IDEAS home Printed from https://ideas.repec.org/a/kap/pubcho/v51y1986i3p267-284.html
   My bibliography  Save this article

Existence of a ‘structurally stable’ equilibrium for a non-collegial voting rule

Author

Listed:
  • Norman Schofield

Abstract

This essay shows that, for any non-collegial voting rule, σ, there exists an integer, s(σ), with this property: if the policy space, W, has dimension no greater than s(σ), then there exists a profile of smooth utilities on W, such that the core for σ at this profile is non-empty and ‘structurally stable’ under sufficiently small perturbation. We also show how we may compute s(σ) for an arbitrary rule. This material is based upon work supported by NSF grant SES-84-18296, to the School of Social Sciences, University of California at Irvine. An early draft was written while the author was Sherman Fairchild Distinguished Scholar at the California Institute of Technology. Thanks are due to Kenneth Shepsle, Dick McKelvey and Gary Cox for helpful comments, to Michael Chwe and Shaun Bowler for research assistance, and to Derek Hearl and Ian Budge for permission to make use of unpublished data. Copyright Martinus Nijhoff Publishers 1986

Suggested Citation

  • Norman Schofield, 1986. "Existence of a ‘structurally stable’ equilibrium for a non-collegial voting rule," Public Choice, Springer, vol. 51(3), pages 267-284, January.
    • Handle: RePEc:kap:pubcho:v:51:y:1986:i:3:p:267-284
    DOI: 10.1007/BF00128877
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF00128877
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF00128877?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Linda Cohen & Steven Matthews, 1980. "Constrained Plott Equilibria, Directional Equilibria and Global Cycling Sets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(5), pages 975-986.
    2. Matthews, Steven A, 1982. "Local Simple Games in Public Choice Mechanisms," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(3), pages 623-645, October.
    3. Kenneth Shepsle & Barry Weingast, 1981. "Structure-induced equilibrium and legislative choice," Public Choice, Springer, vol. 37(3), pages 503-519, January.
    4. Greenberg, Joseph, 1979. "Consistent Majority Rules over Compact Sets of Alternatives," Econometrica, Econometric Society, vol. 47(3), pages 627-636, May.
    5. Schofield, Norman, 1980. "Generic properties of simple Bergson-Samuelson welfare functions," Journal of Mathematical Economics, Elsevier, vol. 7(2), pages 175-192, July.
    6. Norman Schofield, 1978. "Instability of Simple Dynamic Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(3), pages 575-594.
    7. Schofield, Norman, 1984. "Social equilibrium and cycles on compact sets," Journal of Economic Theory, Elsevier, vol. 33(1), pages 59-71, June.
    8. Norman Schofield, 1983. "Generic Instability of Majority Rule," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 695-705.
    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. Shepsle, Kenneth A. & Weingast, Barry R., 1984. "Political Solutions to Market Problems," American Political Science Review, Cambridge University Press, vol. 78(2), pages 417-434, June.
    11. McKelvey, Richard D. & Schofield, Norman, 1986. "Structural instability of the core," Journal of Mathematical Economics, Elsevier, vol. 15(3), pages 179-198, June.
    12. Mathew McCubbins & Thomas Schwartz, 1985. "The politics of flatland," Public Choice, Springer, vol. 46(1), pages 45-60, January.
    13. Judith Sloss, 1973. "Stable outcomes in majority rule voting games," Public Choice, Springer, vol. 15(1), pages 19-48, June.
    14. Cohen, Linda, 1979. "Cyclic sets in multidimensional voting models," Journal of Economic Theory, Elsevier, vol. 20(1), pages 1-12, February.
    15. Riker, William H., 1980. "Implications from the Disequilibrium of Majority Rule for the Study of Institutions," American Political Science Review, Cambridge University Press, vol. 74(2), pages 432-446, June.
    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. Piolatto, Amedeo, 2011. "Plurality versus proportional electoral rule: Which is most representative of voters?," European Journal of Political Economy, Elsevier, vol. 27(2), pages 311-327, June.
    2. Piolatto, Amedeo, 2011. "Plurality versus proportional electoral rule: Which is most representative of voters?," European Journal of Political Economy, Elsevier, vol. 27(2), pages 311-327, June.
    3. Carol Mershon & Olga Shvetsova, 2014. "Change in parliamentary party systems and policy outcomes: Hunting the core," Journal of Theoretical Politics, , vol. 26(2), pages 331-351, April.
    4. Michael Laver, 1989. "Party Competition and Party System Change," Journal of Theoretical Politics, , vol. 1(3), pages 301-324, July.
    5. Tanner, Thomas Cole, 1994. "The spatial theory of elections: an analysis of voters' predictive dimensions and recovery of the underlying issue space," ISU General Staff Papers 1994010108000018174, Iowa State University, Department of Economics.

