POWER INDICES AS AN AID TO INSTITUTIONAL DESIGN : THE GENERALISED APPORTIONMENT PROBLEM

A priori voting power analysis can be useful in helping to design a weighted voting system that has certain intended properties. Power indices can help determine how many weighted votes each member should be allocated and what the decision rule should be. These choices can be made in the light of a requirement that there be a given distribution of power and/or a desired division of powers between individual members and the collective institution. This paper focuses on the former problem: choosing the weights given that the power indices and the decision rule are fixed exogenously.

National, Political and Institutional Influence in European Union Decision Making

The distribution of decisional power among member states of the EU has remained a hot issue in recent discussions about the future design of European Union decision making and the Lisbon revision of the unsuccessful proposal of the Constitutional Treaty. Usually only the distribution of voting weights in the Council of Ministers under the qualified majority voting rule is taken into account. In contrast, in this paper we formulate simplified models of the consultation and co-decision procedures in the decision making of European Union institutions, reflecting the fact that together with the Council of Ministers the Commission and European Parliament are also important actors in EU decision making. The main conclusion of this paper is that the distribution of voting power in the Council of Ministers voting record provides incomplete evidence about national influences in European Union decision making. With rare exceptions decision making is based on the consultation and co-decision procedures involvi ng the Commission and/or European Parliament. Legislative procedures change the inter-institutional distribution of power (among the Council, Commission and European Parliament) reducing the power of the Council and at the same time they change intra-institutional power in the Council (the relative power of the Member States compared to the Council voting without taking into account the Commission and Parliament).Co-decision procedure, committee system, consultation procedure, European Union decision making, Penrose-Banzhaf power indices, qualified majority, simple voting committee, weighted majority game

Power indices as an aid to institutional design: the generalised apportionment problem

A priori voting power analysis can be useful in helping to design a weighted voting system that has certain intended properties. Power indices can help determine how many weighted votes each member should be allocated and what the decision rule should be. These choices can be made in the light of a requirement that there be a given distribution of power and/or a desired division of powers between individual members and the collective institution. This paper focuses on the former problem: choosing the weights given that the power indices and the decision rule are fixed exogenously

Representation-Compatible Power Indices

This paper studies power indices based on average representations of a weighted game. If restricted to account for the lack of power of dummy voters, average representations become coherent measures of voting power, with power distributions being proportional to the distribution of weights in the average representation. This makes these indices representation-compatible, a property not fulfilled by classical power indices. Average representations can be tailored to reveal the equivalence classes of voters defined by the Isbell desirability relation, which leads to a pair of new power indices that ascribes equal power to all members of an equivalence class.Comment: 28 pages, 1 figure, and 11 table

Revealed Political Power

This paper adopts a \revealed preference" approach to the question of what can be inferred about bias in a political system. We model an economy and its political system from the point of view of an \outside observer." The observer sees a nite sequence of policy data, but does not observe either the citizens' preference prole or underlying distribution of political power that produced the policies. The observer makes inferences about distribution of political power as if political power were derived from a wealth-weighted voting system with weights that can vary with the state of the economy. The weights determine the nature and magnitude of the wealth bias. Positive weights on relative income in any period indicate an \elitist" bias in the political system whereas negative weights indicate a \populist" one. As a benchmark, any policy data is shown to be rationalized by any system of wealthweighted voting. However, by augmenting the observer's observations with polling data, nontrivial inference is possible. We show that joint restrictions resulting from the policy and polling data together imply upper and lower bounds on the set of rationalizing biases. These bounds can be explicitly calculated and can be used to discern instances of elitist bias; in other times they show populist bias. Additional restrictions on the preference domain can rule out the unbiased benchmark case of equal representation.wealth-bias, elitist bias, populist bias, weighted majority winner, rationalizing weights, "Anything Goes Theorem"

Computing the Power Distribution in the IMF

The International Monetary Fund is one of the largest international organizations using a weighted voting system. The weights of its 188 members are determined by a fixed amount of basic votes plus some extra votes for so-called Special Drawing Rights (SDR). On January 26, 2016, the conditions for the SDRs were increased at the 14th General Quota Review, which drastically changed the corresponding voting weights. However, since the share of voting weights in general is not equal to the influence, of a committee member on the committees overall decision, so-called power indices were introduced. So far the power distribution of the IMF was only computed by either approximation procedures or smaller games than then entire Board of Governors consisting of 188 members. We improve existing algorithms, based on dynamic programming, for the computation of power indices and provide the exact results for the IMF Board of Governors before and after the increase of voting weights. Tuned low-level details of the algorithms allow the repeated routine with sparse computational resources and can of course be applied to other large voting bodies. It turned out that the Banzhaf power shares are rather sensitive to changes of the quota.Comment: 19 pages, 2 figures, 13 table

Power relations in the International Monetary Fund: a study of the political economy of a priori voting power using the Theory of Simple Games

In general in organisations whose system of governance involves weighted majority voting, power and voting weight differ. Power indices are a value concept for majority voting games which provide a means of analysing this difference. This paper provides new algorithms for computing the two classical power indices (the Banzhaf index and the Shapley-Shubik index) and applies them to the voting distribution in the two governing bodies of the IMF in each year since its foundation. The focus is both substantive, being an analysis of the political economy of the IMF, and methodological, as a study of the use of the power indices. Power relations are studied with respect to two types of decisions: ordinary decisions requiring a simple majority and decisions requiring a special majority of 80% or 85%. Clear cut results are obtained for the former: among the G5 countries discrepancies between power and voting weight have declined over time with the exception of the United States which continues to have much more power than its weight even though that weight has declined. In the nineteen forties the United Kingdom’s power was considerably below its relatively large nominal voting power, similarly to some extent for France. Both power indices give results which are qualitatively comparable. For decisions requiring special majorities, however, few general results emerge because of conflict between the indices. We examine the effect of the size of the majority requirement on the power of the leading members and find that the power of the US declines as the majority requirement increases. This result confirms the warnings of Keynes that the US insistence on retaining a national veto for itself might be counterproductive. We conclude that the special majority requirement creates a distortion in the voting system which can be regarded as a serious lack of transparency. We also examine the effect of the EU countries voting as a block rather than individually and show that it would be dominant and the US power would fall considerably. We conclude that it is not possible to make a clear choice between the two power indices used but that there is some indication that the Banzhaf index may be more plausible