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Recognizing One-Dimensional Euclidean Preference Profiles

Author

Listed:
  • Vicki Knoblauch

    (University of Connecticut)

Abstract

A preference profile has a one-dimensional Euclidean representation if it can be derived from an arrangement of individuals and alternatives on a line, with each individual preferring the nearer of each pair of alternatives. We provide a polynomial-time algorithm that determines whether a given preference profile has a one-dimensional Euclidean representation and, if so, constructs one. This result has electoral and mechanism design applications.

Suggested Citation

  • Vicki Knoblauch, 2008. "Recognizing One-Dimensional Euclidean Preference Profiles," Working papers 2008-52, University of Connecticut, Department of Economics.
    • Handle: RePEc:uct:uconnp:2008-52
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    2. Smeulders, B., 2018. "Testing a mixture model of single-peaked preferences," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 101-113.
    3. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
    4. 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.
    5. Chambers, Christopher P. & Echenique, Federico, 2020. "Spherical preferences," Journal of Economic Theory, Elsevier, vol. 189(C).
    6. Jiehua Chen & Martin Nollenburg & Sofia Simola & Anais Villedieu & Markus Wallinger, 2022. "Multidimensional Manhattan Preferences," Papers 2201.09691, arXiv.org.
    7. 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.
    8. Bredereck, Robert & Chen, Jiehua & Woeginger, Gerhard J., 2016. "Are there any nicely structured preference profiles nearby?," Mathematical Social Sciences, Elsevier, vol. 79(C), pages 61-73.
    9. Jon Eguia, 2013. "On the spatial representation of preference profiles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 103-128, January.
    10. Eguia, Jon X., 2011. "Foundations of spatial preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 200-205, March.
    11. 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.
    12. 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.
    13. Marie-Louise Lackner & Martin Lackner, 2017. "On the likelihood of single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(4), pages 717-745, April.

    More about this item

    Keywords

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    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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