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A family of condorcet domains that are single-peaked on a circle

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  • Arkadii Slinko

    (The University of Auckland)

Abstract

Fishburn’s alternating scheme domains occupy a special place in the theory of Condorcet domains. Karpov (2023) generalised these domains and made an interesting observation proving that all of them are single-peaked on a circle. However, an important point that all generalised Fishburn domains are maximal Condorcet domain remained unproved. We fill this gap and suggest a new combinatorial interpretation of generalised Fishburn’s domains which provide a constructive proof of single-peakedness of these domains on a circle. We show that classical single-peaked domains and single-dipped domains as well as Fishburn’s alternating scheme domains belong to this family of domains while single-crossing domains do not.

Suggested Citation

  • Arkadii Slinko, 2024. "A family of condorcet domains that are single-peaked on a circle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 57-67, August.
    • Handle: RePEc:spr:sochwe:v:63:y:2024:i:1:d:10.1007_s00355-024-01520-7
    DOI: 10.1007/s00355-024-01520-7
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    References listed on IDEAS

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    1. Puppe, Clemens, 2018. "The single-peaked domain revisited: A simple global characterization," Journal of Economic Theory, Elsevier, vol. 176(C), pages 55-80.
    2. Ádám Galambos & Victor Reiner, 2008. "Acyclic sets of linear orders via the Bruhat orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 245-264, February.
    3. Peter Fishburn, 1996. "Acyclic sets of linear orders," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 14(1), pages 113-124.
    4. Alexander Karpov, 2023. "Preferences over Mixed Manna," Springer Optimization and Its Applications, in: Boris Goldengorin & Sergei Kuznetsov (ed.), Data Analysis and Optimization, pages 169-178, Springer.
    5. Slinko, Arkadii & Wu, Qinggong & Wu, Xingye, 2021. "A characterization of preference domains that are single-crossing and maximal Condorcet," Economics Letters, Elsevier, vol. 204(C).
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