply that wm(i)=0? If this implication is true, then blocking power and winning power would simultaneously attain their lowest levels. Clearly, the problem (which is left open in this contribution) of reversing the implication given in Proposition 3 makes sense only if b>0. There exist voting games in which b=0, that is, the players have no opportunity for blocking whatsoever. These games, called strong, are most efficient if efficiency, called by Coleman (1971) the ‘power of a collectivity to act’, is defined as the ratio of w to 2w+b. We define small minimal blocking coalitions as those of size k ranging from kmin to kmax= max {kmin(i): i=1,...,n}. The simplest measure of blocking power can be defined as the ratio of the number of small minimal blocking coalitions containing voter i to the number of all small minimal blocking coalitions, symbolically kmax

∑b

m, k

γ(i ) =

(i )

k =kmin kmax

∑b

m, k

k =kmin

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This parameter, which disregards the size of blocking coalitions, could be refined by means of the same method as the one which led Deegan and Packel (1979) to define their coefficient of winning power. However, their coefficient takes into account all minimal winning coalitions, even if they are weighted by size. The Blocking Structure of a Voting Game The constructors of voting systems for the EU Council seem to be little interested in methods of quantifying blocking power. They have always been more concerned with the shape of any blocking structure with focus on the lowest level, or the distribution of the number of minimal blocking coalitions of the smallest size. The set of such coalitions, of which the number is usually pretty small, can often be determined without the help of an expert. Definition 4: For any voting game with n players, the term blocking structure will be referred to the sequence of sequences (bm,k(i): i=1,..,n) with k ranging from kmin to kmax. In describing the shape of a blocking structure, one needs to take into account the following properties or parameters: •

• • • •

The smallest size of a minimal blocking coalition; this parameter has always been considered important in designing voting games for the EU Council (kmin was always equal to 2, 3 or 4, with the tendency to be raised with successive EU enlargements). The number of levels (kmax-kmin+1) in the blocking structure; in EU games it has never exceeded 3. The number of voters with bm,k(i)>0 at level k; the set of players who take part in minimal blocking coalitions of the smallest size will be referred to as the premier league. Even or uneven distribution of non-zero bm,k(i) on each level. Last but not least, regularity or irregularity of the blocking structure.

Needless to say, all of these categories can also be applied to the winning structure defined analogously. For the weighted voting game used by the Fifteen, both structures, which are displayed in Table 5.2, are two-level and regular in the formal sense given to this property by the following definition. Definition 5: A weighted voting game is said to have a regular blocking structure if the order of voters 1,..,n with respect to the weights p1,..,pn is consistent with their order with respect to bm,k(1),..,bm,k(n), for any k from kmin to kmax. Consistency is defined as the absence of pairs of distinct players i and j such that pi>pj and bm,k(i)PBA, A is said to have the blocking power advantage over B. Notice that a player i has a blocking power advantage over player j if and only if γ(i)>γ(j), that is, the order of players with respect to the values of the blocking power parameter determines their unequal opportunities to block each other’s initiatives. Let us illustrate these parameters with a politically intriguing example. Chancellor Merkel and President Sarkozy might be interested to learn how the political relationship of their countries (D and F) would change if the voting system defined in the Lisbon Treaty were to replace the Nice system in 2007.

The Blocking Power in Voting Systems

The Nice Game IDF = 78.7 CDF = 9.6 PDF = 40.4 PFD = 50.0 Figure 5.1

89

The Lisbon Game IDF = 96.9 CDF = 36.0 PDF = 46.4 PFD = 17.6

The relation between France and Germany in two voting games

For the Nice game, let us take as S the set of minimal blocking threes and fours, for the Lisbon game, the set of minimal blocking fours. What would be the consequences of implementing the Lisbon system? The values of the four indices (given above in per cent) dictate the following answer: • • •

The already high importance of the Franco-German contribution (78.7 per cent) to the total EU blocking structure would increase even more (96.9 per cent). The potential for system-forced co-operation between these states would considerably increase (from 9.6 per cent to 36.0 per cent). But the current moderate power advantage (50.0–40.4=9.6) of France over Germany would be replaced by an enormous power advantage (46.4– 17.6=28.8) of Germany over France.

So far the Franco-German balance of power has been the cornerstone of the EU. Will the Union survive so radical change in this matter? How Are the Theories of Voting Power Related to One Another? The naive theorising which equates voting power with relative weight deserves its name, I must say this as a mathematician. As a social scientist, I cannot reject the theory used by the ‘natives’, even if their approach was dismissed by Felsenthal and Machover (1998: 156) as a ‘widespread fallacy’ to which ‘even experts on

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voting power are not immune’. The way in which the players themselves calculate how strong they are may affect the outcomes of the game. It may well be that the members of a voting body who enjoy high political status on account of their weights can more easily find partners for winning coalitions and thus have more political power, that is, their real influence on collective decisions is greater. The EU politicians and their advisors hardly ever go beyond naive theorising. Since they have always been preoccupied with extending their blocking opportunities, they must have invented their own measure, computed from weights and quotas. The naive coefficient of blocking power, known as the share of blocking minority, is computed by dividing a voter i’s weight pi by the blocking threshold. I learned about this measure from newspaper reports and Moberg (2007). To explain what a ‘blocking threshold’ is, notice that in a voting game with weights p1,..,pn and quota q, the type of any coalition C can be easily determined by finding out which of three successive intervals contains the total weight p(C) of C. The intervals which correspond to losing, blocking, and winning coalitions have the form: [0, p(N)-q], (p(N)-q, q), [q, p(N)]. The lower boundary of the middle interval (p(N)-q) is usually referred to as the blocking threshold. When the weights and quotas are integers, it is better to use the formula r=p(N)-q+1, which implies that any coalition C is blocking if and only if p(C)≥ r and p(C) 0 . The voting behaviour depends on the proposal ω under consideration, i.e., X ν i is a function X ν i (ω) of the proposal ω. We denote the voting behaviour of state S ν in the Council by Yν . So, Yν = 1 if X = ∑ X > 0 and Yν = -1 if X = ∑ X ≤ 0 . If state S ν has a voting weight g ν in the Council, the voting result in the Council is C = ∑ g Y . From basic democratic principles, it is desirable that the outcome of voting in the Council agrees with the popular vote P = ∑ ∑ X of all voters in the Union. In other words, we would like to make the so-called ‘democracy deficit’ Nν

ν

Nν

Nν

ν

i =1

νi

i =1

νi

ν

i =1

νi

M

ν =1

M

M

νi

Nν

∑∑X ν =1 i =1

ν

Nν

ν =1 i =1

∆ = ∆ (g1,..., g M ) = C - P =

ν

M

νi

- ∑ g νYν ν =1

as small as possible. There is no way to make ∆ vanishing for all possible voting results: For any choice of the weights g ν one can find distributions of 1, -1 among the votes such that Council vote and popular vote disagree. Moreover, ∆ still depends on the proposal ω, so we can only hope to make ∆ small ‘in the average’. To define ‘in the average’ rigorously, we consider the proposal ω as random. This induces a probability structure on the set of all possible voting outcomes. We suppose that the system is fed by ‘really random’ proposals, in particular, that a proposal and its negative are equally likely. Consequently, the probability P (X ν1 j1 = a1,..., X νL jL = aL ) is the same as P (X ν1 j1 = -a1,..., X νL jL = -aL ) 1 and P (X ν j = 1) = P (X ν j = -1) = . Given the probability P we want to find 2 voting weights g1,..., g ν such that

(

E (∆2 ) = E (C - P )

2

)

is minimal, where E denotes the expectation with respect to P.

