Jury theorems with multiple alternatives (Q2268382)

This paper develops a model for group decision making with numerical alternatives. Each evaluator votes for the largest acceptable alternative. There is a best alternative and the evaluators receive private probabilistic information. Known results on existence of a symmetric equilibrium for binary decisions are extended to the case of a finite set of more than two alternatives. It is shown that, for non-unanimous rules, the probability of an incorrect decision goes to zero as the number of evaluators increases. Necessary and sufficient conditions for extension of this result to unanimity rules are established. It is shown that, even for the case of only three alternatives, the unanimity condition may lead to a null probability of choice of intermediate alternatives, whatever the number of evaluators.