Anchored preference relations

This note 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 potentially rules out situations in which a decision maker has a choice between two prospects, selects one which subsequently becomes the new reference point, and then regrets her initial choice. 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 non-satiation in which all reference-dependent indifference surfaces are smooth. It is also shown that the condition does admit a class of non-trivial reference-dependent preferences.