The stability of decision making in committees: The one-core

We study the stability of decision making in committees. A policy proposal introduced by a committee member is either adopted or abandoned in favor of a new proposal after deliberations. If a proposal is abandoned, it is in spite of the committee member who introduced it, who does not cooperate in any effort to defeat it. Shenoy (1980) proposes the one-core as a solution concept for this game, and shows that this solution may be empty. We provide a necessary and sufficient condition for the existence of a stable policy under the majority rule. This result highlights a trade-off between the size of a committee, the number of competing policy options, and the existence of a stable outcome. Our findings imply a tension between political stability and the existence of a large number of competing interests in democracies.