(1)

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103

If we assume that voters in state Sν make their decision independently of the voters in other states, it turns out that the optimal weight g ν minimising (1) is given by  Nν  g ν = E  ∑ X ν i  (2)  .   i =1 Equation (2) says that the optimal weight is given by the expected size of the majority in S ν . We remark that ∑ X is the number of ‘YES’ votes minus the expected number of ‘NO’ votes, that is the margin of the voting result in state Sν.   The next task is to compute E  ∑ X  . If we assume that the voters inside each country decide independently from each other then: Nν

i =1

νi

Nν

i =1

 Nν g ν = E  ∑ X νi  i =1

νi

  ≈ N ν  

(3)

for a large number of voters. This is an easy consequence of the central limit theorem. Thus, we obtain again the square root law. The asymptotic (3) remains true as long as the central limit theorem holds, which is the case, roughly speaking, if the correlation between the voters is not too strong. Only, if we assume strong correlation then (3) has to be replaced by  Nν g ν = E  ∑ X νi  i =1

  ≈ N ν α  

(4)

1

for some α with 2 < α ≤ 1 . Models with correlation may serve to model a specific society at a certain moment and to make estimates based on this. However, to establish a voting system in a constitutional act, we cannot (and should not) reflect the momentary status of a particular society, but rather we should be led by general principles and long-term considerations. For this purpose, the only reasonable basis seems to be the assumption of no (or weak) dependence between the voters. For a discussion both of the mathematical aspects of these models and of the political implications, see Kirsch (2007). How to Compose a Good Voting System for the Council From time to time politicians and high-ranking EU officials claim that the voting system in the EU Council is not an important issue since most decisions are made unanimously. Given that the distribution of power was a key issue at various European summits and the summit in Rome at least failed just because of this very problem, it is hard to believe that the question of power in the Council is not a major concern of the European politicians.

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One can reasonably expect that some of the European politicians try to maximise the power of their respective countries. However, this is thinking in short time periods. An unjust voting system for the Council is very likely to block the further development of the European Union. Regardless of the short-term winners of an unfair voting system all members of the Union will lose in the long run. A fair voting system should not rely on ‘smoky backroom’ negotiations of voting weights. It should rather be defined by a formula which gives voting weights (or better, voting power) on the basis of the countries’ populations. In this respect, the draft Constitution is, indeed, a paradigm shift to the better. However, to choose voting weights proportional to the population gives the bigger states an undue share of power. Instead, the power indices of the states should be proportional to the square root of the respective population. To implement such a system, one could try to make the voting weight of a state with population N be (proportional to) N . In general this does not guarantee that the voting power is proportional to N as well. However, it turns out that the voting weights in the EU Council are proportional to N if we choose the weights proportional to the square root and set the quota to 61.4 per cent. This is a result of the papers by Słomczyński and Życzkowski (2004 and 2006), both from the Jagiellonian University at Krakow (see also Kirsch, Machover and Słomczyński 2004). The system they suggested is now known as the ‘Jagiellonian Compromise’. One may argue that the EU is not only a union of people, but also a union of states. Therefore one can very well justify a ‘double majority’. This means that in addition to a weighted voting (obeying the square root law) one might want to add a simple (or qualified) majority rule for the number of supporting states. This would strengthen the smaller states. Such a deliberate deviation from the square root law could turn out to be politically wise. Appendix: Comparison of the various voting systems The following table shows the Banzhaf Indices for the Council in a 27-member EU for the Nice Treaty, the draft Constitution in the Convention’s version (50–60) and in the current version (55–65), which will also be in the Reform Treaty. This is compared with the ideal distribution of power as given by the square root law (SRL).

The Distribution of Power in the Council of Ministers of the European Union

105

Table 6.A.1 Comparison between power indices (for 27 member states) Country

Population (millions) 82.54

Nice

France UK

Germany

7.78

Constitution (50–60) 12.76

Constitution (55–65) 11.87

59.63

7.78

9.09

8.73

8.11

59.33

7.78

9.05

8.69

8.09

SRL 9.54

Italy

57.32

7.78

8.78

8.44

7.95

Spain

41.55

7.42

6.65

6.38

6.77

Poland

38.21

7.42

6.32

5.89

6.49

Romania

21.77

4.26

4.06

4.22

4.90

Netherlands

16.19

3.97

3.39

3.51

4.23

Greece

11.02

3.68

2.76

2.87

3.49

Portugal

10.41

3.68

2.69

2.80

3.39

Belgium

10.36

3.68

2.69

2.80

3.38

Czech Rep.

10.20

3.68

2.66

2.78

3.36

Hungary

10.14

3.68

2.65

2.76

3.34

Sweden

8.94

3.09

2.50

2.62

3.14

Austria

8.07

3.09

2.40

2.52

2.98

Bulgaria

7.85

3.09

2.38

2.50

2.94

Denmark

5.38

2.18

2.07

2.19

2.44

Slovakia

5.38

2.18

2.07

2.19

2.44

Finland

5.21

2.18

2.04

2.17

2.40

Ireland

3.96

2.18

1.89

2.02

2.09

Lithuania

3.46

2.18

1.83

1.96

1.95

Latvia

2.33

1.25

1.68

1.81

1.60

Slovenia

2.00

1.25

1.64

1.78

1.48

Estonia

1.36

1.25

1.57

1.70

1.22

Cyprus

0.72

1.25

1.48

1.62

0.89

Luxembourg

0.45

1.25

1.46

1.59

0.70

Malta

0.40

0.94

1.44

1.58

0.66

The following table gives the relative gains or losses of the EU member states:

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Institutional Design and Voting Power in the European Union

Table 6.A.2 Relative gains or losses of member states Country

Nice

Constitution (50–60)

Constitution (55–65)

Germany

-18.45

33.68

24.34

France

-4.05

12.07

7.67

UK

-3.81

11.84

7.44

Italy

-2.14

10.40

6.06

Spain

9.58

-1.84

-5.74

Poland

14.26

-2.67

-9.35

Romania

-13.10

-17.08

-13.89

Netherlands

-5.98

-19.73

-17.00

Greece

5.66

-20.84

-17.56

Portugal

8.69

-20.75

-17.35

Belgium

8.99

-20.53

-17.12

Czech Rep.

