First and second best voting rules in committees

Abstract

Abstract.A committee of people with common preferences but different abilities in identifying the best alternative (e.g., a jury) votes in order to decide between two alternatives. The first best voting rule is a weighted voting rule that takes the different individual competences into account, and is therefore not anonymous, i.e., the voters' identities matter. Under this rule, it is rational for the committee members to vote according to their true opinions, or informatively. This is not necessarily true for an anonymous voting rule, under which members may have an incentive to vote noninformatively. Thus, strategic, sophisticated voters may vary their voting strategies according to the voting rule rather than naively voting informatively. This paper shows that the identity of the best anonymous and monotone (i.e., quota) voting rule does not depend on whether the committee members are strategic or naive or whether some are strategic and some are naive. One such rule, called the second best rule, affords the highest expected utility in all cases.* We are grateful to Jacob Paroush, Shmuel Nitzan, Steven Brams, Michele Piccione and three anonymous referees for helpful comments and discussions.

Is diversity in capabilities desirable when adding decision makers?

“…Ladha (1995) relaxed the independence assumption. Austen-Smith and Banks (1996) and Ben-Yashar and Milchtaich (2007) generalized the setting to a strategic one. CJT can be generalized to the case of heterogeneous voters.…”

Anonymous Procedures for Condorcet's Model: Robustness, Nonmonotonicity, and Optimality

“…This robustness and nonmonotonicity is not due to any particular procedure, but is an "artifact" of Condorcet's model itself. Other extensions of Condorcet's model include giving each person a continuous, not binary, signal about which alternative is superior (for example Duggan and Martinelli, 2001;Li et al, 2001) and giving some people more informative signals than others (for example Ben-Yashar and Milchtaich, 2007). The assumption of binary signals in our paper greatly simplifies the consideration of anonymous procedures.…”

Beyond Condorcet: optimal aggregation rules using voting records

“…Fortunately, our setting proposes a mechanism that results in the use of the 'first best' voting rule and is therefore immune to strategic non-informative voting. Such strategy-proofness does not hold under 'second best' anonymous aggregation rules, as have been demonstrated by Austen-Smith and Banks (1996), Ben-Yashar and Milchtaich (2007), Feddersen andPesendorfer (1998) andMcLennan (1998). In fact, in this setting, effective deliberation prior to the vote is expected to take place, as established in Coughlan (2000).…”

“…The voters' best interest is, after all, to assign the correct weights to every voter, in order to reach the correct decision. The question of strategic voting, when voters are solely concerned by the common collective interest, was recently examined by Ben-Yashar and Milchtaich (2007). They established that under the 'first best' voting rule, the decision makers do not have an incentive to vote strategically and non-informatively.…”