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.
Power measurement Voting Random electorates;
- D71: Social Choice • Clubs • Committees • Associations
- D72: Political Processes: Rent-Seeking, Lobbying, Elections, Legislatures, and Voting Behavior
Michel Le Breton, and Karine Van Der Straeten, “Influence versus utility in the evaluation of voting rules: a new look at the Penrose formula”, Public Choice, vol. 165, n. 1, October 2015, pp. 103–122.
Public Choice, vol. 165, n. 1, October 2015, pp. 103–122