We study stochastic choice as the outcome of deliberate randomization. We derive a general representation of a stochastic choice function where stochasticity allows the agent to achieve from any set the maximal element according to her underlying preferences over lotteries. We show that in this model stochasticity in choice captures complementarity between elements in the set, and thus necessarily implies violations of Regularity/Monotonicity, one of the most common properties of stochastic choice. This feature separates our approach from other models, e.g., Random Utility.

This paper begins by observing that any reflexive binary (preference) relation (over risky prospects) that satisfies the independence axiom admits a form of expected utility representation. We refer to this representation notion as the coalitional minmax expected utility representation. By adding the remaining properties of the expected utility theorem, namely, continuity, completeness, and transitivity, one by one, we find how this representation gets sharper and sharper, thereby deducing the versions of this classical theorem in which any combination of these properties is dropped from its statement. This approach also allows us to weaken transitivity in this theorem, rather than eliminate it entirely, say, to quasitransitivity or acyclicity. Apart from providing a unified dissection of the expected utility theorem, these results are relevant for the growing literature on boundedly rational choice in which revealed preference relations often lack the properties of completeness and/or transitivity (but often satisfy the independence axiom). They are also especially suitable for the (yet overlooked) case in which the decision‐maker is made up of distinct individuals and, consequently, transitivity is routinely violated. Finally, and perhaps more importantly, we show that our representation theorems allow us to answer many economic questions that are posed in terms of nontransitive/incomplete preferences, say, about the maximization of preferences, the existence of Nash equilibrium, the preference for portfolio diversification, and the possibility of the preference reversal phenomenon.

We investigate the classical Anscombe–Aumann model of decision-making under uncertainty without the completeness axiom. We distinguish between the dual traits of “indecisiveness in beliefs” and “indecisiveness in tastes.” The former is captured by the Knightian uncertainty model, the latter by the single-prior expected multi-utility model. We characterize axiomatically the latter model. Then we show that, under independence and continuity, these two models can be jointly characterized by means of a partial completeness property.

This paper develops axiomatically a revealed preference theory of reference-dependent choice behavior. Instead of taking the reference for an agent as exogenously given in the description of a choice problem, we suitably relax the Weak Axiom of Revealed Preference to obtain, endogenously, the existence of reference alternatives as well as the structure of choice behavior conditional on those alternatives. We show how this model captures some well-known choice patterns such as the attraction effect.