9.80

-20.68

-17.23

Hungary

10.15

-20.80

-17.34

Sweden

-1.54

-20.38

-16.62

Austria

3.63

-19.51

-15.50

Bulgaria

5.08

-19.23

-15.15

Denmark

-10.52

-15.20

-10.04

Slovakia

-10.48

-15.16

-10.00

Finland

-9.01

-14.80

-9.54

Ireland

4.32

-9.46

-3.29

Lithuania

11.57

-6.35

0.30

Latvia

-22.05

4.80

13.07

Slovenia

-15.74

10.80

19.72

Estonia

2.21

28.27

39.22

Cyprus

40.26

66.22

81.38

Luxembourg

77.76

107.12

126.34

Malta

42.30

118.15

138.56

The Distribution of Power in the Council of Ministers of the European Union

107

References Algaba, E., Bilbao, J.M. and Fernández, J.R. 2004. European Convention versus Nice Treaty. Preprint. Banzhaf, J.F. 1966. Multi-member electoral districts – Do they violate the ‘one man, one vote’ principle? Yale Law Journal, 75, 1309–38. Baldwin, R. and Widgrén, M. 2004. Winners and losers under various dual majority Rules for the EU’s Council of Ministers. Preprint. Bobay, F. 2004. Constitution européenne: Redistribution du pouvoir des États au Conseil de l’UE. Economie et Prevision, 163. Felsenthal, D. and Machover, M. 1998. Measurement of Voting Power: Theory and Practice, Problems and Paradoxes. Cheltenham UK: Edward Elgar. Felsenthal, D. and Machover, M. 2003. Analysis of QM Rules in the Draft Constitution For Europe proposed by the European Convention. Preprint. Kirsch, W. 2001. Die Formeln der Macht. Die Zeit, March. Kirsch, W. 2004. Europa-nachgerechnet. Die Zeit, June. Kirsch, W., Machover M., Słomczyński, W. and Życzkowski K. 2004. Voting in the EU Council – A Scientific Approach. Preprint. Kirsch, W. 2007. On Penrose’s Square Root Law and Beyond. Preprint. Kirsch, W., Słomczyński, W. and Życzkowski, K. 2007. Getting the votes right. European Voice, 3–9 May. Laruelle, A. and Widgrén, M. 1998. Is the allocation of power among EU states fair? Public Choice 94 (3–4), 317–39. Penrose, L.S. 1946. The elementary statistics of majority voting. Journal of the Royal Statistical Society, 109(1), 53–7. Plechanovová, B. 2004. Draft Constitution and the Decision-Making Rule for the Council of Ministers of the EU-Looking for alternative solution. Preprint. Pukelsheim, F. 2007. Der Jagiellonische Kompromiss. Neue Zürcher Zeitung, 20 June. Słomczyński, W. and Życzkowski, K. 2004. Rules Governing Voting in the EU Council. Preprint. Słomczyński, W. and Życzkowski, K. 2006. Penrose voting systems and optimal quota. Acta Physica Polonica B, 37(11), 3133–43.

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Part II Distribution of Power in the European Union

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Chapter 7

The Distribution of Power in the European Cluster Game Jesús Mario Bilbao

Introduction Weighted voting games are mathematical models which are used to analyse the distribution of the decision power of a nation in a supranational organisation like the Council of Ministers of the European Union, the Security Council of the United Nations or the International Monetary Fund. In these institutions, each nation is allocated a number of votes and a proposal is approved if a coalition of nations has enough votes to reach an established quota. The power of a country in a supranational organisation is a numerical measure of its capacity to decide the approval of a motion. This decisive character is measured by calculating the number of times that the vote of a country converts to a coalition that does not reach the quota to take decisions in a winning coalition. The power indices are a priori measures of this power, the most useful are the Shapley (Shapley and Shubik 1954) and Banzhaf (1965) indices. Hagemann and De Clerck-Sachsse (2007) made the following observation about coalition formation in the European Union: But it can be concluded that a consistent pattern can be observed in the distinction between large, medium and small members; the following will reveal whether this differentiation also holds after the [EU] enlargement.

In this contribution, we study the European Cluster Game defined by the following six players: • • • • • •

Big1 = {Germany}, Big2 = {France, United Kingdom, Italy}, Big3 = {Spain, Poland}, Med1 = {Romania, Netherlands, Greece, Portugal, Belgium, Czech Rep., Hungary}, Med2 = {Sweden, Austria, Bulgaria, Denmark, Slovakia, Finland, Ireland, Lithuania}, Small = {Latvia, Slovenia, Estonia, Cyprus, Luxembourg, Malta}.

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Institutional Design and Voting Power in the European Union

The new voting rule proposed by the Intergovernmental Conference in order to draw up a future European Treaty changes the power of the countries in the Council in a very remarkable way. The reason is that, under the new rule, the weighted votes that were approved in Nice are removed and a coalition needs 15 votes, which in total represent at least 65 per cent of the population, to approve a decision. Furthermore, the minimum number of countries required to block a proposal is four and abstentions are not counted. Cooperative games under combinatorial restrictions are cooperative games in which the players have restricted communication possibilities, which are defined by a combinatorial structure. The first model in which the restrictions are defined by the connected sub-graphs of a graph is introduced by Myerson (1997). Contributions on graph-restricted games include Owen (1986) and Borm, Owen and Tijs (1992). In these models the possibilities of coalition formation are determined by the positions of the players in a communication graph. Another type of combinatorial structure, introduced by Gilles, Owen and van den Brink (1992) and van den Brink (1997), is equivalent to a sub-class of antimatroids. This line of research focuses on the possibilities of coalition formation determined by the positions of the players in the so-called permission structure. We will analyse the European Cluster Game by using the restricted co-operation model derived from a combinatorial structure called the augmenting system. This structure is a generalisation of the antimatroid structure and the system of connected sub-graphs of a graph. Furthermore, this new set system includes the conjunctive and disjunctive systems derived from a permission structure (Bilbao 2003). We will present a ‘ready-to-apply’ procedure to compute the Shapley-Shubik index power of games restricted by combinatorial structures derived from the European Cluster Game. The second part of this contribution is devoted to the computation of the Owen index for the countries in the European Cluster Game. This game is a weighted multiple majority game with an a priori system of unions. We introduce the procedures to compute this power index by means of generating functions. Finally, we present the implementation of the algorithms used in this work in the computer system Mathematica by Wolfram (1999). Augmenting Systems Let N be a finite set. A set system over N is a pair (N, F ) where F is a family of subsets of N. The sets belonging to F are called feasible. We will write S ∪ i and S∖i instead of S ∪ {i } and S∖{i} respectively. Definition 1. An augmenting system is a set system (N, F ) with the following properties : P1. ∅ ∈ F . P2. For S ,T ∈ F with S ∩ T ≠ ∅, we have S ∪ T ∈ F . P3. For S ,T ∈ F with S ⊂ T , there exists i ∈ T \ S such that S ∪ i ∈ F .

The Distribution of Power in the European Cluster Game

113

Example  The following collections of subsets of N = {1,…,n}, given by F= 2N , F ={∅,{i}} where i ∈ N , and F ={∅,{1},…,{n}}, are augmenting systems over N. Example  In a communication graph G = (N , E ) , the set system (N, F ) given by F = { S ⊆ N :(S,E(S)) is a connected subgraph of G}, is an augmenting system. The next characterisation of the augmenting systems derived from the connected sub-graphs of a graph is proved by Algaba, Bilbao and Slikker (2007). Theorem 2 An augmenting system (N, F ) is the system of connected sub-graphs of the graph G = (N , E ) , where EE=={{SS∈∈FF: :SS ==22}} if and only if {i } ∈ F for all i ∈ N . Example  Gilles (Gilles, Owen, and van den Brink 1992) showed that the feasible coalition system (N, F ) derived from the conjunctive or disjunctive approach contains the empty set, the ground set N, and that it is closed under union. Algaba (Algaba, Bilbao, and Slikker 2004) showed that the coalition systems derived from the conjunctive and disjunctive approach were identified to poset antimatroids and antimatroids with the path property respectively. Thus, these coalition systems are augmenting systems. Let N = {1,…,n} be a set of players with n >2 and we consider a subset S of starting players. If i ∈ S then the coalition {i} is feasible. Each starting player i looks for a player k ∉ S to generate a new feasible coalition {i,k}. These coalitions with cardinality 2 search for new players which agree to join one by one. If we assume that common elements of two feasible coalitions are intermediaries between the two coalitions in order to establish the feasibility of its union, we obtain an augmenting system (N, F ) . Since the individual players k ∉ S are not feasible coalitions, the family F is not generated by the connected sub-graphs of a graph. Moreover, if players i, j ∈ S then {i } , { j } ∈ F and {i, j } ∉ F . Then the augmenting system (N, F ) is not an antimatroid. Example  Let N = {1,2,3,4} and we consider S1 = {1,2,4} and S2 = {1,4}. By using the above coalition formation model we can obtain the augmenting systems in Figure 7.1. The sets of maximal feasible coalitions are partitions of the players into disjoint coalitions: the coalition structures CS1 = {{1},{4},{2,3}} and CS2 = {{1,2},{3,4}}. Example Let us consider N = {1,2,3,4} and F ={∅,{1},{4},{1,2},{3,4},{1,2, 3},{2,3,4},N}. Since {1,2,3} and {2,3,4} are feasible coalitions, property P2 implies that the grand coalition N is also feasible.

