The instability of instability of centered distributions
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- John Ledyard, 1983.
"The Pure Theory of Large Two Candidate Elections,"
569, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- Judith Sloss, 1973. "Stable outcomes in majority rule voting games," Public Choice, Springer, vol. 15(1), pages 19-48, June.
- Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
- 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.
- Banks, Jeffrey & Duggan, John & Le Breton, Michel, 2003.
"Social Choice and Electoral Competition in the General Spatial Model,"
IDEI Working Papers
188, Institut d'Économie Industrielle (IDEI), Toulouse.
- 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.
- Myrna Wooders & Alexander Kovalenkov, 2001.
"Epsilon cores of games with limited side payments Nonemptiness and equal treatment,"
AccessEcon, vol. 28(5), pages A0.
- 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.
- Norman Schofield, 1978. "Instability of Simple Dynamic Games," Review of Economic Studies, Oxford University Press, vol. 45(3), pages 575-594.
- Jean-François Laslier & Jörgen Weibull, 2008.
"Committee decisions: Optimality and Equilibrium,"
- Laslier, Jean-François & Weibull, Jörgen, 2008. "Commitee decisions: optimality and equilibrium," SSE/EFI Working Paper Series in Economics and Finance 692, Stockholm School of Economics, revised 11 Mar 2008.
- Gordon Tullock, 1981. "Why so much stability," Public Choice, Springer, vol. 37(2), pages 189-204, January.
- Victor Ginsburgh & André De Palma & Yorgo Papageorgiou & Jacques-François Thisse, 1999.
"The principle of minimum differentiation holds under sufficient heterogeneity,"
ULB Institutional Repository
2013/3319, ULB -- Universite Libre de Bruxelles.
- de Palma, A, et al, 1985. "The Principle of Minimum Differentiation Holds under Sufficient Heterogeneity," Econometrica, Econometric Society, vol. 53(4), pages 767-81, July.
- Victor Ginsburgh & André De Palma & Yorgo Papageorgiou & Jacques Thisse, 1985. "The principle of Minimum Differentiation Holds under Sufficient Heterogeneity," ULB Institutional Repository 2013/151087, ULB -- Universite Libre de Bruxelles.
- de PALMA, A. & GINSBURGH, V. & PAPAGEOGIOU, Y.Y. & THISSE, J-F., . "The principle of minimum differentiation holds under sufficient heterogeneity," CORE Discussion Papers RP 640, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Victor Ginsburgh & André De Palma & Yorgo Papageorgiou & Jacques-François Thisse, 1995. "The principle of minimum differentiation holds under sufficient heterogeneity," ULB Institutional Repository 2013/3317, ULB -- Universite Libre de Bruxelles.
- Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135.
- Salant, S.W. & Goodstein, E., 1989.
"Predicting Committee Behavior In Majority-Rule Voting Experiments,"
89-25, Michigan - Center for Research on Economic & Social Theory.
- 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.
- Caplin, Andrew & Nalebuff, Barry, 1991.
"Aggregation and Social Choice: A Mean Voter Theorem,"
Econometric Society, vol. 59(1), pages 1-23, January.
- Andrew Caplin & Barry Nalebuff, 1990. "Aggregation and Social Choice: A Mean Voter Theorem," Cowles Foundation Discussion Papers 938, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
- Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
- McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
- McKelvey, Richard D & Schofield, Norman, 1987.
"Generalized Symmetry Conditions at a Core Point,"
Econometric Society, vol. 55(4), pages 923-33, July.
- James Enelow & Melvin Hinich, 1989. "A general probabilistic spatial theory of elections," Public Choice, Springer, vol. 61(2), pages 101-113, May.
- Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
- Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
- Victor Ginsburgh & André De Palma & Yorgo Papageorgiou & Jacques-François Thisse, 1985. "The principle of minimum differentiation holds under sufficient heterogeneity," ULB Institutional Repository 2013/1759, ULB -- Universite Libre de Bruxelles.
- Thomas BrÃ¤uninger, 2007. "Stability in Spatial Voting Games with Restricted Preference Maximizing," Journal of Theoretical Politics, , vol. 19(2), pages 173-191, April.
- Ansolabehere, Stephen & Snyder, James M, Jr, 2000. "Valence Politics and Equilibrium in Spatial Election Models," Public Choice, Springer, vol. 103(3-4), pages 327-36, June.
- Davis, Otto A & DeGroot, Morris H & Hinich, Melvin J, 1972. "Social Preference Orderings and Majority Rule," Econometrica, Econometric Society, vol. 40(1), pages 147-57, January.
- Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-30, March.
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: (Zhang, Lei)
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 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.