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Additive representations on a simplex

Author

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  • Qin, Wei-Zhi
  • Rommeswinkel, Hendrik

Abstract

We characterize additive representations on subsets of product spaces with an empty interior such as simplexes and certain homeomorphisms thereof. Previously, all additive representation theorems only applied to spaces in which any coordinate can be changed without changing any of the other coordinates. We identify a novel preference condition that is necessary and sufficient for the existence of additive representations. Our results provide, for instance, a characterization of utilitarianism on the Pareto frontier of a cake division problem.

Suggested Citation

  • Qin, Wei-Zhi & Rommeswinkel, Hendrik, 2022. "Additive representations on a simplex," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    • Handle: RePEc:eee:mateco:v:103:y:2022:i:c:s0304406822000957
    DOI: 10.1016/j.jmateco.2022.102769
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    References listed on IDEAS

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    1. Chateauneuf, Alain & Wakker, Peter, 1993. "From local to global additive representation," Journal of Mathematical Economics, Elsevier, vol. 22(6), pages 523-545.
    2. Vind, Karl, 1991. "Independent preferences," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 119-135.
    3. W. M. Gorman, 1968. "The Structure of Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(4), pages 367-390.
    4. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Cho, Wonki Jo & Moreno-Ternero, Juan D., 2024. "On reaching social consent," Journal of Mathematical Economics, Elsevier, vol. 110(C).

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