Institutional Design and Voting Power in the European Union

114

{2, 3}

{1}

{2}

{4}

{1, 2}

{3, 4}

{1}

{4}

{}

{}

Figure 7.1 {1, 2, 3, 4}

{1, 2, 3}

{2, 3, 4}

{1, 2}

{3, 4}

{1}

{4}

{}

Figure 7.2

Figure 7.3

The Distribution of Power in the European Cluster Game

115

The set system given by N ={1,2,3,4} and the family of subsets F = {∅,{1},{4},{1,2},{1,3},{2,4},{3,4},{1,2,3},{1,2,4},{1,3,4},{2,3,4},N}. is an augmenting system. Since {1, 4} ∉ F the system (N, F ) is not an antimatroid. Moreover, {1, 2} ∩ {2, 4} = {2} ∉ F and so (N, F ) is not a convex geometry. Definition 3 Let (N, F ) be an augmenting system. For a feasible coalition S ∈ F, we define the set S * = {i ∈ N \ S : S ∪ {i } ∈ F } of augmentations of S and the set S + = S ∪ S * = {i ∈ N : S ∪ {i } ∈ F } . Let (N, F ) be a set system and let S ⊆ N be a subset. The maximal nonempty feasible subsets of S are called components of S. We denote by C F (S ) the collection of all components of a subset S ⊆ N . Observe that the set C F (S ) may be the empty set. This set will play a role in the concept of a game restricted by an augmenting system. Proposition 4 A set system (N, F ) satisfies property P2 if and only if for any S ⊆ N with C F (S ) ≠ ∅, the components of S form a partition of a subset of S. Games Restricted by Augmenting Systems Definition 5 Let v : 2N → R be a cooperative game and let (N, F ) be an augmenting system. F N The restricted game v : 2 → R, is defined by v F (S ) =

∑

v (T ).

T ∈C F (S )

If (N, F ) is the augmenting system given by the connected subgraphs of a graph G = (N , E ) , then the game (N , v F ) is a graph-restricted game which is studied by Myerson (1977) and Owen (1986). Note that if S ∈ F then v F (S ) = v (S ). Let (N , v ) be a game and (N, F ) an augmenting system. The Shapley value for player i ∈ N , in the restricted game (N , v F ) is given by Φi (N , v F ) =

∑

{S ⊆N :i ∈S }

(s - 1) ! (n - s ) ! n!

v F (S ) - v F (S \ {i }) ,  

Institutional Design and Voting Power in the European Union

116

where n = N and s = S . This value is an average of the marginal contributions v F (S ) - v F (S \ {i }) of a player i to the coalitions {S ⊆ N : i ∈ S } . In this value, the sets S of different size get different weight. If the number of players is n, then the function that measures the worst case running time for computing these indices is in O(n2ⁿ). Moreover, to obtain the restricted game (N , v F ) we need to compute the set of the components C F (S ) of every subset S ⊆ N . Then it is necessary to consider all the feasible subsets of S and hence the time complexity is O(t) where n n  t = ∑ s  2s = 3n .   s =0  

Bilbao (2003) obtains the following explicit formula, in terms of v, for the Shapley value of the players in the restricted game v F . The time complexity of the formula is polynomial in the cardinality F . Theorem 6 Let v : 2N → R be a cooperative game and let (N, F ) be an augmenting system. Then the Shapley value for player i ∈ N , in the restricted game (N , v F ) is Φi (N , v

F

)

(t - 1) ! (t + - t ) ! t ! (t + - t - 1) ! = ∑ v (T ) v (T ), ∑ t+ ! t+ ! {T ∈F :i ∈T } {T ∈F :i ∈T + \T }

where t = T and t + = T + . + (Notice that if F= 2N , then T * = N \ T and T = N for every T ∈ F . Thus, the formula obtained in the above theorem is equal to the classical Shapley value [15] for the game (N , v ) ). The algorithm shown in Theorem 6 computes the Shapley value Φ (N , v F ) and written in the Mathematica computer system (Wolfram 1999) it is as follows: = 15) || q[S] >= 24] := 1; v[S_ /; (p[S] < 650 && q[S] < 24) || q[S] < 15] := 0;)

We can also define the game Cluster1, given only by the double majority game without the blocking clause. (v[{}] := 0; v[S_ /; (p[S] >= 650 && q[S] >= 15)] := 1; v[S_ /; (p[S] < 650 || q[S] < 15)] := 0;)

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The classical Shapley values of these games are:

%LJ

%LJ

%LJ

6PDOO

0HG

Figure 7.4

0HG

Star

%LJ

%LJ

%LJ

6PDOO

0HG

Figure 7.5 Wheel

0HG

The Distribution of Power in the European Cluster Game

119

ShaCluster = {0.10, 0.25, 0.10, 0.25, 0.15, 0.15}, ShaCluster1 = {0.067, 0.42, 0.067, 0.22, 0.12, 0.12}.

Let us consider the following star (Figure 7.4) and wheel (Figure 7.5) graphs. The augmenting system given by a graph G is the collection of all the connected sub-graphs of G. For the above graphs, we obtain the following collections of feasible coalitions: F_Star = {{}, {1}, {2}, {3}, {4}, {5}, {6}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 2, 6}, {1, 3, 4}, {1, 3, 5}, {1, 3, 6}, {1, 4, 5}, {1, 4, 6}, {1, 5, 6}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 3, 6}, {1, 2, 4, 5}, {1, 2, 4, 6}, {1, 2, 5, 6}, {1, 3, 4, 5}, {1, 3, 4, 6}, {1, 3, 5, 6}, {1, 4, 5, 6}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 5, 6}, {1, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}} F_Wheel = {{}, {1}, {2}, {3}, {4}, {5}, {6}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {1, 2, 3}, {1, 2, 4}, {1, 2, 5}, {1, 2, 6}, {1, 3, 4}, {1, 3, 5}, {1, 3, 6}, {1, 4, 5}, {1, 4, 6}, {1, 5, 6}, {2, 3, 4}, {3, 4, 5}, {4, 5, 6}, {1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 3, 6}, {1, 2, 4, 5}, {1, 2, 4, 6}, {1, 2, 5, 6}, {1, 3, 4, 5}, {1, 3, 4, 6}, {1, 3, 5, 6}, {1, 4, 5, 6}, {2, 3, 4, 5}, {3, 4, 5, 6}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 6}, {1, 2, 3, 5, 6}, {1, 2, 4, 5, 6}, {1, 3, 4, 5, 6}, {2, 3, 4, 5, 6}, {1, 2, 3, 4, 5, 6}}

The Shapley value for the Cluster and Cluster1 games restricted for these graphs are respectively: ShaStarCluster = {0.37, 0.17, 0.067, 0.17, 0.12, 0.12}, ShaStarCluster1 = {0.33, 0.33, 0.033, 0.13, 0.083, 0.083}, ShaWheelCluster = {0.17, 0.22, 0.12, 0.22, 0.17, 0.12}, ShaWheelCluster1 = {0.13, 0.38, 0.083, 0.18, 0.13, 0.083}.

