Special majority rules. Necessary and sufficient condition for quasi- transitivity with quasi-transitive individual preferences (Q1082227)

Consider a social choice problem with a finite number of alternatives and at least three voters. Suppose that each voter's preference ordering is quasitransitive. Let P be the social prefererence ordering induced by special majorities (strictly greater than 1/2). The main result of the paper is a necessary and sufficient condition for P to be quasitransitive. The condition is a generalization of the familiar condition that there be no Condorcet cycle among three voters.