[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v59y2010i1p88-101.html
   My bibliography  Save this article

A critique of distributional analysis in the spatial model

Author

Listed:
  • Tovey, Craig A.
Abstract
Distributional analysis is widely used to study social choice in Euclidean models ([35], [36], [1], [5], [11], [19], [7] and [4], e.g). This method assumes a continuum of voters distributed according to a probability measure. Since infinite populations do not exist, the goal of distributional analysis is to give an insight into the behavior of large finite populations. However, the properties of finite populations do not necessarily converge to the properties of infinite populations. Thus the method of distributional analysis is flawed. In some cases (Arrow, 1969) it will predict that a point is in the core with probability 1, while the true probability converges to 0. In other cases it can be combined with probabilistic analysis to make accurate predictions about the asymptotic behavior of large populations, as in Caplin and Nalebuff (1988). Uniform convergence of empirical measures (Pollard, 1984) is employed here to yield a simpler, more general proof of [alpha]-majority convergence, a short proof of yolk shrinkage, and suggests a rule of thumb to determine the accuracy of distribution-based predictions. The results also help clarify the mathematical underpinnings of statistical analysis of empirical voting data.

Suggested Citation

  • Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
    • Handle: RePEc:eee:matsoc:v:59:y:2010:i:1:p:88-101
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-4896(09)00084-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    References listed on IDEAS

    as
    1. 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.
    2. Norman Schofield, 1983. "Generic Instability of Majority Rule," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 695-705.
    3. 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.
    4. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
    5. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    6. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    7. 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.
    8. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    9. Tovey, Craig A., 2010. "The almost surely shrinking yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 74-87, January.
    10. Demange, Gabrielle, 1982. "A limit theorem on the minmax set," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 145-164, January.
    11. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2006. "Social choice and electoral competition in the general spatial model," Journal of Economic Theory, Elsevier, vol. 126(1), pages 194-234, January.
    12. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    13. Gordon Tullock, 1981. "Why so much stability," Public Choice, Springer, vol. 37(2), pages 189-204, January.
    14. Gordon Tullock, 1967. "The General Irrelevance of the General Impossibility Theorem," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 81(2), pages 256-270.
    15. Norman Schofield, 1978. "Instability of Simple Dynamic Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(3), pages 575-594.
    16. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    17. Schofield, N. & Tovey, C.A., 1992. "Probability and Convergence for Supramajority rule with Euclidean Preferences," Papers 163, Washington St. Louis - School of Business and Political Economy.
    18. Davis, Otto A. & Hinich, Melvin J. & Ordeshook, Peter C., 1970. "An Expository Development of a Mathematical Model of the Electoral Process," American Political Science Review, Cambridge University Press, vol. 64(2), pages 426-448, June.
    19. 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. Sadiraj, Vjollca & Tuinstra, Jan & van Winden, Frans, 2010. "Identification of voters with interest groups improves the electoral chances of the challenger," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 210-216, November.
    2. Tasos Kalandrakis, 2022. "Generalized medians and a political center," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 58(2), pages 301-319, February.
    3. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    4. McKelvey, Richard & Tovey, Craig A., 2010. "Approximation of the yolk by the LP yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 102-109, January.
    5. Tovey, Craig A., 2010. "The almost surely shrinking yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 74-87, January.
    6. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2019. "Dominance in Spatial Voting with Imprecise Ideals: A New Characterization of the Yolk," THEMA Working Papers 2019-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    7. Crès, Hervé & Utku Ünver, M., 2017. "Toward a 50%-majority equilibrium when voters are symmetrically distributed," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 145-149.

    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. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    2. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2021. "Dominance in spatial voting with imprecise ideals," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 181-195, July.
    3. Tovey, Craig A., 2010. "The almost surely shrinking yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 74-87, January.
    4. Crès, Hervé & Utku Ünver, M., 2017. "Toward a 50%-majority equilibrium when voters are symmetrically distributed," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 145-149.
    5. Pierre-Guillaume Méon, 2006. "Majority voting with stochastic preferences: The whims of a committee are smaller than the whims of its members," Constitutional Political Economy, Springer, vol. 17(3), pages 207-216, September.
    6. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2006. "Social choice and electoral competition in the general spatial model," Journal of Economic Theory, Elsevier, vol. 126(1), pages 194-234, January.
    7. 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.
    8. 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.
    9. Larry Samuelson, 1987. "A test of the revealed-preference phenomenon in congressional elections," Public Choice, Springer, vol. 54(2), pages 141-169, January.
    10. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2019. "Dominance in Spatial Voting with Imprecise Ideals: A New Characterization of the Yolk," THEMA Working Papers 2019-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    11. Edward Wesep, 2012. "Defensive Politics," Public Choice, Springer, vol. 151(3), pages 425-444, June.
    12. 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.
    13. Itai Sened, 1991. "Contemporary Theory of Institutions in Perspective," Journal of Theoretical Politics, , vol. 3(4), pages 379-402, October.
    14. Hervé Crès & Mich Tvede, 2001. "Proxy fights in incomplete markets: when majority voting and sidepayments are equivalent," Working Papers hal-01065004, HAL.
    15. Daniel E. Ingberman & Robert P. Inman, 1987. "The Political Economy of Fiscal Policy," NBER Working Papers 2405, National Bureau of Economic Research, Inc.
    16. Thomas Bräuninger, 2007. "Stability in Spatial Voting Games with Restricted Preference Maximizing," Journal of Theoretical Politics, , vol. 19(2), pages 173-191, April.
    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. Eguia, Jon X., 2011. "Foundations of spatial preferences," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 200-205, March.
    19. repec:hal:spmain:info:hdl:2441/10282 is not listed on IDEAS
    20. De Donder, Philippe & Gallego, Maria, 2017. "Electoral Competition and Party Positioning," TSE Working Papers 17-760, Toulouse School of Economics (TSE).
    21. Kenneth Shepsle & Barry Weingast, 2012. "Why so much stability? Majority voting, legislative institutions, and Gordon Tullock," Public Choice, Springer, vol. 152(1), pages 83-95, July.

    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:matsoc:v:59:y:2010:i:1:p:88-101. 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/inca/505565 .

    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.