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Euclidean preferences

Author

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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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    1. Milyo, Jeffrey, 2000. "A problem with Euclidean preferences in spatial models of politics," Economics Letters, Elsevier, vol. 66(2), pages 179-182, February.
    2. Laslier, Jean-François, 2006. "Spatial Approval Voting," Political Analysis, Cambridge University Press, vol. 14(02), pages 160-185, March.
    3. Bailey, Michael, 2001. "Ideal Point Estimation with a Small Number of Votes: A Random-Effects Approach," Political Analysis, Cambridge University Press, vol. 9(03), pages 192-210, January.
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    5. Steven J. Brams & Michael A. Jones & D. Marc Kilgour, 2002. "Single-Peakedness and Disconnected Coalitions," Journal of Theoretical Politics, , vol. 14(3), pages 359-383, July.
    6. Philippe De Donder, 2000. "Majority voting solution concepts and redistributive taxation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 601-627.
    7. Gevers, L. & Jacquemin, J. C., 1987. "Redistributive taxation, majority decisions and the minmax set," European Economic Review, Elsevier, vol. 31(1-2), pages 202-211.
    8. McKelvey, Richard D., 1976. "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory, Elsevier, vol. 12(3), pages 472-482, June.
    9. Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-157, January.
    10. repec:cup:apsrev:v:57:y:1963:i:02:p:368-377_24 is not 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. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
    3. Vicki Knoblauch, 2008. "Recognizing a Single-Issue Spatial Election," Working papers 2008-26, University of Connecticut, Department of Economics.
    4. Kalandrakis, Tasos, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society.
    5. Eguia, Jon X., 2011. "Foundations of spatial preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 200-205, March.
    6. Greco, Salvatore & Ishizaka, Alessio & Resce, Giuliano & Torrisi, Gianpiero, 2017. "Measuring well-being by a multidimensional spatial model in OECD Better Life Index framework," MPRA Paper 83526, University Library of Munich, Germany.
    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. Knoblauch, Vicki, 2010. "Recognizing one-dimensional Euclidean preference profiles," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 1-5, January.
    9. 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).
    10. 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.

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