Belief-weighted Nash aggregation of Savage preferences

Abstract

The 'belief-weighted Nash social welfare functions' are methods for aggregating Savage preferences defined over a set of acts. Each such method works as follows. Fix a 0-normalized subjective expected utility representation of every possible preference and assign a vector of individual weights to each profile of beliefs. To compute the social preference at a given preference profile, rank the acts according to the weighted product of the individual 0-normalized subjective expected utilities they yield, where the weights are those associated with the belief profile generated by the preference profile. We show that these social welfare functions are characterized by the weak Pareto principle, a continuity axiom, and the following informational robustness property : the social ranking of two acts is unaffected by the addition of any outcome that every individual deems at least as good as the one she originally found worst. This makes the belief-weighted Nash social welfare functions appealing in contexts where the 'best' relevant outcome for an individual is difficult to identify.