The Instability of Robust Aggregation

We discuss the feasibility of Levi's (1990) robust mode of aggregating individuals' evaluations of acts into a social choice function. We examine 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. We find that any stable robust social choice rule must collapse back into ex ante aggregation. We also provide sufficient conditions, such as Pareto optimality, under which robust aggregation leads to an infinite series of reversals of group choice. For ex ante aggregation, we find that stability is ubiquitous and that it follows from independence of irrelevant alternatives.