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

Michel Le Breton and Karine van der Straeten
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Michel Le Breton: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Karine van der Straeten: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, IAST - Institute for Advanced Study in Toulouse

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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.

Keywords: Power measurement; Voting; Random electorates (search for similar items in EconPapers)
Date: 2015-11-06
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Published in Public Choice, 2015, 165 (1-2), pp.103-122. ⟨10.1007/s11127-015-0296-1⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-04315114

DOI: 10.1007/s11127-015-0296-1

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