  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.