It should be noted that the blocking clause changes the Shapley values of the European Cluster Game when we consider all feasible coalitions and also the games restricted for the considered graphs. The Owen Value of Games with a priori unions Let us consider a finite set N. We will denote by P(N) the set of all partitions of N. A partition P ∈ P (N ) is called a coalition structure or a system of unions of the set N. The Owen value, proposed and characterised by Owen (1977), is an

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Institutional Design and Voting Power in the European Union

extension of the Shapley value for games with a priori unions. This value can be derived from a two-level bargaining process. First, unions split the total amount according to the Shapley value in the induced game played by the unions. Then, each union allocates its total reward among its members taking into account the possibilities that they might join another union using again the Shapley type of allocation. For simple games with an a priori system of unions, a power index is a function which assigns to a simple game with an a priori system of unions (N,v,P) a vector g(N,v,P), where the i-component is the power of player i in the game (N,v,P) according to g. The Owen index can be written in this way: gi (N , v, P ) =

∑ ∑

L ⊆M \k T ⊆Pk \i

pLi ,T (v (Q ∪ T ∪ i ) - v (Q ∪ T )),

for any i ∈ N , where M = {1, …, m }, P = {P1, …, Pm }, Q = ∪ l ∈L Pl , and Pk is the coalition of the partition P such that i ∈ Pk . For the Owen index the coefficient: pLi ,T =

l ! (m - l - 1) ! t ! (pk - t - 1) ! , m! pk

which corresponds to the coefficients of the Shapley value in the games played by the unions and the members of the coalition Pk , respectively. For large games, the computation of the Owen index needs a great number of operations and the computational complexity grows exponentially. The generating functions method is one of the procedures to compute this index. Generating functions give a procedure to enumerate the cardinality of elements c(r) of a finite set, when these elements have a configuration that depends on a characteristic r. These methods have been applied to compute the power of the countries in the International Monetary Fund by Alonso-Meijide and Bowles (2005), and also in the European Union by Algaba, Bilbao and Fernández (2007). We next consider the European Cluster Game as a game with the following a priori system of unions: P1 = {Germany}, P2 = {France, United Kingdom, Italy}, P3 = {Spain, Poland}, P4 = {Romania, Netherlands, Greece, Portugal, Belgium, Czech Rep., Hungary}, P5 = {Sweden, Austria, Bulgaria, Denmark, Slovakia, Finland, Ireland, Lithuania}, P6 = {Latvia, Slovenia, Estonia, Cyprus, Luxembourg, Malta}.

The Distribution of Power in the European Cluster Game

121

The double majority voting system, as agreed in the 2004 IGC, will take effect on 1 November 2014, until which date the present qualified majority system (the Nice rules) will continue to apply. After that, during a transitional period until 31 March 2017, when a decision is to be adopted by qualified majority, a member of the Council may request that the decision be taken in accordance with the qualified majority as defined in the Nice rules of the present Treaty of the European Union. The weights with respect to the population and the number of countries in the double majority voting system are given by: Pop27 = {171,123,123,118,86,79,45,33,23,22,21,21,21,18,17,16,11,11,11,8,7,5,4,3,1,1, 1}; Countries = {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1};

where the quotas are 650 and 15 votes, respectively. Moreover, in the European Cluster Game we consider the following partition according to the population size of the countries of the European Union: P={{1},{2,3,4},{5,6},{7,8,9,10,11,12,13},{14,15,16,17,18,19,20,21},{22,23,2 4,25,26,27}};

We define the games Partition and Partition1 by using the double majority system with and without the blocking clause, respectively. In order to compute the Owen value of these games, we apply the generating functions algorithms given by Alonso-Meijide, Bilbao, Casas-Méndez and Fernández (2007). The results obtained are: OwenPartition = {0.0667, 0.139, 0.139, 0.139, 0.0417, 0.0250, 0.0333, 0.0306, 0.0306, 0.0306, 0.0306, 0.0306, 0.0306, 0.0161, 0.0161, 0.0161, 0.0137, 0.0137, 0.0137, 0.0137, 0.0137, 0.0194, 0.0194, 0.0194, 0.0194, 0.0194, 0.0194} OwenPartition1 = {0.100, 0.0833, 0.0833, 0.0833, 0.0583, 0.0417, 0.0381, 0.0353, 0.0353, 0.0353, 0.0353, 0.0353, 0.0353, 0.0202, 0.0202, 0.0202, 0.0179, 0.0179, 0.0179, 0.0179, 0.0179, 0.0250, 0.0250, 0.0250, 0.0250, 0.0250, 0.0250}

The above results show the consequences of the blocking clause for the power of the European countries in the double majority voting system with the defined a priori system of unions. Germany, Spain and Poland are the only big countries that increase their power by using the blocking clause. In contrast, France, the United Kingdom and Italy lose power. Furthermore, the 19 medium and small European countries gain power, so that the small countries increase their power more.

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Acknowledgments This research has been partially supported by the Spanish Ministry of Education and Science and the European Regional Development Fund, under grant SEJ200600706, and by the FQM 237 grant of the Andalusian Government. References Algaba, E., Bilbao, J.M., van den Brink, R. and Jiménez-Losada, A. 2004. Cooperative games on antimatroids. SIAM Journal on Discrete Mathematics, 282, 1–15. Algaba, E., Bilbao, J.M. and Fernández, J.R. 2007. The distribution of power in the European Constitution. European Journal of Operational Research, 176(3), 1752–66. Algaba, E., Bilbao, J.M. and Slikker, M. 2007. A value for games restricted by augmenting systems, Preprint. Alonso-Meijide, J.M., Bilbao, J.M., Casas-Méndez, B. and Fernández J.R. 2007. Generating functions for coalitional power indices in weighted multiple majority games, Preprint. Alonso-Meijide, J.M. and Bowles, C. 2005. Generating functions for coalitional power indices: An application to the IMF. Annals of Operations Research, 137, 21–44. Banzhaf, J.F. 1965. Weighted voting doesn’t work: A mathematical analysis, Rutgers Law Review, 19(2), 317–43. Bilbao, J.M. 2003. Cooperative games under augmenting systems. SIAM Journal on Discrete Mathematics, 17(1), 122–33. Borm, P., Owen, G. and Tijs, S.H. 1992. On the position value for communications situations, SIAM Journal on Discrete Mathematics, 5(1), 305–20. Brink, R. van den 1997. An axiomatization of the disjunctive permission value for games with a permission structure. International Journal of Game Theory, 26, 27–43. Gilles, R.P., Owen, G. and van den Brink, R. 1992. Games with permission structures: The conjunctive approach. International Journal of Game Theory, 20(3), 277–93. Hagemann, S. and De Clerck-Sachsee, J. 2007. Old Rules, New Game. DecisionMaking in the Council of Ministers after the 2004 Enlargement. Paper to the CEPS Annual Conference, Brussels, 2007. Myerson, R.B. 1977. Graphs and co-operation in games. Mathematics of Operations Research, 2(3), 225–9. Owen, G. 1986. Values of graph-restricted games. SIAM Journal on Algebraic and Discrete Methods, 7(2), 210–20.

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Owen, G. 1997. Values of games with a priori unions, in: Mathematical Economics and Game Theory, edited by R. Henn and O. Moeschlin. Berlin: SpringerVerlag, 76–88. Shapley, L.S. and Shubik, M. 1954. A method for evaluating the distribution of power in a committee system. American Political Science Review, 48(3), 787– 92. Wolfram, S. 1999. The Mathematica Book. 4th edition. Cambridge: Wolfram Media & Cambridge University Press.

