Aggregating preferences cannot be fair

SOMMARIO/ABSTRACT Preferences typically define a partial ordering over outcomes. A number of formalisms like soft constraints and CP-nets exists to specify such partial or-derings. In situations involving multiple agents, we need to combine the preferences of several individuals. In this paper, we consider each agent as voting on whether they prefer one outcome to another. We prove that, under certain conditions on the kind of partial orders that are allowed to express the preferences of the agents and of the result, if there are at least two agents and three outcomes to order, no preference aggregation system can be fair. That is, no preference aggregation system can be free (give any possible result), monotonic (improving a vote for an outcome only ever helps), independent to irrelevant assumptions (the result between two outcomes only depends on how the agents vote on these two outcomes), and non-dictatorial (there is not one agent who is never contradicted). This result generalizes Ar-row's impossibility theorem for combining total orders [1].