Deliberation, preference uncertainty, and voting rules

A deliberative committee is a group of at least two individuals who first debate about what alternative to choose prior to these same individuals voting to determine the choice. We argue, first, that uncertainty about individuals' private preferences is necessary for full information sharing and, second, demonstrate in a very general setting that the condition under which unanimity can support full information revelation in debate amounts to it being common knowledge that all committee members invariably share identical preferences over the alternatives. It follows that if ever there exists an equilibrium with fully revealing debate under unanimity rule, there exists an equilibrium with fully revealing debate under any voting rule. Moreover, the converse is not true of majority rule if there is uncertainty about individuals' preferences.