Cyclically Mixed Preferences—A Necessary and Sufficient Condition for Transitivity of the Social Preference Relation

Abstract

In a series of papers several authors have given both sufficient and necessary and sufficient conditions for transitivity of the social preference relation under the simple majority decision rule. The aim of this paper is not only to introduce a new necessary and sufficient condition for transitivity of the social relation, but also to establish the connection between this condition of ‘cyclically mixed preferences’ and the well known conditions of ‘extremal restriction’, ‘value restriction’, ‘limited agreement’, and ‘dichotomous preferences’. While the latter conditions rule out the joint occurrence of certain individual preference orderings our condition excludes no individual ranking.