IDEAS home Printed from https://ideas.repec.org/p/wop/safiwp/98-08-072.html
   My bibliography  Save this paper

Abstention Causes Bifurcations in Two-Party Voting Dynamics

Author

Listed:
  • Bärbel M. R. Stadler

Abstract

In a recent dynamical systems model of platform adaptation in spatial voting models, Miller and Stadler showed that, assuming concave voter utility functions and complete participation, there is a globally stable equilibrium located at the mean voter position. Here we show that abstention depending on the distances between voters and platforms may lead to bifurcations rendering the mean voter equilibrium unstable. We find up to seven equilibria, up to four of which are local attractors for the platform dynamics.

Suggested Citation

  • Bärbel M. R. Stadler, 1998. "Abstention Causes Bifurcations in Two-Party Voting Dynamics," Working Papers 98-08-072, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:98-08-072
    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.

    References listed on IDEAS

    as
    1. Kramer, Gerald H, 1973. "On a Class of Equilibrium Conditions for Majority Rule," Econometrica, Econometric Society, vol. 41(2), pages 285-297, March.
    2. Enelow,James M. & Hinich,Melvin J., 1984. "The Spatial Theory of Voting," Cambridge Books, Cambridge University Press, number 9780521275156.
    3. Axelrod, Robert, 1986. "An Evolutionary Approach to Norms," American Political Science Review, Cambridge University Press, vol. 80(4), pages 1095-1111, December.
    4. Axelrod, Robert & Bennett, D. Scott, 1993. "A Landscape Theory of Aggregation," British Journal of Political Science, Cambridge University Press, vol. 23(2), pages 211-233, April.
    5. John S. Irons, 1997. "Voter Turnout, Ideological Candidates, and Platforms Setting with Non-Quadratic Preferences," Research in Economics 97-06-053e, Santa Fe Institute.
    6. Coughlin, Peter & Nitzan, Shmuel, 1981. "Directional and local electoral equilibria with probabilistic voting," Journal of Economic Theory, Elsevier, vol. 24(2), pages 226-239, April.
    7. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135-135.
    8. A. Smithies, 1941. "Optimum Location in Spatial Competition," Journal of Political Economy, University of Chicago Press, vol. 49, pages 423-423.
    9. Kollman, Ken & Miller, John H. & Page, Scott E., 1998. "Political Parties and Electoral Landscapes," British Journal of Political Science, Cambridge University Press, vol. 28(1), pages 139-158, January.
    10. Larry Samuelson, 1984. "Electoral equilibria with restricted strategies," Public Choice, Springer, vol. 43(3), pages 307-327, January.
    11. Kollman, Ken & Miller, John H. & Page, Scott E., 1997. "Landscape formation in a spatial voting model," Economics Letters, Elsevier, vol. 55(1), pages 121-130, August.
    12. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    13. McKelvey, Richard D. & Ordeshook, Peter C., 1976. "Symmetric Spatial Games Without Majority Rule Equilibria," American Political Science Review, Cambridge University Press, vol. 70(4), pages 1172-1184, December.
    14. 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.
    15. Kollman, Ken & Miller, John H. & Page, Scott E., 1992. "Adaptive Parties in Spatial Elections," American Political Science Review, Cambridge University Press, vol. 86(4), pages 929-937, December.
    16. Miller, J. H. & Stadler, P. F., 1998. "The dynamics of locally adaptive parties under spatial voting," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 171-189, September.
    Full references (including those not matched with items on IDEAS)

    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. Baerbel M. R. Stadler, 2000. "Abstention in Dynamical Models of Spatial Voting," Working Papers 00-07-040, Santa Fe Institute.
    2. 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.
    3. Scott de Marchi, 1999. "Adaptive Models and Electoral Instability," Journal of Theoretical Politics, , vol. 11(3), pages 393-419, July.
    4. Larry Samuelson, 1987. "A test of the revealed-preference phenomenon in congressional elections," Public Choice, Springer, vol. 54(2), pages 141-169, January.
    5. Kirchgassner, Gebhard, 2000. "Probabilistic Voting and Equilibrium: An Impossibility Result," Public Choice, Springer, vol. 103(1-2), pages 35-48, April.
    6. Thomas Bräuninger, 2007. "Stability in Spatial Voting Games with Restricted Preference Maximizing," Journal of Theoretical Politics, , vol. 19(2), pages 173-191, April.
    7. Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
    8. Sacha Bourgeois-Gironde & João V. Ferreira, 2020. "Conflicted voters: A spatial voting model with multiple party identifications," Post-Print hal-02909682, HAL.
    9. Edward Wesep, 2012. "Defensive Politics," Public Choice, Springer, vol. 151(3), pages 425-444, June.
    10. Alan E. Wiseman, 2006. "A Theory of Partisan Support and Entry Deterrence in Electoral Competition," Journal of Theoretical Politics, , vol. 18(2), pages 123-158, April.
    11. John Jackson, 2014. "Location, location, location: the Davis-Hinich model of electoral competition," Public Choice, Springer, vol. 159(1), pages 197-218, April.
    12. Bendor, Jonathan & Diermeier, Daniel & Ting, Michael M., 2000. "A Behavioral Model of Turnout," Research Papers 1627, Stanford University, Graduate School of Business.
    13. Michael Ensley & Scott Marchi & Michael Munger, 2007. "Candidate uncertainty, mental models, and complexity: Some experimental results," Public Choice, Springer, vol. 132(1), pages 231-246, July.
    14. Amihai Glazer & Bernard Grofman, 1988. "Limitations of the spatial model," Public Choice, Springer, vol. 58(2), pages 161-167, August.
    15. 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.
    16. Miller, J. H. & Stadler, P. F., 1998. "The dynamics of locally adaptive parties under spatial voting," Journal of Economic Dynamics and Control, Elsevier, vol. 23(2), pages 171-189, September.
    17. Jie-Shin Lin, 2005. "An Analysis on Simulation Models of Competing Parties," Computing in Economics and Finance 2005 284, Society for Computational Economics.
    18. Melvin J. Hinich & Michael C. Munger, 1992. "A Spatial Theory of Ideology," Journal of Theoretical Politics, , vol. 4(1), pages 5-30, January.
    19. Tovey, Craig A., 2010. "The almost surely shrinking yolk," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 74-87, January.
    20. A. J. McGann, 2002. "The Advantages of Ideological Cohesion," Journal of Theoretical Politics, , vol. 14(1), pages 37-70, 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:wop:safiwp:98-08-072. 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: Thomas Krichel (email available below). General contact details of provider: https://edirc.repec.org/data/epstfus.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.