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.
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- Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
- 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.
- 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.
- Caplin, Andrew S & Nalebuff, Barry J, 1988. "On 64%-Majority Rule," Econometrica, Econometric Society, vol. 56(4), pages 787-814, July.
- John Ledyard, 1984.
"The pure theory of large two-candidate elections,"
Springer, vol. 44(1), pages 7-41, January.
- John Ledyard, 1983. "The Pure Theory of Large Two Candidate Elections," Discussion Papers 569, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Jean-François Laslier & Jörgen Weibull, 2008. "Committee decisions: Optimality and Equilibrium," Working Papers halshs-00121741, HAL.
- 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.
- 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.
- Salant, S.W. & Goodstein, E., 1989. "Predicting Committee Behavior In Majority-Rule Voting Experiments," Papers 89-25, Michigan - Center for Research on Economic & Social Theory.
- Norman Schofield, 1978. "Instability of Simple Dynamic Games," Review of Economic Studies, Oxford University Press, vol. 45(3), pages 575-594.
- Thomas BrÃ¤uninger, 2007. "Stability in Spatial Voting Games with Restricted Preference Maximizing," Journal of Theoretical Politics, , vol. 19(2), pages 173-191, April.
- 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.
- 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.
- Myrna Wooders & Alexander Kovalenkov, 2001. "Epsilon cores of games with limited side payments Nonemptiness and equal treatment," Economics Bulletin, AccessEcon, vol. 28(5), pages 1.
- Kramer, Gerald H., 1977. "A dynamical model of political equilibrium," Journal of Economic Theory, Elsevier, vol. 16(2), pages 310-334, December.
- Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, 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.
- McKelvey, Richard D & Schofield, Norman, 1987. "Generalized Symmetry Conditions at a Core Point," Econometrica, Econometric Society, vol. 55(4), pages 923-933, July.
- McKelvey, Richard D. & Schofield, Norman., 1985. "Generalized Symmetry Conditions at a Core Point," Working Papers 552, California Institute of Technology, Division of the Humanities and Social Sciences.
- McKelvey, Richard D, 1979. "General Conditions for Global Intransitivities in Formal Voting Models," Econometrica, Econometric Society, vol. 47(5), pages 1085-1112, September.
- Grandmont, Jean-Michel, 1978. "Intermediate Preferences and the Majority Rule," Econometrica, Econometric Society, vol. 46(2), pages 317-330, March.
- Tovey, Craig A., 2010. "A critique of distributional analysis in the spatial model," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 88-101, January.
- 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.
- 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.
- de PALMA, A. & GINSBURGH, V. & PAPAGEOGIOU, Y.Y. & THISSE, J-F., "undated". "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.
- 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.
- 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.
- repec:ulb:ulbeco:2013/1759 is not listed on IDEAS
- 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.
- 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.
- 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.
- Judith Sloss, 1973. "Stable outcomes in majority rule voting games," Public Choice, Springer, vol. 15(1), pages 19-48, June.
- 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.
- Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
- 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.
- James Enelow & Melvin Hinich, 1989. "A general probabilistic spatial theory of elections," Public Choice, Springer, vol. 61(2), pages 101-113, May.
- 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)
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