IDEAS home Printed from https://ideas.repec.org/p/cvs/starer/08-01.html
   My bibliography  Save this paper

The Foundations of Spatial Preferences

Author

Listed:
  • Eguia, Jon X.

Abstract

I provide an axiomatic foundation for the assumption of specific utility functions in a multidimensional spatial model, endogenizing the spatial representation of the set of alternatives. Given a set of objects with multiple attributes, I find simple necessary and sufficient conditions on preferences such that there exists a mapping of the set of objects into a Euclidean space where the utility function of the agent is linear city block, quadratic Euclidean, or more generally, it is the [delta] power of one of Minkowski (1886) metric functions. In a society with multiple agents I characterize the set of preferences that are representable by weighted linear city block utility functions, and I discuss how the result extends to other Minkowski utility functions.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Eguia, Jon X., 2008. "The Foundations of Spatial Preferences," Working Papers 08-01, C.V. Starr Center for Applied Economics, New York University.
  • Handle: RePEc:cvs:starer:08-01
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Martin J. Osborne, 1995. "Spatial Models of Political Competition under Plurality Rule: A Survey of Some Explanations of the Number of Candidates and the Positions They Take," Canadian Journal of Economics, Canadian Economics Association, vol. 28(2), pages 261-301, May.
    2. Grynaviski, Jeffrey D. & Corrigan, Bryce E., 2006. "Specification Issues in Proximity Models of Candidate Evaluation (with Issue Importance)," Political Analysis, Cambridge University Press, vol. 14(4), pages 393-420, October.
    3. Richard D. McKelvey & Richard E. Wendell, 1976. "Voting Equilibria in Multidimensional Choice Spaces," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 144-158, May.
    4. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    5. Phipps Arabie, 1991. "Was euclid an unnecessarily sophisticated psychologist?," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 567-587, December.
    6. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    7. Richter, Marcel K. & Wong, K.-C.Kam-Chau, 2004. "Concave utility on finite sets," Journal of Economic Theory, Elsevier, vol. 115(2), pages 341-357, April.
    8. McKelvey, Richard D & Schofield, Norman, 1987. "Generalized Symmetry Conditions at a Core Point," Econometrica, Econometric Society, vol. 55(4), pages 923-933, July.
    9. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    10. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
    11. Degan, Arianna & Merlo, Antonio, 2009. "Do voters vote ideologically?," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1868-1894, September.
    12. Marcello D’Agostino & Valentino Dardanoni, 2009. "What’s so special about Euclidean distance?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 211-233, August.
    13. Barbera Salvador & Gul Faruk & Stacchetti Ennio, 1993. "Generalized Median Voter Schemes and Committees," Journal of Economic Theory, Elsevier, vol. 61(2), pages 262-289, December.
    14. ,, 2010. "Rationalizable voting," Theoretical Economics, Econometric Society, vol. 5(1), January.
    15. Bogomolnaia, Anna & Laslier, Jean-Francois, 2007. "Euclidean preferences," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 87-98, February.
    16. Azrieli, Yaron, 2009. "Characterization of multidimensional spatial models of elections with a valence dimension," MPRA Paper 14513, University Library of Munich, Germany.
    17. Westholm, Anders, 1997. "Distance versus Direction: The Illusory Defeat of the Proximity Theory of Electoral Choice," American Political Science Review, Cambridge University Press, vol. 91(4), pages 865-883, December.
    18. Wendell, Richard E & Thorson, Stuart J, 1974. "Some Generalizations of Social Decisions under Majority Rule," Econometrica, Econometric Society, vol. 42(5), pages 893-912, September.
    19. Knoblauch, Vicki, 2010. "Recognizing one-dimensional Euclidean preference profiles," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 1-5, January.
    20. 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.
    21. Norman Schofield, 2007. "The Mean Voter Theorem: Necessary and Sufficient Conditions for Convergent Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 965-980.
    22. 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.
    23. Rae, Douglas & Taylor, Michael, 1971. "Decision Rules and Policy Outcomes," British Journal of Political Science, Cambridge University Press, vol. 1(1), pages 71-90, January.
    24. Berinsky, Adam J. & Lewis, Jeffrey B., 2007. "An Estimate of Risk Aversion in the U.S. Electorate," Quarterly Journal of Political Science, now publishers, vol. 2(2), pages 139-154, May.
    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. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
    2. 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).
    3. Martínez-Mora Francisco & Puy M. Socorro, 2012. "Asymmetric Single-peaked Preferences," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 12(1), pages 1-26, December.
    4. Gershkov, Alex & Moldovanu, Benny & Shi, Xianwen, 2020. "Monotonic norms and orthogonal issues in multidimensional voting," Journal of Economic Theory, Elsevier, vol. 189(C).
    5. Chambers, Christopher P. & Echenique, Federico, 2020. "Spherical preferences," Journal of Economic Theory, Elsevier, vol. 189(C).
    6. Knoblauch, Vicki, 2010. "Recognizing one-dimensional Euclidean preference profiles," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 1-5, January.
    7. Naveen Durvasula, 2022. "Utility-Based Communication Requirements for Stable Matching in Large Markets," Papers 2212.04024, arXiv.org.
    8. Jiehua Chen & Martin Nollenburg & Sofia Simola & Anais Villedieu & Markus Wallinger, 2022. "Multidimensional Manhattan Preferences," Papers 2201.09691, arXiv.org.

    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. 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.
    2. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    3. Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
    4. Azrieli, Yaron, 2011. "Axioms for Euclidean preferences with a valence dimension," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 545-553.
    5. Banks, Jeffrey S. & Duggan, John, 2008. "A Dynamic Model of Democratic Elections in Multidimensional Policy Spaces," Quarterly Journal of Political Science, now publishers, vol. 3(3), pages 269-299, October.
    6. 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.
    7. 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).
    8. Norman Schofield, 1995. "Coalition Politics," Journal of Theoretical Politics, , vol. 7(3), pages 245-281, July.
    9. Norman Schofield, 2007. "Modelling Politics," ICER Working Papers 33-2007, ICER - International Centre for Economic Research.
    10. Itai Sened, 1991. "Contemporary Theory of Institutions in Perspective," Journal of Theoretical Politics, , vol. 3(4), pages 379-402, October.
    11. Bade, Sophie, 2011. "Electoral competition with uncertainty averse parties," Games and Economic Behavior, Elsevier, vol. 72(1), pages 12-29, May.
    12. Norman Schofield, 2013. "The “probability of a fit choice”," Review of Economic Design, Springer;Society for Economic Design, vol. 17(2), pages 129-150, June.
    13. Xefteris, Dimitrios, 2017. "Multidimensional electoral competition between differentiated candidates," Games and Economic Behavior, Elsevier, vol. 105(C), pages 112-121.
    14. Daniel E. Ingberman & Robert P. Inman, 1987. "The Political Economy of Fiscal Policy," NBER Working Papers 2405, National Bureau of Economic Research, Inc.
    15. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
    16. Jacob Bower-Bir & William Bianco & Nicholas D’Amico & Christopher Kam & Itai Sened & Regina Smyth, 2015. "Predicting majority rule: Evaluating the uncovered set and the strong point," Journal of Theoretical Politics, , vol. 27(4), pages 650-672, October.
    17. 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.
    18. 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.
    19. Norman Schofield, 2015. "Climate Change, Collapse and Social Choice Theory," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 9(1), pages 007-035, October.
    20. Tovey, Craig A., 2010. "The almost surely shrinking yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 74-87, January.

    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:cvs:starer:08-01. 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: Anne Stubing (email available below). General contact details of provider: https://edirc.repec.org/data/aenyuus.html .

    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.