On the Predictions of Cumulative Prospect Theory for Third and Fourth Order Preferences

This is the first paper to provide a comprehensive theoretical analysis of the third and fourth order lottery preferences implied by cumulative prospect theory (CPT). We consider the lottery choices from three alternative reference points: the status quo, the expected payout and the MaxMin. We report a large number of new results given the standard assumptions about probability weighting. We demonstrate, for example, the general result that from the status quo reference point there is no third order reflection effect but there is a fourth order reflection effect. When the average payout or the MaxMin is the reference point, we lose generality but can demonstrate that representative individuals with power value functions can make prudent or imprudent, temperate or intemperate choices depending on the precise magnitude of lottery payoffs. In addition to this, we show that these representative CPT individuals can exhibit some surprising combinations of second with third and fourth order risk attitudes. Throughout the paper, we contrast our theoretical predictions with results reported in the literature and we are able to reconcile some conflicting evidence on higher order risk preferences.