    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. Itai Sened, 1991. "Contemporary Theory of Institutions in Perspective," Journal of Theoretical Politics, , vol. 3(4), pages 379-402, October.
    2. Norman Schofield, 1995. "Coalition Politics," Journal of Theoretical Politics, , vol. 7(3), pages 245-281, July.
    3. Kenneth Shepsle & Barry Weingast, 1981. "Structure-induced equilibrium and legislative choice," Public Choice, Springer, vol. 37(3), pages 503-519, January.
    4. Banks, Jeffrey S., 1995. "Singularity theory and core existence in the spatial model," Journal of Mathematical Economics, Elsevier, vol. 24(6), pages 523-536.
    5. John Carter & David Schap, 1987. "Executive veto, legislative override, and structure-induced equilibrium," Public Choice, Springer, vol. 52(3), pages 227-244, January.
    6. Knudson, Mathew, 2020. "Two candidate competition on differentiated policy sets," Games and Economic Behavior, Elsevier, vol. 121(C), pages 413-434.
    7. Paulo Pereira, 2000. "From Schumpeterian Democracy to Constitutional Democracy," Constitutional Political Economy, Springer, vol. 11(1), pages 69-86, March.
    8. Norman Schofield, 2007. "Modelling Politics," ICER Working Papers 33-2007, ICER - International Centre for Economic Research.
    9. David Austen-Smith & Jeffrey S. Banks, 1999. "Cycling of simple rules in the spatial model," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 663-672.
    10. Hervé Crès & Mich Tvede, 2001. "Proxy fights in incomplete markets: when majority voting and sidepayments are equivalent," Working Papers hal-01065004, HAL.
    11. Daniel E. Ingberman & Robert P. Inman, 1987. "The Political Economy of Fiscal Policy," NBER Working Papers 2405, National Bureau of Economic Research, Inc.
    12. 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.
    13. Thomas Bräuninger, 2007. "Stability in Spatial Voting Games with Restricted Preference Maximizing," Journal of Theoretical Politics, , vol. 19(2), pages 173-191, April.
    14. 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.
    15. repec:hal:spmain:info:hdl:2441/10282 is not listed on IDEAS
    16. De Donder, Philippe & Gallego, Maria, 2017. "Electoral Competition and Party Positioning," TSE Working Papers 17-760, Toulouse School of Economics (TSE).
    17. 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.
    18. 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.
    19. 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.
    20. Hervé Crès & Mich Tvede, 2001. "Proxy fights in incomplete markets: when majority voting and sidepayments are equivalent," SciencePo Working papers Main hal-01065004, HAL.
    21. repec:spo:wpecon:info:hdl:2441/10282 is not listed on IDEAS
    22. Hervé Crès & Mich Tvede, 2001. "Proxy fights in incomplete markets: when majority voting and sidepayments are equivalent," SciencePo Working papers hal-01065004, HAL.

    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:kap:pubcho:v:51:y:1986:i:3:p:267-284. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.