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Euclidean preferences

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  • Bogomolnaia, Anna
  • Laslier, Jean-Francois

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.
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Suggested Citation

  • Bogomolnaia, Anna & Laslier, Jean-Francois, 2007. "Euclidean preferences," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 87-98, February.
    • Handle: RePEc:eee:mateco:v:43:y:2007:i:2:p:87-98
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. 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.
    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. Vicki Knoblauch, 2008. "Recognizing a Single-Issue Spatial Election," Working papers 2008-26, University of Connecticut, Department of Economics.
    5. ,, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society, vol. 5(1), January.
    6. 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).
    7. 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.
    8. Chambers, Christopher P. & Echenique, Federico, 2020. "Spherical preferences," Journal of Economic Theory, Elsevier, vol. 189(C).
    9. Knoblauch, Vicki, 2010. "Recognizing one-dimensional Euclidean preference profiles," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 1-5, January.
    10. Naveen Durvasula, 2022. "Utility-Based Communication Requirements for Stable Matching in Large Markets," Papers 2212.04024, arXiv.org.
    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. 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.
    13. Eguia, Jon X., 2011. "Foundations of spatial preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 200-205, March.
    14. Josue Ortega & Philipp Hergovich, 2017. "The Strength of Absent Ties: Social Integration via Online Dating," Papers 1709.10478, arXiv.org, revised Sep 2018.
    15. 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.
    16. 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.
    17. 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).

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