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An axiomatic characterization of the Borda mean rule

Author

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  • Florian Brandl

    (Technical University of Munich)

  • Dominik Peters

    (University of Oxford)

Abstract

A social dichotomy function maps a collection of weak orders to a set of dichotomous weak orders. Every dichotomous weak order partitions the set of alternatives into approved alternatives and disapproved alternatives. The Borda mean rule returns all dichotomous weak orders that approve all alternatives with above-average Borda score and disapprove alternatives with below-average Borda score. We show that the Borda mean rule is the unique social dichotomy function satisfying neutrality, reinforcement, faithfulness, and the quasi-Condorcet property. Our result holds for all domains of weak orders that are sufficiently rich, including the domain of all linear orders and the domain of all weak orders.

Suggested Citation

  • Florian Brandl & Dominik Peters, 2019. "An axiomatic characterization of the Borda mean rule," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 685-707, April.
    • Handle: RePEc:spr:sochwe:v:52:y:2019:i:4:d:10.1007_s00355-018-1167-8
    DOI: 10.1007/s00355-018-1167-8
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    References listed on IDEAS

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    Cited by:

    1. Terzopoulou, Zoi & Endriss, Ulle, 2021. "The Borda class," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 31-40.
    2. Martin Lackner & Jan Maly, 2020. "Approval-Based Shortlisting," Papers 2005.07094, arXiv.org, revised May 2022.

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