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Chapter 8

The Constitutional Power of Voters in the European Parliament Silvia Fedeli and Francesco Forte

Introduction It is often asserted that the national seat allocation in the European Parliament (EP) favours the voters of big countries who vote for big parties. The opposite claim is also made: the distribution of votes among countries is deemed ‘unfair’, particularly after EU enlargement, because it is biased in favour of small countries. This chapter is devoted to assess which of these claims is true for the fifth and the sixth terms, and whether the enlargements have substantially modified the results. Following Owen (1975, 1982), Nurmi (1997) studied the voting powers of the political-national sub-groups in the EP for the fourth term, in order to ascertain whether, particularly in small countries, voters should restrict their choice to the largest political groups rather than to small parties, or not to vote at all, to enhance the pursuit of their interests in the assembly. In this perspective, Nurmi (1997) considered as a benchmark the power of voters in an ideal system of direct democracy (square-root rule) and assumed that, when voting in the assembly, the members of the EP (MEPs) of every country follow party discipline, always voting as a bloc, while the party’s policy is assumed to be decided by the members of the various parties under simple majority vote (SMV). Here, we likewise consider that MEPs are organised in political groups. However, votes in the EP often involve cross-party issues, involving ‘national’ interests. Two well known cases support our view. (1) The Parliament’s failure to approve the European take-over directive until the fifth term. In July 2001 the EP, with a 50 per cent vote, rejected the text prepared by the conciliatory committee. In this decision, which destroyed 12 years of negotiations, the contrary vote of the German MEPs was decisive. The approval of the take-over directive in December 2003 was obtained subject to the introduction of strategic amendments to the Commission’s draft, which made optional the key provisions of the legislation. (2) The ‘Bolkestein’ directive on services in the internal market was harshly criticised   Nurmi discusses the no-show paradox by Fishburn and Brams (1983), Moulin (1988) and Berg and Nurmi (1988) according to which, whenever a group of voters would gain a better outcome by not voting at all than by voting according to its true preferences, the votes cast by the group are wasted.

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by left-wing parties and by mass protests in various Western Europe countries. On 22 March 2005, EU leaders agreed on a revision of the directive. The EP considered the directive again, adding few changes to the original text. On 16 February 2006, the MEPs voted in favour of the proposed revision. The two largest groups in the EP declared they would vote for the revised bill; GUE and the Greens declared against. In fact, there was a lining up of Western European countries (France, the Netherlands, Germany, Belgium, Sweden and Denmark) against the reform, which was supported by Eastern European countries plus Great Britain. These voting behaviours clearly show that MEPs play the national games by crossing the institutional schemes of political parties laid down for the EP, in order to pursue the interests of their voters as citizens of a given nation. In these cases, the party leaders in the EP do not call for party loyalty and MEPs explicitly vote according to national interests without incurring party discipline. In other words, when it comes to voting on relevant amendments, rather than playing the political game, MEPs often combine in national blocs, playing a ‘multipartisan’ game, in which they merge with their compatriots of different ideology to adopt a common (national) line. For the electorate, the problem arises of choosing the proper representative while keeping in mind a cross-party strategy of the pursuit of national interests. To capture this complexity of EP decision-making, we analyse the assembly as being composed of homogeneous sub-groups or ‘cells’ consisting of MEPs belonging to both a given nationality and a given political group. These are represented in Tables 8.1, 8.2 and 8.3 for the fifth (EU15) and sixth (EU25 and EU27) terms respectively. We assume that when political or national interests are at stake, the cells try to orient the decision of the assembly by forming voting blocs with other cells (presumed to be either politically or nationally more homogeneous), under the assumption that other cells are forming similar blocs. In section two, we assess the Penrose ( ψ ) and Banzhaf ( β ) voting-power indices of the cells in two basic composite games: the political-game, in which each national cell belonging to a given party tries to address the policy of its political group in the assembly, and the national-game, in which cells of different parties combine into a national group, trying to promote some specific national interest. As a benchmark we consider the uncoordinated or anarchic-game, in which each cell plays separately. In these contexts, fairness is associated with the principle of ‘one-person-one-vote’ (OPOV), by which the voting power of the representatives (of each cell) should

  On this issue, see Riker and Brams (1973).   A number of power indices are available. Here we refer to the Penrose and Banzhaf indices, because the interpretation in terms of I-power (Felsenthal-Machover, 1998) fits well with the parliament of a union of states. On the basis of results by Owen (1975, 1982) these indices can be used directly in the analysis of compound voting games like those depicted.

Table 8.1 Country Belgium Denmark Germany Greece Spain France Ireland Italy Luxembourg Netherlands Austria Portugal Finland Sweden UK

EP fifth term (1999–2004) PPE-DE

PSE

ELDR

6 1 53 9 28 21 5 34 2 9 7 9 5 7 36

5 3 35 9 24 22 1 16 2 6 7 12 3 6 30

5 6

Verts/ ALE 7 4

3 1 8 1 8

5 4 11

4 9 2 2 1 4 2 2 2 6

GUE/ NLG

UEN

EDD

1 7 7 4 11

1

4

3 6 10

9

NI 2

6 1

1 12 11

3 5

2 1 3

2

2

2

Total seats 25 16 99 25 64 87 15 87 6 31 21 25 16 22 87

Share of seats 0.0399 0.0256 0.1581 0.0399 0.1022 0.1390 0.0240 0.1390 0.0096 0.0495 0.0335 0.0399 0.0256 0.0351 0.1390

Share of population 0.027 0.014 0.219 0.028 0.105 0.157 0.010 0.154 0.001 0.042 0.022 0.027 0.014 0.024 0.158

232 181 52 45 43 22 18 33 626 1 1 Total Note: PPE-DE=European People’s Party and European Democrats; PSE=Party of European Socialists; ELDR=European Liberal, Democratic and Reformist Party; VERTS/ALE=Greens/European Free Alliance; GUE/NGL=European United Left/Nordic Green Left; UEN=Union for a Europe of Nations; EDD=Europe of Democracies and Diversities; NI=Non-attached Members.

Table 8.2 Country

EP sixth term (25 countries, distribution of seats and population at 2004) PPE-DE

PSE

ALDE

VertsALE 2 2

GUENLG

INDDEM

UEN

NI

Total Share of Share of seats seats population Austria 6 7 3 18 0.0246 0.0176 Belgium 6 7 6 3 24 0.0328 0.0225 Cyprus 3 1 2 6 0.0082 0.0016 CzechRep. 14 2 6 1 1 24 0.0328 0.0221 Denmark 1 5 4 1 1 1 1 14 0.0191 0.0117 Estonia 1 3 2 6 0.0082 0.0029 Finland 4 3 5 1 1 14 0.0191 0.0113 France 17 31 11 6 3 3 7 78 0.1066 0.1423 Germany 49 23 7 13 7 99 0.1352 0.1785 Greece 11 8 4 1 24 0.0328 0.0239 Hungary 13 9 2 24 0.0328 0.0219 Ireland 5 1 1 1 1 4 13 0.0178 0.0087 Italy 24 16 12 2 7 4 9 4 78 0.1066 0.1250 Latvia 3 1 1 4 9 0.0123 0.0050 Lithuania 2 2 7 2 13 0.0178 0.0075 Luxembourg 3 1 1 1 6 0.0082 0.0010 Malta 2 3 5 0.0068 0.0009 Netherlands 7 7 5 4 2 2 27 0.0369 0.0352 Poland 19 8 4 10 7 6 54 0.0738 0.0826 Portugal 9 12 3 24 0.0328 0.0227 Slovakia 8 3 3 14 0.0191 0.0116 Slovenia 4 1 2 7 0.0096 0.0043 Spain 24 24 2 3 1 54 0.0738 0.0913 Sweden 5 5 3 1 2 3 19 0.0260 0.0194 United Kingdom 28 19 12 5 1 11 2 78 0.1066 0.1287 TOTAL 268 200 88 42 41 37 27 29 732 1 1 Note: PPE-DE=European People’s Party and European Democrats; PSE=Party of European Socialists; ALDE=Alliance of Liberals and Democrats for Europe; Verts/ALE=Greens/European Free Alliance; GUE/NGL=European United Left/Nordic Green Left; IND/DEM=Independence/Democracy; UEN=Union for a Europe of Nations; NI=Non-attached Members.

