Endogenous competence and a limit to the Condorcet Jury Theorem

Abstract

The seminal contribution known as the Condorcet Jury Theorem observes that under a specific set of conditions an increase in the size of a group tasked with making a binary decision (“guilty or “innocent, say) leads to an improvement in the group’s ability to make the correct choice. An assumption that is not properly appreciated in the relevant literature is that the competency of the group members is assumed to be exogenous. In numerous applications, members of the group make investments to improve the accuracy of their decision making (e.g., pre-meeting efforts). We consider the collective action problem that arises. We show that if individual competence is endogenous, then increases in the group size encourages free riding. This trades off with the value of information aggregation. Thus, the value of the larger group size is muted. Extensions illustrate that if committee members are allowed to exit/not participate, the equilibrium committee size is reduced. Additionally, supermajority voting rules encourage investments and, consequently, individual competence.