Endogenous Competence and a Limit to the Condorcet Jury Theorem

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 decision leads to an improvement in the group's ability to make a good decision. An assumption under-appreciated is that the competency of the members of the group 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 competence is endogenous, then increases in the size of the group encourages free riding. This trades off with the value of information aggregation. Thus, the value of increased group size is muted. Extensions illustrate that if committee members are allowed to exit/not participate, then the equilibrium committee size is reduced. Additionally, (non-decisive supermajority voting rules encourage the investments and, consequently, individual competence.