Aggregation for general populations without continuity or completeness

McCarthy, David and Mikkola, Kalle and Thomas, Teruji (2017): Aggregation for general populations without continuity or completeness.

Abstract

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. The addition of weak or strong Pareto has essentially the same implications in the general case as it does in Harsanyi's original setting.

• Item Type: MPRA Paper
• Language: English
• Keywords: Harsanyi's utilitarian theorem; discontinuous preferences; incomplete preferences; infinite populations
• Subjects: D - Microeconomics > D6 - Welfare Economics > D60 - General; D - Microeconomics > D6 - Welfare Economics > D63 - Equity, Justice, Inequality, and Other Normative Criteria and Measurement; D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty

References

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Hausner, M., Wendel, J., 1952. `Ordered vector spaces.' Proceedings of the American Mathematical Society 3, 977-982.

McCarthy, D., Mikkola, K., Thomas, T., 2017a. `Representation of strongly independent preorders by sets of scalar-valued functions.' MPRA Paper No. 79284 https://mpra.ub.uni-muenchen.de/79284/

McCarthy, D., Mikkola, K., Thomas, T., 2017b. `Representation of strongly independent preorders by vector-valued functions.' MPRA Paper No. 80806. https://mpra.ub.uni-muenchen.de/80806/