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

Voting Power Derives from the Poll Distribution. Shedding Light on Contentious Issues of Weighted Votes and the Constitutional Treaty

Analysis of the Constitutional Treaty of the European Union shows that there is a serious discrepancy between the voting power gradient of Member States computed by the Shapley-Shubik and Banzhaf indices. Given the lack of compelling arguments to choose between these indices on purely axiomatic grounds, we turn to a probabilistic approach as pioneered by Straffin (1977) focusing on the probability distribution of voting poll outcomes. We present a unifying model of power indices as expected decisiveness, which shows that the defining feature of each approach is a particular distribution of the voting poll. Empirical evidence drawn from voting situations, in addition to a consideration of first principles, leads us to reject one of these approaches. The unified formulation allows us to develop useful related concepts of efficiency and blocking leverage, previously used solely by a 'Banzhaf' approach, for the case of Shapley-Shubik, and a comparison of results is shown.Voting power indices, Power gradient, Coefficient of representation, Expected decisiveness, Efficiency, Blocking leverage, Constitution of the European Union

Power Indices: Shapley-Shubik OR Penrose-Banzhaf?

Shapley-Shubik and Penrose-Banzhaf (absolute and relative) power measures and their interpretations are analysed. Both of them could be successfully derived as cooperative game values, and at the same time both of them can be interpreted as probabilities of some decisive position (pivot, swing) without using cooperative game theory at all. In the paper we show that one has to be very careful in interpretation of results based on relative PB-power index and not to use it without absolute PB-power index, what is frequently the case in many published studies.absolute power; cooperative games; I-power; pivot; power indices; relative power; P-power; swing

How much of Federalism in the European Union

The European Union (EU) is not de jure a federation, but after 50 years of institutional evolution it possesses attributes of a federal state. One can conclude that EU is “something between” federation and intergovernmental organization. If we measure “something between” by interval [0, 1], where 0 means fully intergovernmental organization and 1 means de facto federation, the questions are: What is the location of recent EU on this interval? What tendency of development of this location can be observed in time? In this paper we propose such a measure based on game-theoretical model of European Union decision making system.Co-decision procedure, committee system, consultation procedure, European Union decision making, federation, intergovernmental organization, qualified majority, power indices, simple voting committee

On the inverse power index problem

Weighted voting games are frequently used in decision making. Each voter has a weight and a proposal is accepted if the weight sum of the supporting voters exceeds a quota. One line of research is the efficient computation of so-called power indices measuring the influence of a voter. We treat the inverse problem: Given an influence vector and a power index, determine a weighted voting game such that the distribution of influence among the voters is as close as possible to the given target value. We present exact algorithms and computational results for the Shapley-Shubik and the (normalized) Banzhaf power index.Comment: 17 pages, 2 figures, 12 table

Switching-Algebraic Calculation of Banzhaf Voting Indices

This paper employs switching-algebraic techniques for the calculation of a fundamental index of voting powers, namely, the total Banzhaf power. This calculation involves two distinct operations: (a) Boolean differencing or differentiation, and (b) computation of the weight (the number of true vectors or minterms) of a switching function. Both operations can be considerably simplified and facilitated if the pertinent switching function is symmetric or it is expressed in a disjoint sum-of-products form. We provide a tutorial exposition on how to implement these two operations, with a stress on situations in which partial symmetry is observed among certain subsets of a set of arguments. We introduce novel Boolean-based symmetry-aware techniques for computing the Banzhaf index by way of two prominent voting systems. These are scalar systems involving six variables and nine variables, respectively. The paper is a part of our ongoing effort for transforming the methodologies and concepts of voting systems to the switching-algebraic domain, and subsequently utilizing switching-algebraic tools in the calculation of pertinent quantities in voting theory

Thesis Digest: Mathematical Interpretation of Political Power and the Arkansas State Government

On the whole, political power can he very difficult to quantify. A person may be powerful due to his or her personal charm, wealth, fame, credibility, or influential connections. Political bodies do not account for these qualities when creating voting procedures; they only assign voting rules to specific positions. For example, most would say that in the United States government that a Senator is more powerful than a Representative, but less powerful than the President, without knowing any way to quantify or verify those differences. Since the 1950\u27s, mathematicians and political scientists have attempted to create mathematical models that partially describe an individual\u27s power as a voting member of a committee, board, or legislative body. These models have resulted in four major power indexes that describe the percentage of a body\u27s total power held by each individual member. The four most prominent power indexes are the Shapley-Shubik, Banzhaf, Johnston, and Deegan-Packel, each of which uses a different theory to calculate the probability that an individual\u27s vote will decide whether a proposal passes or fails. The research in this paper develops formulas to calculate the four-power indexes for legislatures that are unicameral, bicameral, unicameral with committees, and bicameral with committees. These formulas have several variables (up to ten) and have many (up to several thousand) terms for typical sizes of state legislative chambers. Using Mathematica computer software the four power indices are computed for various legislative configurations and the indices\u27 behavior are studied. Then these methods are applied to the Arkansas State Government by calculating the power indexes of the Governor, Senate, House, House Committee members, and Senate Committee members. By examining the theories behind the four power indexes and available historical evidence, the paper concludes by analyzing which indexes, if my, provide the best model for the political power structure of the Arkansas State Government

Effective number of relevant parties

This paper proposes a new method to evaluate the number of relevant parties in an assembly. The most widespread indicator of fragmentation used in comparative politics is the "Effective Number of Parties", designed in 1979 by M. Laakso and R.Taagepera. Taking both the number of parties and their relative weights into account, the ENP is arguably a good parsimonious operationalization of the number of "relevant"parties. This index however produces misleading results in single-party majority situations as it still indicates that more than one party is relevant in terms of government formation. We propose to modify the ENP formula by replacing proportions of seats by voting power measures. This improved index behaves more in line with Sartori's definition of relevance, without requiring additional information (such as policy positions) in its construction. We thus advocate for the use of our "Effective Number of Relevant Parties"in future comparative research