Paterson, Iain (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria)
Abstract
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.
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Publisher Info
Paper provided by Institute for Advanced Studies in its series Economics Series with number
187.
Find related papers by JEL classification: C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games D02 - Microeconomics - - General - - - Institutions: Design, Formation, and Operations D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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