Voting Rules in Sequential Search by Committees: Theory and Experiments

We propose a committee extension of the individual sequential search model called the "secretary problem," where collective decisions on when to stop the search are reached via a prespecified voting rule. We offer a game-theoretic analysis of our model and then report two experiments on three-person committees with either uncorrelated or perfectly correlated preferences under three different voting rules followed by a third experiment on single decision makers. Relative to equilibrium predictions, committees with uncorrelated preferences oversearched under minority and majority voting rules but, otherwise, undersearched or approximated equilibrium play. Individually, committee members were often less strategic when their preferences were uncorrelated than when they were perfectly correlated. Collectively, committees' decisions were more strategic than single decision makers' only under the unanimity rule, although still not significantly better in terms of the decision makers' welfare. Finally, across our experiments that involved committee search, the unanimity rule always optimized committee welfare.