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 different 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 different 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 66.6% of the population.