Do Larger Committees make Better Majority Decisions with Costly Expert

I present a two-stage model of committee voting with costly expert information. For every member of the committee to observe and synthesise independent testimony of some fixed and known quality, a majority of the agents must contribute to its acquisition. When testimony is observed with positive probability, I show that adding agents to the committee depresses the probability with which any single agent contributes - due to free-riding - and demonstrate how, with some careful assumptions, the probability of reaching the correct decision should correspondingly fall with the committee size. Moreover, I show individuals will make more accurate decisions than all groups whose aggregated signals are, collectively, inferior to the expert testimony. In keeping with Mukhopadhayas (2003) seminal work on the acquisition of private signals, these findings argue against arbitrarily enlarging committees to improve the quality of majority decisions but instead propose the dichotomous choice between individual decision-makers, and collectives whose aggregated signals are more accurate than the expert signal. Further research might permit agents to choose the amount of information they acquire, or model both private and expert information as costly