Probabilistic Evaluation of Preference Aggregation Functions: A Statistical Approach in Social Choice Theory

A statistical criterion for evaluating the appropriateness of preference aggregation functions for a fixed group of persons is introduced. Specifically, we propose a method comparing aggregation procedures by relying on probabilistic information on the homogeneity structure of the group members’ preferences. For utilizing the available information, we give a minimal axiomatization as well as a proposal for measuring homogeneity and discuss related work. Based on our measure, the group specific probability governing the constitution of preference profiles is approximated, either relying on maximum entropy or imprecise probabilities. Finally, we investigate our framework by comparing aggregation rules in a small study