Anchored preference relations

This paper explores the implications of a simple and intuitive restriction on reference dependent preferences assuming the status quo serves as the reference point. The condition imposed rules out situations in which a decision maker has a choice between two prospects, selects one, subsequently changes her mind and selects the other – even if the change is costly. It is shown that a surprising number of models in a riskless and risky setting violate this behavioral assumption, including Cumulative Prospect Theory as well as any theory exhibiting local nonsatiation in which all reference dependent indifference surfaces are smooth. It is also shown that one can construct simple alternative models that do satisfy the condition, axiomatically derived or otherwise. These alternative theories take the form of maxmin representations over a set of expected (or Choquet-expected) utility differences, where utility difference is measured between the prospect evaluated and the reference point.