Unequivocal majority and Maskin-monotonicity

The unequivocal majority of a social choice rule F is the minimum number of agents that must agree on their best alternative in order to guarantee that this alternative is the only one prescribed by F . If the unequivocal majority of F is larger than the minimum possible value, then some of the alternatives prescribed by F are undesirable (there exists a di¤erent alternative which is the most preferred by more than 50% of the agents). Moreover, the larger the unequivocal majority of F , the worse these alternatives are (since the proportion of agents that prefer the same di¤erent alternative increases). We show that the smallest unequivocal majority compatible with Maskin-monotonicity is n n 1 m , where n 3 is the number of agents and m 3 is the number of alternatives. This value represents no less than 66:6̂% of the population. Key Words: Maskin-monotonicity; Majority; Condorcet winner. J.E.L. Classi…cation Numbers: C70, D78. I thank Bernardo Moreno and William Thomson for their comments. Financial assistance from MEC under project SEJ2005-04805 and Junta de Andalucía under project SEJ552 is gratefully acknowledged. The …nal version of this paper was made while the author was visiting CORE, to which he is grateful for its hospitality.