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Aggregation for potentially infinite populations without continuity or completeness

Author

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  • David McCarthy

    (Department of Philosophy, University of Hong Kong)

  • Kalle Mikkola

    (Department of Mathematics and Systems Analysis, Aalto University)

  • Teruji Thomas

    (Global Priorities Institute, University of Oxford)

Abstract

We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown to be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling.

Suggested Citation

  • David McCarthy & Kalle Mikkola & Teruji Thomas, 2019. "Aggregation for potentially infinite populations without continuity or completeness," Papers 1911.00872, arXiv.org.
  • Handle: RePEc:arx:papers:1911.00872
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    1. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.
    2. Eric Danan, 2021. "Partial utilitarianism," Working Papers hal-03327900, HAL.

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