On the optimal composition of committees

See Grofman and Feld (1988), Young (1995), Ben-Yashar and Nitzan (1997), Berend and Sapir (2007), Dietrich and List (2008, 2013a), and Peleg and Zamir (2012). Further, Ahn and Oliveros (2010), Bozbay et al. (2011), and De Clippel and Eliaz (2012) study how to efficiently aggregate judgments when several issues are involved, as a link may then exist between the optimal decision for each issue. Their concern is whether the aggregation should be based on premise or outcome, and about the associated doctrinal paradox.

As, for example, in a legal system where decisions are made by courts having three judges and where judges can be either more experienced or less experienced.

Thus, there are at mostpossible compositions of committees in terms of the experts’ abilities.

This is equivalent to maximizing the expected number of correct decisions. Given our framework, it is a Nash equilibrium and therefore reasonable to assume that the experts vote according to their true assessment, i.e., informatively (Austen-Smith and Banks 1996; Ben-Yashar and Milchtaich 2007). Under other circumstances, strategic considerations may influence the experts’ voting behavior (Feddersen and Pesendorfer 1998; Dekel and Piccione 2000; Austen-Smith and Feddersen 2006; Gerardi and Yariv 2007). With the experts voting informatively and deciding by a simple majority rule, our results hold whether the proposals are independent or dependent. Thus, there is no need to assume even logical independence of the proposals (Dietrich and List 2013b).

That is,if expert \(i\) and expert \(i^{\prime }\) are members of the same committee.

To see this, suppose that \(Z=2\) and that the six experts have different skills. Furthermore, assume that \(q_{1}q_{2}=q_{3}q_{4}\), \(q_{5}=(q_{1}q_{2})^{1/2}\), and \(q_{6}=(q_{1}q_{2})^{1/2+\epsilon }\), where \(\epsilon >0\). Then,Hence, the partition \(\{1,2,5\}\) and \(\{3,4,6\}\) of experts and the partition \(\{1,2,6\}\) and \(\{3,4,5\}\) of experts have the same sum of the products of the experts’ skills in each committee. Furthermore, if \(\epsilon \) is sufficiently small, the sum is smaller than for any other partition. Accordingly, there are two optimal compositions of the committees.

Preferably, such “experts” should be prevented from being committee members or should be made to abstain in the voting. In a model with costly voting, Börgers (2004) shows that abstentions should be allowed.

The second-order conditions for a minimum are satisfied.