First and Second Best Voting Rules in Committees

A group of people with identical preferences but different abilities in identifying the best alternative (e.g., a jury) takes a vote to decide between two alternatives. The first best voting rule is a weighted voting rule that takes into account the different individual competences, and is therefore not anonymous (i.e., the voters' identities matter). Under this rule, it is rational for group members to vote according to their true opinions, or informatively. This is not true for an anonymous voting rule, under which some group members may have an incentive to vote non-informatively. Sophisticated, strategic voters may therefore vary their voting strategies according to the voting rule used, rather than simply voting informatively. However, this paper shows that the best anonymous and monotone voting rule does not depend on whether the voters, or some of them, actually do so. A single, second best, rule gives the highest expected utility for any number of strategic voters