Anonymous and Strategy-Proof Voting under Subjective Expected Utility Preferences

We study three axioms in the model of constrained social choice under uncertainty where (i) agents have subjective expected utility preferences over acts and (ii) different states of nature have (possibly) different sets of available outcomes. Anonymity says that agents' names or labels should never play a role in the mechanism used to select the social act. Strategy-proofness requires that reporting one's true preferences be a (weakly) dominant strategy for each agent in the associated direct revelation game. Range unanimity essentially says that a feasible act must be selected by society whenever it is reported as every voter's favorite act within the range of the mechanism. We first show that every social choice function satisfying these three axioms can be factored as a product of voting rules that are either constant or binary (always yielding one of two pre-specified outcomes in each state). We describe four basic types of binary factors: three of these types are novel to this literature and exploit the voters' subjective beliefs. Our characterization result then states that a social choice function is anonymous, strategy-proof and range-unanimous if and only if every binary factor (in its canonical factorization) is of one of these four basic types.