The instability of robust aggregation

Abstract

Levi's 'robust aggregation' suggests a generalization of the standard 'ex ante' mode of aggregating individuals' expected utilities into a social choice function. This generalization applies some social choice rule not only to the actual individuals but also to hypothetical individuals with all possible combinations of the actual individuals' probabilities and utilities. We show that robust aggregation can lead to preference reversals in the social choice when the very same decision situation is described with different degrees of detail, thus violating a desirable stability condition. We also show that any stable robust social choice rule must collapse back into the ex ante mode without recourse to hypothetical individuals. Under sufficient conditions, such as strong Pareto optimality, robust aggregation even leads to an infinite series of reversals in group choices. By contrast, stability is ubiquitous in the standard ex ante mode and is closely related to independence of irrelevant alternatives.

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