A counterexample to Dhillon (1998)

In an important paper, Amrita Dhillon [3] provided a multi-profile version of Harsanyi’s [5] single-profile theorem on utilitarianism. Like Harsanyi, she assumed that the social alternatives are lotteries. Individuals’ preferences satisfy the von Neumann-Morgenstern (vN-M) axioms, and have thus an expected utility representation. A social welfare function maps profiles of individuals’ preferences into society’s preference. Society’s preference also satisfies the vN-M axioms. Harsanyi [5] showed that for every preference profile for which the social welfare function satisfies the Pareto axiom society’s preferences can be represented by a weighted sum of individuals’ utility functions. Harsanyi’s result did not, however, provide any connection between the weights at different profiles of individuals’ preferences. The Pareto axiom is a single-profile axiom, and does not imply any constraints across different preference profiles.