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Influence Vs. Utility in the Evaluation of Voting Rules: A New Look at the Penrose Formula

Le Breton, Michel and Van Der Straeten, Karine (2014) Influence Vs. Utility in the Evaluation of Voting Rules: A New Look at the Penrose Formula. TSE Working Paper, n. 14-511, Toulouse

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In this paper, we clarify the relationship between influence/power measurement and utility measurement, the most popular two 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 show that the two objectives coincide. The IC probabilistic model assumes that voter preferences are independent. In this article, we prove a general version of the Penrose formula, allowing for correlations in the electorate. We show that in that case, the two social objectives no longer coincide, and qualitative conclusions can be very different.

Item Type: Monograph (Working Paper)
Language: English
Date: July 2014
Place of Publication: Toulouse
Uncontrolled Keywords: Power measurement, Voting, Random electorates
JEL Classification: D71 - Social Choice; Clubs; Committees; Associations
D72 - Economic Models of Political Processes - Rent-Seeking, Elections, Legislatures, and Voting Behavior
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 16 Mar 2015 14:49
Last Modified: 20 Mar 2018 15:29
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