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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Michel Le Breton & Karine van der Straeten, 2015. "Influence versus utility in the evaluation of voting rules: a new look at the Penrose formula," Post-Print hal-04315114, HAL.
    • Handle: RePEc:hal:journl:hal-04315114
    DOI: 10.1007/s11127-015-0296-1
    as

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