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The Mathematics and Statistics of Voting Power

Gelman, Andrew and Katz, Jonathan N. and Tuerlinckx, Francis (2002) The Mathematics and Statistics of Voting Power. Social Science Working Paper, 1141. California Institute of Technology , Pasadena, CA. (Unpublished)

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In an election, voting power—the probability that a single vote is decisive—is affected by the rule for aggregating votes into a single outcome. Voting power is important for studying political representation, fairness and strategy, and has been much discussed in political science. Although power indexes are often considered as mathematical definitions, they ultimately depend on statistical models of voting. Mathematical calculations of voting power usually have been performed under the model that votes are decided by coin flips. This simple model has interesting implications for weighted elections, two-stage elections (such as the U.S. Electoral College) and coalition structures. We discuss empirical failings of the coin-flip model of voting and consider, first, the implications for voting power and, second, ways in which votes could be modeled more realistically. Under the random voting model, the standard deviation of the average of n votes is proportional to 1/√n, but under more general models, this variance can have the form cn^(−α) or √a−b log n. Voting power calculations under more realistic models present research challenges in modeling and computation.

Item Type:Report or Paper (Working Paper)
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Katz, Jonathan N.0000-0002-5287-3503
Additional Information:¤We thank Peter Dodds, Amit Gandhi, Yuval Peres, Hal Stern, Jan Vecer, and Tian Zheng for helpful discussions. This work was supported in part by grants SES-9987748 and SES-0084368 of the U.S. National Science Foundation. Published as Gelman, A., Katz, J.N., & Tuerlinckx, F. (2002). The mathematics and statistics of voting power. Statistical Science, 420-435.
Group:Social Science Working Papers
Funding AgencyGrant Number
Subject Keywords:Banzhaf index, coalitions, cooperation, decisive vote, elections, electoral college, political science, prisoner's dilemma, trees.
Series Name:Social Science Working Paper
Issue or Number:1141
Record Number:CaltechAUTHORS:20170802-153714426
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:79787
Deposited By: Jacquelyn Bussone
Deposited On:02 Aug 2017 23:51
Last Modified:19 Nov 2020 18:31

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