Power and size: A new paradox

Steven J. Brams; Paul J. Affuso

doi:10.1007/BF00141101

Power and size: A new paradox

Steven J. Brams, Paul J. Affuso

Research output: Contribution to journal › Article › peer-review

Abstract

An analysis of several different indices of voting power reveals that the voting power of a member of a weighted voting body may increase, rather than decrease, when new members are added to the original body. Real instances of this phenomenon, called the paradox of new members, are shown to have occurred when new states were added to the U.S. Electoral College and new countries to the European Community Council of Ministers. Conditions for the existence of the paradox, and probabilities of its occurrence in small and moderate-size voting bodies, are given. Efficient algorithms for the calculation of the voting power indices, based on generating functions, are also outlined.

Original language	English (US)
Pages (from-to)	29-56
Number of pages	28
Journal	Theory and Decision
Volume	7
Issue number	1-2
DOIs	https://doi.org/10.1007/BF00141101
State	Published - Feb 1976

ASJC Scopus subject areas

General Decision Sciences
Developmental and Educational Psychology
Arts and Humanities (miscellaneous)
General Economics, Econometrics and Finance
Applied Psychology
Computer Science Applications
General Social Sciences

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10.1007/BF00141101

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AB - An analysis of several different indices of voting power reveals that the voting power of a member of a weighted voting body may increase, rather than decrease, when new members are added to the original body. Real instances of this phenomenon, called the paradox of new members, are shown to have occurred when new states were added to the U.S. Electoral College and new countries to the European Community Council of Ministers. Conditions for the existence of the paradox, and probabilities of its occurrence in small and moderate-size voting bodies, are given. Efficient algorithms for the calculation of the voting power indices, based on generating functions, are also outlined.

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Power and size: A new paradox

Abstract

ASJC Scopus subject areas

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