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A simple construction of complete single-peaked domains by recursive tiling

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  • Ping Zhan

    (Edogawa University)

Abstract

Single-peakedness was introduced by Black (J Political Econ 56:23–34, 1948) as a sufficient condition to overcome Condorcet paradox. Since then it has been attracting interest from researchers in various fields. In this paper, we propose a simple recursive procedure of constructing complete single-peaked domains of tiling type explicitly for any finite alternative sets, by combining two results published in recent years, and some observations of known results and examples by the author. The underlying basic structure of tiling type and properties of single-peaked domains provided here give a good visualization and make further developments on single-peakedness more easy.

Suggested Citation

  • Ping Zhan, 2019. "A simple construction of complete single-peaked domains by recursive tiling," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 90(3), pages 477-488, December.
    • Handle: RePEc:spr:mathme:v:90:y:2019:i:3:d:10.1007_s00186-019-00685-7
    DOI: 10.1007/s00186-019-00685-7
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    References listed on IDEAS

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    1. Bernard Monjardet, 2009. "Acyclic Domains of Linear Orders: A Survey," Studies in Choice and Welfare, in: Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), The Mathematics of Preference, Choice and Order, pages 139-160, Springer.
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    3. Gopakumar Achuthankutty & Souvik Roy, 2018. "On single-peaked domains and min–max rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 753-772, December.
    4. Steven J. Brams & William V. Gehrlein & Fred S. Roberts (ed.), 2009. "The Mathematics of Preference, Choice and Order," Studies in Choice and Welfare, Springer, number 978-3-540-79128-7, December.
    5. Moulin, Hervé, 2017. "One dimensional mechanism design," Theoretical Economics, Econometric Society, vol. 12(2), May.
    6. Ernesto Savaglio & Stefano Vannucci, 2019. "Strategy-proof aggregation rules and single peakedness in bounded distributive lattices," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 295-327, February.
    7. Bade, Sophie, 2019. "Matching with single-peaked preferences," Journal of Economic Theory, Elsevier, vol. 180(C), pages 81-99.
    8. 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.
    9. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
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    Cited by:

    1. Alexander Karpov, 2020. "The likelihood of single-peaked preferences under classic and new probability distribution assumptions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 629-644, December.
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    3. Yoshio Sano & Ping Zhan, 2021. "Extended Random Assignment Mechanisms on a Family of Good Sets," SN Operations Research Forum, Springer, vol. 2(4), pages 1-30, December.

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