The instability of robust aggregation (Q1762857)

The paper addresses the issue of aggregating individual expected utilities into a social choice function. It starts from the aggregation framework proposed by Levi that considers not only the individuals' actual evaluations, but also the so-called empathetic evaluations. Empathetic evaluations are evaluation that real individuals would have, if they were to keep their own utilities but adopted another individual's probabilities, or conversely. Startling from this point and shows that robust aggregation can lead to preference reversals in the social choice when the same decision situation is described in different degrees of detail, thus violating a desirable stability condition. The paper shows also that any stable robust social rule must collapse into the ex ante mode without recourse to hypothetical individuals. Moreover, under sufficient conditions such as Pareto strong optimality, it is shown that robust aggregation leads even to an infinite series of reversals in group choices, while stability is ubiquitous in the standard ex ante mode and is closely related to independence of irrelevant alternatives.