Fair Reweighting of the Votes in the EU Council of Ministers and the Choice of Majority Requirement for Qualified Majority Voting during Successive Enlargements.

This paper examines the system of Qualified Majority Voting, used by the Council of Ministers of the European Union, from the perspective of enlargement of the Union. It uses an approach based on power indices due to Penrose, Banzhaf and Coleman to make two analyses: (1) the question of the voting power of member countries from the point of view of fairness, and (2) the question of how the majority quota required for QMV should be determined.VOTING ; QUOTA SYSTEM ; INDEXES

THE USE OF COLEMAN'S POWER INDICES TO INFORM THE CHOICE OF VOTING RULE WITH REFERENCE TO THE IMF GOVERNING BODY AND THE EU COUNCIL OF MINISTERS

In his well known 1971 paper the mathematical sociologist James S. Coleman, proposed three measures of voting power : (1) "the power of a collectivity to act", (2) "the power to prevent action" and (3) "the power to initiate action". (1) is a measure of the overall decisiveness of a voting body taking into account its size, decision rule and the weights of its members, while (2) and (3) are separate indices of the power of individual members, in being able to block or achieve decisions. These measures seem to have been little used for a variety of reasons, although the paper itself is widely cited. First, much of the power indices literature has focused on normalised indices which gives no role to (1) and means that (2) and (3) are identical. Second, Coleman's coalition model is different from that of Shapley and Shubik which has sometimes tended to dominate in discussions of voting power. Third, (2) and (3) are indistinguishable when the decision quota is a simple majority, the distinction becoming important in other voting situations. In this paper I propose that these indices, which are based on a fundamentally different notion of power than that assumed by game-theoretic approaches, have a useful role in aiding a better understanding of collective institutions in which decisions are taken by voting. I use them to illustrate different aspects of the design of a weighted voting system such as the governing body of the IMF or World Bank, or the system of QMV in the European Council.

The use of Coleman's power indices to inform the choice of voting rule with reference to the IMF governing body and the EU Council of Ministers

In his well known 1971 paper the mathematical sociologist James S. Coleman, proposed three measures of voting power: (1) "the power of a collectivity to act", (2) "the power to prevent action" and (3) "the power to initiate action". (1) is a measure of the overall decisiveness of a voting body taking into account its size, decision rule and the weights of its members, while (2) and (3) are separate indices of the power of individual members, in being able to block or achieve decisions. These measures seem to have been little used for a variety of reasons, although the paper itself is widely cited. First, much of the power indices literature has focused on normalised indices which gives no role to (1) and means that (2) and (3) are identical. Second, Coleman's coalition model is different from that of Shapley and Shubik which has sometimes tended to dominate in discussions of voting power. Third, (2) and (3) are indistinguishable when the decision quota is a simple majority, the distinction becoming important in other voting situations. In this paper I propose that these indices, which are based on a fundamentally different notion of power than that assumed by game-theoretic approaches, have a useful role in aiding a better understanding of collective institutions in which decisions are taken by voting. I use them to illustrate different aspects of the design of a weighted voting system such as the governing body of the IMF or World Bank, or the system of QMV in the European Council

Computation of power indices

Power indices are a useful tool for studying voting systems in which different members have different numbers of votes. Many international organisations are organised in this way in order to accommodate differences in size of countries, including the system of QMV in the European Union Council of Ministers. A power index is a measure of power based on the idea that a member’s power is his ability to swing a decision by changing the way his vote is cast. This paper addresses the problem of the computation of the two most widely used power indices, the so-called classical power indices, the Banzhaf index (and also the related Coleman indices) and the Shapley-Shubik index. It discusses the various methods that have been proposed in the literature: Direct Enumeration, Monte Carlo Simulation, Generating Functions, Multilinear Extensions Approximation, the Modified MLE Approximation Method. The advantages and disadvantages of the algorithms are discussed including computational complexity. It also describes methods for so called “oceanic games”. The paper also discusses the so-called “inverse problem” of finding what the weights should be given the desired power indices. The method is potentially useful as providing a basis for designing a voting system with a given desired distribution of power among the members, for example, to reflect differences in population or financial contributions. Examples are given from the International Monetary Fund, shareholder voting and the European Union Council

