The inconsistency of expected utility theory with certain classes of single-peaked preference functions

Abstract

The "psychophysics of gambling" model, in which a person is assumed to have a single-peaked or monotonic preference function on each of the primary psychological dimensions of a gamble, is compared to the expected utility model for two-outcome gambles. Two theorems are proved, the first of which shows that expected utility (EU) theory is inconsistent with single-peaked preference functions on both skewness and variance, while the second shows that subjectively-expected utility (SEU) theory is inconsistent with single-peaked preference functions on both skewness and range. The applicability of the theorems is discussed and a weak test of SEU theory is made employing the second theorem.