A Theory of Certainty Equivalents for Uncertain Alternatives

Certainty equivalents (CEs) of gambles are assumed to have a ratio scale representation that is strictly increasing in each consequence and the slalus quo is a singular point. A rankand sign-dependent weighted linear representation arises as follows. Gambles with both gains and losses are reduced to the formally equivalent binary alternative with the CEs of the subgambles of gains and of losses as consequences. A plausible and partially sustained, but non-rational, assumption yields a bilinear, non-additive form. Those gambles composed entirely of gains o r entirely of losses are assumed to be rationally edited by subtracting from each consequence the utility of the consequence nearest the status quo and adding that amount to the utility of the modified gamble. A rank-dependent, weighted average representation results in each domain separately. Because data using judged CEs of binary alternatives exhibit a pronounced non-monotonicity at the status quo, a version of the theory is given that takes this into account.