Optimal Voting Rules in Committee Search

We analyze a discrete-time search problem in which committee members inspect alternatives sequentially over a finite search horizon. A collective decision to stop searching and accept the current alternative is reached when it is supported by a threshold number of individual votes. We investigate optimal voting rules that maximize the committee’s expected welfare. If future utilities are not too heavily time discounted, then the optimal threshold number of votes for an alternative to be accepted is non-decreasing in the length of the search horizon; but if the discount factor is too low, then the optimal threshold number of votes could decrease in the length of the search horizon. Our conclusions are consistent with previous studies on infinite-horizon search. Our results are driven by a tension between committee welfare and individual strategies of accepting mediocre alternatives to avoid adverse mutual vetoing in the future.