IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v59y2010i1p53-73.html
   My bibliography  Save this article

The instability of instability of centered distributions

Author

Listed:
  • Tovey, Craig A.

Abstract

Democratic simple majority voting is perhaps the most widely used method of group decision making in our time. Standard theory, based on "instability" theorems, predicts that a group employing this method will almost always fail to reach a stable conclusion. But empirical observations do not support the gloomy predictions of the instability theorems. We show that the instability theorems are themselves unstable in the following sense: if the model of voter behavior is altered however slightly to incorporate any of the several plausible characteristics of decision making, then the instability theorems do not hold and in fact the probability of stability converges to 1 as the population increases, when the population is sampled from a centered distribution. The assumptions considered include: a cost of change; bounded rationality; perceptual thresholds; a discrete proposal space, and others. Evidence from a variety of fields justifies these assumptions in all or most circumstances. One consequence of this work is to render precise and rigorous, the solution proposed by Tullock to the impossibility problem. All of the stability results given here hold for an arbitrary dimension. We generalize the results to establish stability with probability converging to 1 subject to trade-offs between the assumptions and the degree of non-centeredness of the population. We also extend the results from Euclidean preferences to the more general class of intermediate preferences.

Suggested Citation

  • Tovey, Craig A., 2010. "The instability of instability of centered distributions," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 53-73, January.
  • Handle: RePEc:eee:matsoc:v:59:y:2010:i:1:p:53-73
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-4896(09)00082-1
    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. repec:cup:apsrev:v:80:y:1986:i:01:p:65-87_18 is not listed on IDEAS
    2. Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    3. repec:cup:apsrev:v:90:y:1996:i:01:p:34-45_20 is not listed on IDEAS
    4. Ansolabehere, Stephen & Snyder, James M, Jr, 2000. "Valence Politics and Equilibrium in Spatial Election Models," Public Choice, Springer, vol. 103(3-4), pages 327-336, June.
    5. Gordon Tullock, 1967. "The General Irrelevance of the General Impossibility Theorem," The Quarterly Journal of Economics, Oxford University Press, vol. 81(2), pages 256-270.
    6. Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
    7. John Ledyard, 1984. "The pure theory of large two-candidate elections," Public Choice, Springer, vol. 44(1), pages 7-41, January.
    8. Jean-François Laslier & Jörgen Weibull, 2008. "Committee decisions: Optimality and Equilibrium," Working Papers halshs-00121741, HAL.
    9. Stephen W. Salant & Eban Goodstein, 1990. "Predicting Committee Behavior in Majority Rule Voting Experiments," RAND Journal of Economics, The RAND Corporation, vol. 21(2), pages 293-313, Summer.
    10. repec:cup:apsrev:v:95:y:2001:i:01:p:155-167_00 is not listed on IDEAS
    11. Norman Schofield, 1978. "Instability of Simple Dynamic Games," Review of Economic Studies, Oxford University Press, vol. 45(3), pages 575-594.
    12. Thomas Bräuninger, 2007. "Stability in Spatial Voting Games with Restricted Preference Maximizing," Journal of Theoretical Politics, , vol. 19(2), pages 173-191, April.
    13. Jeong, Gyung-Ho, 2008. "Testing the Predictions of the Multidimensional Spatial Voting Model with Roll Call Data," Political Analysis, Cambridge University Press, vol. 16(02), pages 179-196, March.
    14. Kovalenkov, Alexander & Wooders, Myrna Holtz, 2001. "Epsilon Cores of Games with Limited Side Payments: Nonemptiness and Equal Treatment," Games and Economic Behavior, Elsevier, vol. 36(2), pages 193-218, August.
    15. Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
    16. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    17. repec:cup:apsrev:v:79:y:1985:i:03:p:673-692_22 is not listed on IDEAS
    18. McKelvey, Richard D & Schofield, Norman, 1987. "Generalized Symmetry Conditions at a Core Point," Econometrica, Econometric Society, vol. 55(4), pages 923-933, July.
    19. McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
    20. Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
    21. Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
    22. Rothkopf, Michael H & Teisberg, Thomas J & Kahn, Edward P, 1990. "Why Are Vickrey Auctions Rare?," Journal of Political Economy, University of Chicago Press, vol. 98(1), pages 94-109, February.
    23. de Palma, A, et al, 1985. "The Principle of Minimum Differentiation Holds under Sufficient Heterogeneity," Econometrica, Econometric Society, vol. 53(4), pages 767-781, July.
    24. repec:ulb:ulbeco:2013/1759 is not listed on IDEAS
    25. 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.
    26. repec:cup:apsrev:v:72:y:1978:i:02:p:575-598_15 is not listed on IDEAS
    27. 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.
    28. Judith Sloss, 1973. "Stable outcomes in majority rule voting games," Public Choice, Springer, vol. 15(1), pages 19-48, June.
    29. 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.
    30. repec:cup:apsrev:v:64:y:1970:i:02:p:426-448_12 is not listed on IDEAS
    31. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    32. 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.
    33. James Enelow & Melvin Hinich, 1989. "A general probabilistic spatial theory of elections," Public Choice, Springer, vol. 61(2), pages 101-113, May.
    34. Gordon Tullock, 1981. "Why so much stability," Public Choice, Springer, vol. 37(2), pages 189-204, 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. Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
    2. Nicholas R. Miller, 2015. "The spatial model of social choice and voting," Chapters,in: Handbook of Social Choice and Voting, chapter 10, pages 163-181 Edward Elgar Publishing.

    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:53-73. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.