Partial utilitarianism

Mongin (1994) proved a multi-profile version of Harsanyi (1955)'s Aggregation Theorem: within the expected utility model, a social welfare functional mapping profiles of individual utility functions into social preference relations satisfies the Pareto and Independence of Irrelevant Alternatives principles if and only if it is utilitarian. The present paper extends Mongin's analysis by allowing individuals to have incomplete preferences, represented by sets of utility functions. An impossibility theorem is first established: social preferences cannot satisfy all the expected utility axioms, precluding utilitarian aggregation in this extended setting. Adapting the objective vs. subjective rationality approach of Gilboa et al. (2010) to the present social choice settings representation theorems are then obtained by relaxing either the Completeness or the Independence axioms at the social level, yielding two forms of partial utilitarianism