This paper takes choice theory to risk or uncertainty. Well-known decision models are axiomatized under the premise that agents can randomize. Under a reversal of order assumption, this convexifies choice sets, and even after imposing the weak axiom of revealed preference and nonemptiness of...

Preferences may arise from regret, i.e., from comparisons with alternatives forgone by the decision maker. When each outcome in a random variable is compared with the parallel outcome in an alternative random variable, regret preferences are transitive iff they are expected utility. In this...