Table 8.3

EP sixth term (27 countries, distribution of seats at July 2007 and population at 2005)

Country Belgium BE Bulgaria BG CzechRep. CZ Denmark DK Germany DE Estonia EE Ireland IE Greece GR Spain ES France FR Italy IT Cyprus CY Latvia LV Lithuania LT Luxemburg LU Hungary HU Malta MT Netherlands NL Austria AT Poland PL Portugal PT Romania RO Slovenia SI Slovakia SK Finland FI Sweden SE United Kingdom GB Total

PPE-DE

PSE

6 5 14 1 49 1 5 11 24 17 24 3 3 2 3 13 2 7 6 15 9 9 4 8 4 6 27 278

7 5 2 5 23 3 1 8 24 31 14 2 1 9 3 7 7 9 12 12 1 3 3 5 19 216

ELDRALDE 6 5

UEN

4 7 2 1

1

2 11 13 1 1 7 1 2 5 1 5

VertsALE 2 1 13

4

13 4 2

20

3 6 2 1

44

INDDEM

6 1 7

1 1

1 4 1 3 7 2

1 1

2

2

3

ITS 3 3

7 2

NI

1

3

1 4 2

3

8 2 5 3 12 104

GUENLG

1 1 5 42

1 2 1 41

3

1

1 2

6 3 2 10 24

1 23

3 13

Total seats 24 18 24 14 99 6 13 24 54 78 78 6 9 13 6 24 5 27 18 54 24 35 7 14 14 19 78 785

Share of seats 0.03 0.02 0.03 0.02 0.13 0.01 0.02 0.03 0.07 0.10 0.10 0.01 0.01 0.02 0.01 0.03 0.01 0.03 0.02 0.07 0.03 0.04 0.01 0.02 0.02 0.02 0.10 1

share of pop. 0.02 0.02 0.02 0.01 0.17 0.00 0.01 0.02 0.09 0.13 0.12 0.00 0.00 0.01 0.00 0.02 0.00 0.03 0.02 0.08 0.02 0.04 0.00 0.01 0.01 0.02 0.12 1

Note: PPE-DE=European People’s Party and European Democrats; PSE=Party of European Socialists; ELDR=Alliance of Liberals and Democrats for Europe; Verts/ALE=Greens/European Free Alliance; GUE/NGL=European United Left/Nordic Green Left; IND/DEM=Independence/Democracy; UEN=Union for Europe of Nations, ITS=Identity tradition sovereignty; NI=Non-attached Members.

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be proportional to the population represented. The fairness is measured by an index of electors’ voting rights given by the ratio of the share of voting power of each cell in the EP to the share of EU population that it represents. Section three analyses the results for EU15, EU25 and EU27 in terms of representation of the electorate. The results show that neither the voters of the large countries nor those of the large parties are favoured in both the fifth and sixth terms, as compared with voters of small countries and of small parties. Theoretical Framework Weighted Voting System in the EP and Basic Strategic Options of the Cells The simplest notion of weighted voting game with a quota q refers to a collection of winning coalitions W of voters i=1..n of an assembly N, where a non-negative voting endowment, wi, is assigned to each voter, i, such that 0 < q ≤ ∑ wi . When i ∈N approving a motion in the EP, however, the notion of weighted voting game becomes more articulate. The representatives, once elected, enter into political groups, according to their choices, presumably known before the election. We represent this distribution of EP representatives in Table 8.4. That is, in the EP, the elected representatives of a given country C (C=1,…,Z) of weight RC • (as laid down by the EU Treaty), after the election choose to enrol in a given political group P (P=1,…K), that is, the representatives of a country split into cells. We refer to the voting endowment of a cell i of country C and party P as wiPC , given by the number of MEPs elected for party P in country C. The endowment of party P in the assembly, across countries, is R•P = ∑ wi , whereas RC • = ∑ wi is the C P voting endowment of country C. We assume fully homogeneous members within each cell, which implies that each cell acts as an individual player. Given the above representation of the EP, three basic strategic games among cells seem interesting. PC

PC

  The ‘equitability index’ adopted by Felsenthal-Machover (2000), with the benchmark of hypothetical direct democracy, compares the direct voting power of the electorate with the electorate’s voting power in the EP obtained via their representatives. The fairness measure thus emerging in terms of hypothetical direct power of the electors may be questionable for EP, where ‘proportional representation’, not direct democracy, is the constitutional requirement.   Following Felsenthal-Machover’s (1998) notation and definitions, a simple voting game in a democratic body is defined as a collection W of subsets of voters i=1...n of an assembly N, satisfying the following conditions: N∈W; ∅∉W; if X⊆Y⊆N and X∈W then Y∈W. A proper voting game requires that if X∈W and Y∈W, then Y∩X≠∅. A set of voters M, subset of N, is a ‘coalition’. M is a winning coalition if M∈W. If M∉W it is a losing coalition. A voter i is W-critical in M∈W if K-{i}∉W. If i is not critical in any M, i is a dummy in W.

The Constitutional Power of Voters in the European Parliament

Table 8.4   Country_1

131

Distribution of elected representatives by cells in the parliament of a federation Party_1

…

Party_P

…

Party_K

Total

wi11

 

wiP 1

 

wiK 1

R1• = ∑ wiP 1 P

…. Country_C

wi1C

   

wiPC

   

wiKC

RC • = ∑ wiPC P

… Country_Z

wi1Z

   

wiPZ

   

wiKZ

RZ • = ∑ wiPZ P

Total

R•1 = ∑ wi1C C

 

R•P = ∑ wiPC C

 

R•K = ∑ wiKC C

(I) The anarchic-game: under SMV, the cells play individually, forming random coalitions with each other. In this case, the Penrose power of a cell, iCP  , K ×Z ) playing independently in the assembly is simply ψAnar i (WK×Z ) = Si K(W , where 2 ×Z -1 KXZ = number of cells playing independently of each other, WK ×Z = set of winning coalitions in this game, and SiCP = swing function that assigns to any voting game and any voter iCP a value SiCP (WK ×Z ) equal to the number of coalitions in which iCP is critical. The Banzhaf index, β Anar iCP , is the ratio of the swings of a given player over the total swings of all players. β Anar iCP can also be obtained by normalising the Penrose power of a given player over the sum of the Penrose values of all voters in the assembly considered. (II) The political-game (game with bloc formation under the same political affiliation) is made up of two games, both under SMV: CP

CP

1. Internal decision of a political group: the policy of the party is decided on the basis of a voting game among its cells belonging to various countries (the game is among the cells in each column of Table 8.5). 2. Decision of the EP as resulting from the vote of different political groups: once each party P has decided its policy, it (all its members) votes accordingly as a bloc of weight R•P , with P=1,.,K (that is, the game is among the parties in the last row of Table 8.5). In the political game, the composite Penrose power of a cell via the political groups, ψiCP viaP , is the product of the Penrose power of the cell in the game internal to the party, ψiP (WZP ), times the Penrose power of the party in the whole EP, ψP (WK ), CP with the corresponding Banzhaf index obtained assuming that national cells share their party’s power in the assembly with weights given by their Banzhaf power in the internal game.

