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Standard Voting Power Indexes Don't Work: An Empirical Analysis

Gelman, Andrew and Katz, Jonathan N. and Bafumi, Joseph (2004) Standard Voting Power Indexes Don't Work: An Empirical Analysis. British Journal of Political Science, 34 (4). pp. 657-674. ISSN 0007-1234. doi:10.1017/S0007123404000237.

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Voting power indexes such as that of Banzhaf are derived, explicitly or implicitly, from the assumption that all votes are equally likely (i.e., random voting). That assumption implies that the probability of a vote being decisive in a jurisdiction with n voters is proportional to 1/√n. In this article the authors show how this hypothesis has been empirically tested and rejected using data from various US and European elections. They find that the probability of a decisive vote is approximately proportional to 1/n. The random voting model (and, more generally, the square-root rule) overestimates the probability of close elections in larger jurisdictions. As a result, classical voting power indexes make voters in large jurisdictions appear more powerful than they really are. The most important political implication of their result is that proportionally weighted voting systems (that is, each jurisdiction gets a number of votes proportional to n) are basically fair. This contradicts the claim in the voting power literature that weights should be approximately proportional to √n.

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Katz, Jonathan N.0000-0002-5287-3503
Additional Information:© 2004 Cambridge University Press. Published online: 08 September 2004. We thank David Park, the Editor of the Journal and several reviewers for helpful comments and the US National Science Foundation for grants SES-9987748, SES-0084368 and SES-0318115.
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Issue or Number:4
Record Number:CaltechAUTHORS:20140314-120456292
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:44331
Deposited By: Jonathan Katz
Deposited On:17 Mar 2014 15:45
Last Modified:10 Nov 2021 16:50

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