Relative utilitarianism under uncertainty
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In the context of uncertainty, belief-weighted relative utilitarianism consists in comparing acts according to a weighted sum of the (0, 1) -normalized subjective expected utilities they yield. The weights may change with the profile of beliefs but do not depend upon the profile of individual utilities for the outcomes. This class of social welfare functions is characterized by the Pareto principle, the sure-thing principle, a continuity condition, and an independence condition requiring that the social ranking of two acts is unaffected by the addition of an outcome that leaves everyone’s best and worst outcomes unchanged. The weights must be constant if the social ranking of constant acts is independent of individual beliefs. Anonymity then pins down plain relative utilitarianism: acts are compared according the sum of (0, 1)-normalized subjective expected utilities they generate.
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