Subjective expected utility with signed threshold

Abstract

This paper generalizes subjective expected utility by incorporating signed threshold, whose positive (respectively, negative) value enhances (respectively, reduces) subjective expected utility of chosen alternative against unchosen one. It can be interpreted, for example, that positivity of the signed threshold reflects domination of rejoicing feeling against regret feeling. Since the signed threshold representation is a special case of skew-symmetric additive (SSA) representation, we prove that in addition to SSA axiomatization, restriction of probabilistic sophistication to pairs of acts which are regret-free separates subjective expected utility and signed threshold. It is assumed that regret-freeness is measured by monetary differences or ex post strength of preferences.