We generalize Harsanyi's social aggregation theorem. We allow the population to be infinite,
and merely assume that individual and social preferences are given by strongly independent
preorders on a convex set of arbitrary dimension. Thus we assume neither completeness
nor any form of continuity. Under Pareto indifference, the conclusion of Harsanyi's theorem
nevertheless holds almost entirely unchanged when utility values are taken to be vectors
in a product of lexicographic function spaces. T…

Read moreWe generalize Harsanyi's social aggregation theorem. We allow the population to be infinite,
and merely assume that individual and social preferences are given by strongly independent
preorders on a convex set of arbitrary dimension. Thus we assume neither completeness
nor any form of continuity. Under Pareto indifference, the conclusion of Harsanyi's theorem
nevertheless holds almost entirely unchanged when utility values are taken to be vectors
in a product of lexicographic function spaces. The addition of weak or strong Pareto has
essentially the same implications in the general case as it does in Harsanyi's original setting.