We study collective search processes in which members of a committee decide whether to accept the current proposal or continue searching. The acceptance decision is made according to majority rule. We study which members have more impact on the decision, as well as the degree of randomness of the decision. When proposals vary along a single dimension, the acceptance set is small, and at most two members determine the outcome whatever the majority rule. When proposals vary along many dimensions, the acceptance set is large except under unanimity and all members affect the distribution of decisions. Various implications are drawn.

The coalitional Nash bargaining solution is defined to be the core allocation for which the product of players' payoffs is maximal. We consider a non-cooperative model with discounting in which one team may form and every player is randomly selected to make a proposal in every period. The grand team, consisting of all players, generates the largest surplus. But a smaller team may form. We show that as players get more patient if an efficient and stationary equilibrium exists, it must deliver payoffs that correspond to the coalitional Nash bargaining solution. We also characterize when an efficient and stationary equilibrium exists, which requires conditions that go beyond the nonemptiness of the core.