The instability of robust aggregation

Levis 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.I wish to thank Christs College, Cambridge and the California Institute of Technology for their generous financial and academic support. I am grateful to three anonymous referees for their helpful comments. I am much indebted to Isaac Levi, Philippe Mongin and Teddy Seidenfeld for their help and encouragement.