IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v43y2007i2p87-98.html
   My bibliography  Save this article

Euclidean preferences

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4068(06)00111-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bailey, Michael, 2001. "Ideal Point Estimation with a Small Number of Votes: A Random-Effects Approach," Political Analysis, Cambridge University Press, vol. 9(3), pages 192-210, January.
    2. 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.
    3. Stokes, Donald E., 1963. "Spatial Models of Party Competition," American Political Science Review, Cambridge University Press, vol. 57(2), pages 368-377, June.
    4. Rabinowitz, George & Macdonald, Stuart Elaine, 1989. "A Directional Theory of Issue Voting," American Political Science Review, Cambridge University Press, vol. 83(1), pages 93-121, March.
    5. 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.
    6. Milyo, Jeffrey, 2000. "A problem with Euclidean preferences in spatial models of politics," Economics Letters, Elsevier, vol. 66(2), pages 179-182, February.
    7. Laslier, Jean-François, 2006. "Spatial Approval Voting," Political Analysis, Cambridge University Press, vol. 14(2), pages 160-185, April.
    8. 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.
    9. 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.
    10. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    4. 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.
    5. Eguia, Jon X., 2011. "Foundations of spatial preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 200-205, March.
    6. Chambers, Christopher P. & Echenique, Federico, 2020. "Spherical preferences," Journal of Economic Theory, Elsevier, vol. 189(C).
    7. Knoblauch, Vicki, 2010. "Recognizing one-dimensional Euclidean preference profiles," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 1-5, January.
    8. 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.
    9. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
    10. 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).
    11. Vicki Knoblauch, 2008. "Recognizing a Single-Issue Spatial Election," Working papers 2008-26, University of Connecticut, Department of Economics.
    12. Naveen Durvasula, 2022. "Utility-Based Communication Requirements for Stable Matching in Large Markets," Papers 2212.04024, arXiv.org.
    13. ,, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society, vol. 5(1), January.
    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. 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).
    16. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. John Jackson, 2014. "Location, location, location: the Davis-Hinich model of electoral competition," Public Choice, Springer, vol. 159(1), pages 197-218, April.
    2. Zakharov Alexei, 2005. "Candidate location and endogenous valence," EERC Working Paper Series 05-17e, EERC Research Network, Russia and CIS.
    3. Fabian Gouret & Guillaume Hollard & Stéphane Rossignol, 2011. "An empirical analysis of valence in electoral competition," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(2), pages 309-340, July.
    4. Zakharov, Alexei & Fantazzini, Dean, 2009. "Economic Factors in a Model of Voting: The Case of The Netherlands, Great Britain, and Israel," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 14(2), pages 57-73.
    5. Canegrati, Emanuele, 2006. "Yardstick competition: a spatial voting model approach," MPRA Paper 1017, University Library of Munich, Germany.
    6. Daniel E. Ingberman & Robert P. Inman, 1987. "The Political Economy of Fiscal Policy," NBER Working Papers 2405, National Bureau of Economic Research, Inc.
    7. Martínez-Mora, Francisco & Puy, M. Socorro, 2014. "The determinants and electoral consequences of asymmetric preferences," European Journal of Political Economy, Elsevier, vol. 33(C), pages 85-97.
    8. Thomas Bräuninger, 2007. "Stability in Spatial Voting Games with Restricted Preference Maximizing," Journal of Theoretical Politics, , vol. 19(2), pages 173-191, April.
    9. Nicholas R. Miller, 2015. "The spatial model of social choice and voting," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 10, pages 163-181, Edward Elgar Publishing.
    10. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2020. "Arrow on domain conditions: a fruitful road to travel," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 237-258, March.
    11. Sauermann, Jan & Schwaninger, Manuel & Kittel, Bernhard, 2022. "Making and breaking coalitions: Strategic sophistication and prosociality in majority decisions," European Journal of Political Economy, Elsevier, vol. 71(C).
    12. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    13. Philippe De Donder & Jean Hindriks, 1998. "The political economy of targeting," Public Choice, Springer, vol. 95(1), pages 177-200, April.
    14. Arianna Degan, 2003. "A Dynamic Model of Voting," PIER Working Paper Archive 04-015, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 May 2004.
    15. Eguia, Jon X., 2011. "Foundations of spatial preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 200-205, March.
    16. De Donder, Philippe & Gallego, Maria, 2017. "Electoral Competition and Party Positioning," TSE Working Papers 17-760, Toulouse School of Economics (TSE).
    17. David Koehler, 2001. "Instability and Convergence Under Simple-Majority Rule: Results from Simulation of Committee Choice in Two-Dimensional Space," Theory and Decision, Springer, vol. 50(4), pages 305-332, June.
    18. Kenneth Koford, 1982. "Why so much stability? An optimistic view of the possibility of rational legislative decisionmaking," Public Choice, Springer, vol. 38(1), pages 3-19, March.
    19. Borissov, Kirill & Pakhnin, Mikhail & Puppe, Clemens, 2017. "On discounting and voting in a simple growth model," European Economic Review, Elsevier, vol. 94(C), pages 185-204.
    20. Mathieu Martin & Zéphirin Nganmeni & Ashley Piggins & Élise F. Tchouante, 2022. "Pure-strategy Nash equilibrium in the spatial model with valence: existence and characterization," Public Choice, Springer, vol. 190(3), pages 301-316, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:43:y:2007:i:2:p:87-98. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.