The Voting Paradox and the Possibility of a Social Welfare Function

In this paper, the author argues that a majority voting rule dominates a rule requiring unanimous agreement when a small number of voters is resolving questions of distribution. This is true, even though the majority rule yields no consistent ranking of alternatives, because of Condorcet's (voting) paradox. Nevertheless, under the assumptions given, no voter will have an expected utility from majority voting below his expected utility outcome under the unanimity rule. Each will be better off with majority voting if the change of rules makes any difference. In nontrivial cases, this is a consequence of the comparative efficiency of bargaining under the two rules.