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Influence versus utility in the evaluation of voting rules: a new look at the Penrose formula

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  • Michel Breton
  • Karine Straeten

Abstract

In this paper, we present a contribution to the analysis of the relationship between influence/power measurement and utility measurement, the two most popular social objective criteria used when evaluating voting mechanisms. For one particular probabilistic model describing the preferences of the electorate, the so-called impartial culture (IC) model used by Banzhaf, the Penrose formula shows that the two objectives coincide. The IC probabilistic model assumes that voter preferences are independent and neutral. In this article, we prove a general version of the Penrose formula, allowing for preference correlations and biases in the electorate. We use that formula to illustrate, for a spectrum of well-known probabilistic models, how the divergence between the two social objectives impacts the ranking and performances of the voting mechanisms. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Michel Breton & Karine Straeten, 2015. "Influence versus utility in the evaluation of voting rules: a new look at the Penrose formula," Public Choice, Springer, vol. 165(1), pages 103-122, October.
    • Handle: RePEc:kap:pubcho:v:165:y:2015:i:1:p:103-122
    DOI: 10.1007/s11127-015-0296-1
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    Cited by:

    1. Laurent, Thibault & Le Breton, Michel & Lepelley, Dominique & de Mouzon, Olivier, 2017. "Exploring the Effects on the Electoral College of National and Regional Popular Vote Interstate Compact: An Electoral Engineering Perspective," TSE Working Papers 17-861, Toulouse School of Economics (TSE), revised May 2018.
    2. de Mouzon, Olivier & Laurent, Thibault & Le Breton, Michel & Moyouwou, Issofa, 2020. "“One Man, One Vote” Part 1: Electoral Justice in the U.S. Electoral College: Banzhaf and Shapley/Shubik versus May," TSE Working Papers 20-1074, Toulouse School of Economics (TSE).
    3. Olivier Mouzon & Thibault Laurent & Michel Breton & Dominique Lepelley, 2019. "Exploring the effects of national and regional popular vote Interstate compact on a toy symmetric version of the Electoral College: an electoral engineering perspective," Public Choice, Springer, vol. 179(1), pages 51-95, April.
    4. de Mouzon, Olivier & Laurent, Thibault & Le Breton, Michel, 2020. "One Man, One Vote Part 2: Measurement of Malapportionment and Disproportionality and the Lorenz Curve," TSE Working Papers 20-1089, Toulouse School of Economics (TSE).

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    More about this item

    Keywords

    Power measurement; Voting; Random electorates; D71; D72;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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