Journal article: 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 accpetance 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 unaminity and all members affect the distribution of decisions. Various implications are drawn.