Institutional Design and Voting Power in the European Union

132

Table 8.5

Strategic bloc formation under the same political affiliation

 

Party_1

…

Party_P

…

Party_K

Total

Country_1

wi11

 

wiP 1

 

wiK 1

R1• = ∑ wiP 1

wiKC

RC • = ∑ wiPC

RZ • = ∑ wiPZ

…. Country_C

 

wi1C

…

 

 

wiPC

 

Country_Z Total

 

P

 

wi1Z

 

wiPZ

 

wiKZ

R•1 = ∑ wi1C

 

R•P = ∑ wiPC

 

R•K = ∑ wiKC

C

P

C

P

C

(III) The national-game is made up of two games, both under SMV: 1. Internal decision of the national bloc: The policy of each national bloc is assumed to be decided by the vote of its cells, which have different political affiliations (that is, the game is among the cells in each row of Table 8.6). 2. Final decision of the parliament as resulting from the vote of different national blocs: Once each national group of MEPs has decided its policy, it (all its members) votes in the EP as a bloc of weight RC • , with C=1,.,Z (that is, the game is among countries in the last column of Table 8.6). Table 8.6   Country_1

Strategic bloc formation under the same national affiliation Party_1

…

Party_P

…

Party_K

Total

wi11

 

wiP 1

 

wiK 1

R1• = ∑ wiP 1

wiKC

RC • = ∑ wiPC

 

wiKZ

RZ • = ∑ wiPZ

 

R•K = ∑ wiKC

  Country_C

wi1C

 

wiPC

  Country_Z Total

wi1Z R•1 = ∑ wi1C C

P

   

P

 

 

wiPZ

 

R•P = ∑ wiPC C

P

C

The composite power of a cell of a given political affiliation entering a national bloc, ψiCP viaC , is the product of the Penrose power of the cell in the game internal

The Constitutional Power of Voters in the European Parliament

133

to the national bloc, ψiCCP (WKC ) , times the Penrose power of the national bloc in the whole EP fixed by the Treaty, ψC (WZ ) . The Banzhaf index of the cell iCP, βiCP viaC , is the country’s power in the assembly, βC , times the cell’s Banzhaf power in the country’s internal game, βiCCP . Equality of Electoral Rights of the Citizens Taking as a benchmark the OPOV principle, as an expression of the equality of voting rights of the citizens, for each game we take the ratio between the Banzhaf power of a cell βiCP and the share of the population it represents: FiCP = βiCP /Share of popiCP The index thus obtained considers whether and how much the voting power of the cell iCP elected in country C for party P is distanced from the population it is expected to represent under the OPOV principle. If Fi > (≤)1 , the citizens concerned, voting for a given party, are endowed with a voting power greater(less/ equal) than the measure of fairness implied by OPOV. An aggregate measure of the index for each country, in each game, is given by FC = ∑ βiCP Share of population of country C CP

P

FC considers, for each strategic game, the sum of the Banzhaf index of the cells of a given country and the share of population of that country in the EU. Results in Terms of Representation of Countries and Cells Now we focus on the ability of any given country and on the ability of any given cell to represent its own electorate (given the rule for seat assignment) with its voting powers in the EP for the three strategic games in the fifth and sixth terms under SMV. We assess, by FC and FiCP , the fairness of distribution of the voting power of the electors of the EP in small and large countries and of small and large parties, focusing on the voting powers of the EP national/political cells. Countries’ Representation The present distribution of seats among EU countries, in either scenario, does not follow a proportionality principle but a degressive criterion in terms of population. Nevertheless, the distribution of seats in the two terms and after the last enlargement does differ. Table 8.7 reports, for the three games in EU15, EU25 and EU27, the FC and the share of seats to share of population. Although the FC is quite a coarse index, the results are interesting because they give a picture of the democratic representation of the aggregate power of the

Table 8.7

EU 15 Germany GB France Italy Spain Netherlands Greece Belgium Sweden Portugal Austria Denmark Finland Ireland Luxembourg

Countries’ representation (with countries ordered by seats/population ratio)

Anar.game 0.756 0.884 0.874 0.902 0.972 1.160 1.397 1.437 1.462 1.474 1.528 1.780 1.818 2.355 8.221

FC (EU15) National- Politicalgame game 0.759 0.688 0.912 0.829 0.917 1.022 0.938 1.014 1.013 0.842 1.053 1.210 1.315 1.247 1.363 1.580 1.373 1.475 1.395 1.316 1.421 1.565 1.681 1.801 1.724 1.942 2.185 2.215 7.522 6.822

seats /pop. 0.723 0.880 0.885 0.905 0.975 1.179 1.423 1.467 1.490 1.502 1.558 1.806 1.859 2.402 8.383

EU25 France Germany Spain GB Italy Poland Netherlands Sweden Greece Austria Portugal Belgium Czech Rep. Hungary Denmark Slovakia Finland Ireland Slovenia Lithuania Latvia Estonia Cyprus Malta Luxembourg    

FC (EU25) Anar.- National- Politicalgame game game 0.750 0.761 0.738 0.787 0.806 0.857 0.809 0.798 0.690 0.827 0.841 0.816 0.849 0.865 0.896 0.886 0.878 0.896 1.038 1.027 0.995 1.308 1.298 1.339 1.357 1.340 1.256 1.385 1.362 1.310 1.434 1.412 1.148 1.441 1.419 1.512 1.467 1.444 1.539 1.485 1.458 1.325 1.593 1.576 1.713 1.616 1.590 1.719 1.656 1.639 1.683 1.987 1.964 2.183 2.177 2.154 2.316 2.361 2.308 2.817 2.392 2.372 2.591 2.738 2.738 2.738 5.062 5.062 5.694 7.746 7.630 6.937 8.088 8.190 8.190  

 

 

seats /pop. 0.749 0.758 0.808 0.828 0.852 0.893 1.049 1.337 1.373 1.401 1.447 1.458 1.484 1.498 1.638 1.643 1.694 2.040 2.215 2.383 2.451 2.806 5.186 7.897 8.391  

EU27 Germany France Spain GB Italy Poland Romania Netherlands Sweden Greece Austria Portugal Belgium Bulgaria Czech Rep. Hungary Denmark Slovakia Finland Ireland Slovenia Lithuania Latvia Estonia Cyprus Malta Luxembourg

FC (EU27) Anar.- National- Politicalgame game game 0.778 0.791 0.823 0.782 0.793 0.711 0.787 0.776 0.670 0.812 0.826 0.933 0.831 0.856 0.814 0.880 0.862 1.048 1.001 0.975 0.950 1.025 0.993 0.948 1.304 1.362 1.182 1.342 1.240 1.143 1.357 1.376 1.250 1.413 1.399 1.156 1.422 1.363 1.391 1.435 1.328 1.436 1.457 1.441 1.446 1.474 1.458 1.293 1.600 1.724 1.515 1.609 1.550 2.060 1.654 1.687 1.687 1.957 2.031 2.091 2.167 2.211 2.187 2.349 2.293 2.881 2.414 2.555 2.874 2.753 2.185 2.586 4.955 3.932 5.047 7.674 7.309 6.091 8.156 8.631 7.876

seats /pop. 0.750 0.780 0.785 0.812 0.834 0.885 1.011 1.035 1.319 1.354 1.372 1.425 1.437 1.450 1.468 1.486 1.618 1.626 1.672 1.978 2.191 2.374 2.441 2.783 5.009 7.759 8.246

The Constitutional Power of Voters in the European Parliament

135

cells, which can also be found below for individual cells. Notice, in Table 8.7, the worse-off countries in terms of seats/population. In the fifth term, the five biggest countries (DE, GB, FR, IT and ES) were those underrepresented in terms of seats (share of seats to population lower than 1). After the enlargements, Poland joins the underrepresented countries in terms of seats. In terms of representation of power in EU25, the FC over/below 1 follows by and large the same distribution, whereas Poland gains power in the political game in EU27. The Netherlands and Romania, having a ratio of seats to population above 1, have a FC