Single-Peaked Choice

Single-peaked preferences have played an important role in the literature ever since they were used by black (j polit econ 56:23–34, 1948) to formulate a domain restriction that is sufficient for the exclusion of cycles according to the majority rule. In this paper, we approach single-peakedness from a choice-theoretic perspective. We show that the well-known axiom of independence of irrelevant alternatives (a form of contraction consistency) and a continuity requirement characterize a class of single-peaked choice functions. Moreover, we examine rationalizability and representability of these choice functions.