Fair reweighting of the votes in the EU Council of Ministers and the choice of majority requirement for qualified majority voting during successive enlargements

This paper examines the system of Qualified Majority Voting, used by the Council of Ministers of the European Union, from the perspective of enlargement of the Union. It uses an approach based on power indices due to Penrose, Banzhaf and Coleman to make two analyses: (1) the question of the voting power of member countries from the point of view of fairness, and (2) the question of how the majority quota required for QMV should be determined. It studies two scenarios for change from 2005 onwards envisaged by the Nice Treaty: (1) no enlargement, the EU comprising 15 member countries, and (2) full enlargement to 27 members by the accession of all the present twelve candidates. The proposal is made that fair weights be determined algorithmically as a technical or routine matter as the membership changes. The analysis of how the quota affects power shows the trade-offs that countries face between their blocking power and the power of the Council to act. The main findings are: (1) that the weights laid down in the Nice Treaty are close to being fair, the only significant discrepancies being the under representation of Germany and Romania, and the over representation of Spain and Poland; (2) the majority quota required for a decision is set too high for the Council of Ministers to be an effective decision making body

Political Influence in Multi-Choice Institutions: Cyclicity, Anonymity and Transitivity

We study political influence in institutions where members choose from among several options their levels of support to a collective goal, these individual choices determining the degree to which the goal is reached. Influence is assessed by newly defined binary relations, each of which compares any two individuals on the basis of their relative performance at a corresponding level of participation. For institutions with three levels of support (e.g., voting games in which each voter may vote "yes", "abstain", or vote "no"), we obtain three influence relations, and show that the strict component of each of them may be cyclical. The cyclicity of these relations contrasts with the transitivity of the unique influence relation of binary voting games. Weak conditions of anonymity are sufficient for each of them to be transitive. We also obtain a necessary and sufficient condition for each of them to be complete. Further, we characterize institutions for which the rankings induced by these relations, and the Banzhaf-Coleman and Shapley-Shubik power indices coincide. We argue that the extension of these relations to firms would be useful in efficiently allocating workers to different units of production. Applications to various forms of political and economic organizations are provided.Level-based influence relations, Multi-choice institutions, cyclicity, anonymity, transitivity

Coalitional power indices applied to voting systems

We describe voting mechanisms to study voting systems. The classical power indices applied to simple games just consider parties, players or voters. Here, we also consider games with a priori unions, i.e., coalitions among parties, players or voters. We measure the power of each party, player or voter when there are coalitions among them. In particular, we study real situations of voting systems using extended Shapley–Shubik and Banzhaf indices, the so-called coalitional power indices. We also introduce a dynamic programming to compute them.Peer ReviewedPostprint (published version

Unifying EU Representation at the IMF Executive Board

The consequences of consolidating EU representation at the IMF Executive Board by regrouping the 27 Member States into two EU constituencies, euro area and non-euro area, are discussed. In particular we contrast voting power as proposed by Penrose-Banzhaf (PBI) and Shapley-Shubik (SSI), and other respectively related measures of blocking (or veto) power and decision efficiency as proposed by Coleman and Paterson. Hitherto, IMF-specific literature is PBI-based. However, theoretical reasons and empirical plausibility arguments for the SSI are compelling. The (SSI) voting power of the two large constituencies – U.S.A. and euro area – reflects their corresponding voting shares over a range of majority thresholds, whereas PBI voting power reduces to only half of vote share at the majority threshold of 85% needed for some Executive Board decisions. SSI-related estimates of veto power are generally lower than the Coleman indices. Correspondingly, the efficiency of collective decision-making is considerably underestimated by the Coleman measure;International Monetary Fund, European Union, Voting power analysis, Veto power