A subjective spin on roulette wheels

We provide a simple behavioral definition of 'subjective mixture' of acts for a large class of (not necessarily expected-utility) preferences. Subjective mixtures enjoy the same algebraic properties as the 'objective mixtures' used to great advantage in the decision setting introduced by Anscombe and Aumann (1963). This makes it possible to formulate mixture-space axioms in a fully subjective setting. For illustration, we present simple subjective axiomatizations of some models of choice under uncertainty, including Bewley's model of choice with incomplete preferences (2002).