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The one-dimensional Euclidean domain: finitely many obstructions are not enough

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  • Jiehua Chen

    (TU Berlin)

  • Kirk R. Pruhs

    (University of Pittsburgh)

  • Gerhard J. Woeginger

    (TU Eindhoven)

Abstract

We show that one-dimensional Euclidean preference profiles can not be characterized in terms of finitely many forbidden substructures. This result is in strong contrast to the case of single-peaked and single-crossing preference profiles, for which such finite characterizations have been derived in the literature.

Suggested Citation

  • Jiehua Chen & Kirk R. Pruhs & Gerhard J. Woeginger, 2017. "The one-dimensional Euclidean domain: finitely many obstructions are not enough," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 409-432, February.
    • Handle: RePEc:spr:sochwe:v:48:y:2017:i:2:d:10.1007_s00355-016-1011-y
    DOI: 10.1007/s00355-016-1011-y
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    Cited by:

    1. Edith Elkind & Piotr Faliszewski & Piotr Skowron, 2020. "A characterization of the single-peaked single-crossing domain," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(1), pages 167-181, January.
    2. Jiehua Chen & Martin Nollenburg & Sofia Simola & Anais Villedieu & Markus Wallinger, 2022. "Multidimensional Manhattan Preferences," Papers 2201.09691, arXiv.org.
    3. Jiehua Chen & Sven Grottke, 2021. "Small one-dimensional Euclidean preference profiles," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 117-144, July.
    4. Bruno Escoffier & Olivier Spanjaard & Magdaléna Tydrichová, 2024. "Euclidean preferences in the plane under $$\varvec{\ell _1},$$ ℓ 1 , $$\varvec{\ell _2}$$ ℓ 2 and $$\varvec{\ell _\infty }$$ ℓ ∞ norms," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 63(1), pages 125-169, August.

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