Single-plateaued choice

Single-plateaued preferences generalize single-peaked preferences by allowing for multiple best elements. These preferences have played an important role in areas such as voting, strategy-proofness and matching problems. We examine the notion of single-plateauedness in a choice-theoretic setting. Single-plateaued choice is characterized by means of a collinear interval continuity property in the presence of independence of irrelevant alternatives. Further results establish that our notion of single-plateauedness conforms to the motivation underlying the term and we analyze the consequences of alternative continuity properties. The importance of basic assumptions such as closedness and convexity is discussed.