Collectively rational voting rules for simple preferences

We offer a rationality foundation of majority voting on two restricted domains of individual preferences proposed by Inada (1964). One is the domain consisting of (dichotomous) preferences that have at most two indifference classes, and the other is the domain where any set of three alternatives is partitioned into two non-empty subsets and alternatives in one set are strictly preferred to alternatives in the other set. On these two domains, we investigate whether majority voting is the unique way of generating transitive, quasi-transitive, or acyclic social preferences. First of all, we rule out non-standard voting rules by imposing monotonicity, anonymity, and neutrality. Our main results show that majority rule is the unique voting rule satisfying transitivity, yet all other voting rules satisfy acyclicity (also quasi-transitivity on the second domain). Thus we find a very thin border dividing majority and other voting rules, namely, the gap between transitivity and acyclicity.