Expected utility, independence, and continuity

In this paper, we examine some characterizing implications of the expected utility model with a particular focus on independence and continuity. Many well documented choice anomalies under risk (e.g., the common consequence and ratio effects) show that even weaker forms of independence can be violated by experimental subjects. We demonstrate that these violations have a close relation when continuity holds, but their connection becomes less pronounced when continuity is dropped. We show that while retaining the independence axiom, replacing continuity with two intuitive conditions, substitution and monotonicity, can characterize the expected utility model. In this case, weakening the independence axiom can still yield an expected utility, but in a weaker sense implying that our axiomatization is tight