Anchored Preference Relations

This paper axiomatically explores minimal conditions under which reference dependent preferences over risky prospects are normatively admissible. It is shown that two simple and intuitive conditions are sufficient to place strong requirements over such preferences. The first condition is tantamount to ‘no-cycling ’ when the reference point is the status quo; the second condition requires the reference dependent representations to be continuous with respect to the reference point. In particular, these conditions rule out Cumulative Prospect Theory as well as any theory in which all reference dependent indifference surfaces are smooth – the latter case also holds for risk-less theories of the endowment effect (e.g., Tversky and Kahneman (1991)). It is also shown that one can construct satisfactory alternatives, axiomatically derived or otherwise, to Cumulative Prospect Theory as well as Tversky and Kahneman’s (1991) theory of the risk-less endowment effect. The alternative theories I propose take the form of max-min representations over a set of expected (or Choquet-expected) utility differences, where utility difference is measured between the prospect evaluated and the reference point.