Preference exclusions for social rationality

I develop sufficient conditions for transitivity and acyclicity of social preferences, continuing the investigation of restricted domains begun by Black (J Polit Econ 56:23–34, 1948; The theory of committees and elections. Cambridge University Press, Cambridge, 1958), Arrow (Social choice and individual values. Wiley, New York, 1951), and Sen (Econometrica 34:491–499, 1966; Rev Econ Stud 36:381–393, 1969). The approach, which excludes certain triples of rankings over triples of alternatives, contributes to the literature in three ways. First, I generalize majority rule to classes of social preference relations defined by their decisiveness properties. Second, I consider not only transitivity of weak and strict social preference, but I provide conditions for acyclic strict preference as well. Third, the well-known conditions of value restriction, single peakedness, and order restriction are shown to satisfy corresponding exclusion conditions, so transitivity results on these domains follow from the more general analysis; in particular, the results are applied to weakly single-peaked preference profiles, and a result on acyclicity due to Austen-Smith and Banks (Positive political theory I. University of Michigan Press, Ann Arbor, 1999) is obtained as a special case. In contrast to the latter authors, the approach fixes a single preference profile and does not rely on the properties of social preferences as individual preferences are varied.