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Euclidean preferences

Author

Listed:
  • Anna Bogomolnaia

    (Rice University [Houston])

  • Jean-François Laslier

    (CECO - Laboratoire d'économétrie de l'École polytechnique - X - École polytechnique - CNRS - Centre National de la Recherche Scientifique)

Abstract

This note is devoted to the question: How restrictive is the assumption that preferences be Euclidean in d dimensions. In particular it is proven that a preference profile with I individuals and A alternatives can be represented by Euclidean utilities with d dimensions if and only if d=min(I,A-1). The paper also describes the systems of A points which allow for the representation of any profile over A alternatives, and provides some results when only strict preferences are considered.

Suggested Citation

  • Anna Bogomolnaia & Jean-François Laslier, 2004. "Euclidean preferences," Working Papers hal-00242941, HAL.
    • Handle: RePEc:hal:wpaper:hal-00242941
    Note: View the original document on HAL open archive server: https://hal.science/hal-00242941
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Scott Moser & John W. Patty & Elizabeth Maggie Penn, 2009. "The Structure of Heresthetical Power," Journal of Theoretical Politics, , vol. 21(2), pages 139-159, April.
    2. Vicki Knoblauch, 2008. "Recognizing a Single-Issue Spatial Election," Working papers 2008-26, University of Connecticut, Department of Economics.
    3. Andre Veski & Kaire Põder, 2016. "Strategies in the Tallinn School Choice Mechanism," Research in Economics and Business: Central and Eastern Europe, Tallinn School of Economics and Business Administration, Tallinn University of Technology, vol. 8(1).
    4. Marc Henry & Ismael Mourifié, 2013. "Euclidean Revealed Preferences: Testing The Spatial Voting Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(4), pages 650-666, June.
    5. 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.
    6. Naveen Durvasula, 2022. "Utility-Based Communication Requirements for Stable Matching in Large Markets," Papers 2212.04024, arXiv.org.
    7. ,, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society, vol. 5(1), January.
    8. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
    9. Knoblauch, Vicki, 2010. "Recognizing one-dimensional Euclidean preference profiles," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 1-5, January.
    10. Eckert, Daniel & Klamler, Christian, 2010. "An equity-efficiency trade-off in a geometric approach to committee selection," European Journal of Political Economy, Elsevier, vol. 26(3), pages 386-391, September.
    11. Gonczarowski, Yannai A. & Nisan, Noam & Ostrovsky, Rafail & Rosenbaum, Will, 2019. "A stable marriage requires communication," Games and Economic Behavior, Elsevier, vol. 118(C), pages 626-647.
    12. Eguia, Jon X., 2011. "Foundations of spatial preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 200-205, March.
    13. Josue Ortega & Philipp Hergovich, 2017. "The Strength of Absent Ties: Social Integration via Online Dating," Papers 1709.10478, arXiv.org, revised Sep 2018.
    14. 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.
    15. Greco, Salvatore & Ishizaka, Alessio & Resce, Giuliano & Torrisi, Gianpiero, 2020. "Measuring well-being by a multidimensional spatial model in OECD Better Life Index framework," Socio-Economic Planning Sciences, Elsevier, vol. 70(C).
    16. Chambers, Christopher P. & Echenique, Federico, 2020. "Spherical preferences," Journal of Economic Theory, Elsevier, vol. 189(C).

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