Stable Aggregation of Preferences

We arrive at new conclusions for social choice theory by considering the process in which we refine decision{theoretic models and account for previously irrelevant parameters of a decision situation (cf. Savage's 'small worlds'). Suppose that, for each individual, we consider a coarse-grained and a fine-grained decision-theoretic model, both of which are consistent with each other in a sense to be defined. We desire any social choice rule to be stable under refinements in the sense that the group choice based on fine-grained individual models and the group choice based on coarse-grained individual models agree for choices among coarse-grained alternatives. For ex ante aggregation, we find that stability is ubiquitous since it follows from independence of irrelevant alternatives. In ex post aggregation, individuals' utilities are pooled separately from their beliefs before the group's choice function is constructed. We find that any 'non-exceptional' rule (e.g., any Pareto optimal rule) for ex post aggregation must be unstable. If the rule is, in addition, independent of irrelevant alternatives, we find an infinite series of reversals of binary group choices. We consider applications to risk management and the theory of consensus formation.