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Stability and Centrality of Legislative Choice in the Spatial Context

Published online by Cambridge University Press:  01 June 1987

Bernard Grofman ,
Guillermo Owen ,
Nicholas Noviello  and
Amihai Glazer
Bernard Grofman
Affiliation:
University of California, Irvine
Guillermo Owen
Affiliation:
University of California, Irvine
Nicholas Noviello
Affiliation:
University of California, Irvine
Amihai Glazer
Affiliation:
University of California, Irvine
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Abstract

Majority-rule spatial voting games lacking a core still always present a “near-core” outcome, more commonly known as the Copeland winner. This is the alternative that defeats or ties the greatest number of alternatives in the space. Previous research has not tested the Copeland winner as a solution concept for spatial voting games without a core, lacking a way to calculate where the Copeland winner was with an infinite number of alternatives. We provide a straightforward algorithm to find the Copeland winner and show that it corresponds well to experimental outcomes in an important set of experimental legislative voting games. We also provide an intuitive motivation for why legislative outcomes in the spatial context may be expected to lie close to the Copeland winner. Finally, we show a connection between the Copeland winner and the Shapley value and provide a simple but powerful algorithm to calculate the Copeland scores of all points in the space in terms of the (modified) power values of each of the voters and their locations in the space.

Type
Articles
Information
American Political Science Review , Volume 81 , Issue 2 , June 1987 , pp. 539 - 553
Copyright
Copyright © American Political Science Association 1987

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References

Banks, Jeffrey S. 1985. Sophisticated Voting Out-comes and Agenda Control. Social Choice and Welfare 1:295–306.10.1007/BF00649265CrossRefGoogle Scholar
Black, Duncan. 1958. The Theory of Committees and Elections. Cambridge: Cambridge University Press.Google Scholar
Cobb, Roger W., and Elder, Charles D.. 1972. Participation in American Politics: The Dynamics of Agenda Building. Boston: Allyn and Bacon.Google Scholar
Copeland, A. H. 1951. A Reasonable Social Welfare Function. Typescript.Google Scholar
Eavey, Cheryl, and Miller, Gary. 1982. Experimental Evidence on the Fallibility of the Core. Paper presented at the annual meeting of the Public Choice Society, San Antonio, TX.Google Scholar
Farquharson, Robin. 1969. Theory of Voting. New Haven: Yale University Press.Google Scholar
Feld, Scott L., Grofman, Bernard, and Miller, Nicholas. 1985. The Uncovered Set in the Spatial Context. Revised version of paper presented at the Weingart Conference on Models of Voting, California Institute of Technology.Google Scholar
Ferejohn, John A., Fiorina, Morris P., and Packel, Edward W.. 1980. Nonequilibrium Solutions for Legislative Systems. Behavioral Science 25: 140–48.10.1002/bs.3830250206CrossRefGoogle Scholar
Ferejohn, John A., Fiorina, Morris F., and Weisberg, Herbert F.. 1978. Toward a Theory of Legislative Decision-Making. In Came Theory and Political Science, ed. Ordeshook, P. C., 165–90. New York: New York University Press.Google Scholar
Ferejohn, John A., McKelvey, Richard D., and Packel, Edward W.. 1984. Limiting Distributions for Continuous State Markov Models. Social Choice and Welfare 1:45–67.CrossRefGoogle Scholar
Fiorina, Morris P., and Plott, Charles R.. 1978. Committee Decisions under Majority Rule: An Experimental Study. American Political Science Review 72:575–98.CrossRefGoogle Scholar
Glazer, Amihai, Grofman, Bernard, and Owen, Guillermo. 1985. Imperfect Information Models of Spatial Competition in Electoral Politics. Paper presented at the annual meeting of the Public Choice Society, New Orleans, LA.Google Scholar
Grofman, Bernard. 1969. Some Notes on Voting Schemes and the Will of the Majority. Public Choice 7:65–80.CrossRefGoogle Scholar
Grofman, Bernard. 1982. A Dynamic Model of Protocoalition Formation. Behavioral Science 27:77–90.CrossRefGoogle Scholar
Grofman, Bernard, and Feld, Scott L.. 1986. Research Note: Agenda Manipulation via Committee Jurisdictional Assignments. University of California, Irvine. Typescript.Google Scholar
Grofman, Bernard, and Uhlaner, Carole. 1985. Metapreferences and the Reasons for Stability in Social Choice: Thoughts on Broadening and Clarifying the Debate. Theory and Decision 19: 31–50.10.1007/BF00134353CrossRefGoogle Scholar
Hoffman, Elizabeth, and Packel, Edward. 1981. The Stochastic Model df Committee Voting with Exogenous Costs: Theory and Experiments. Behavioral Science 27:43–56.CrossRefGoogle Scholar
Kramer, Gerald. 1977. A Dynamic Model of Political Equilibrium. Journal of Economic Theory 16:310–34.CrossRefGoogle Scholar
McKelvey, Richard D. 1976. Intransitivities in Multidimensional Voting Models and Some Implications for Agenda Control. Journal of Economic Theory 12:472–82.CrossRefGoogle Scholar
McKelvey, Richard D. 1979. General Conditions for Global Intransitivities in Formal Voting Models. Econometrica 47:1085–1112.CrossRefGoogle Scholar
McKelvey, Richard. 1986. Covering, Dominance, and Institution Free Properties of Social Choice. American Journal of Political Science 30: 283–314.CrossRefGoogle Scholar
McKelvey, Richard D., Ordeshook, P., and Winer, M.. 1978. The Competitive Solution for n-Person Games without Transferable Utility. American Political Science Review 72:599–615.CrossRefGoogle Scholar
McKelvey, Richard D., and Wendell, R. E.. 1976. Voting Equilibria in Multidimensional Choice Spaces. Mathematics of Operations Research 1: 144–58.10.1287/moor.1.2.144CrossRefGoogle Scholar
Margolis, Howard. 1982. Altruism, Selfishness, and Rationality. Chicago: University of Chicago Press.Google Scholar
Miller, Nicholas. 1977. Graph-theoretical Approaches to the Theory of Voting. American Journal of Political Science 21:769–803.CrossRefGoogle Scholar
Miller, Nicholas. 1980. A New “Solution Set” for Tournaments and Majority Voting. American Journal of Political Science 24:68–96.10.2307/2110925CrossRefGoogle Scholar
Miller, Nicholas, Grofman, Bernard, and Feld, Scott L.. 1985. Cycle Avoiding Trajectories and the Uncovered Set. Paper presented at the Weingart Conference on Models of Voting, California Institute of Technology.Google Scholar
Moulin, Hervé. 1984. Choosing from a Tournament. Virginia Polytechnic Institute and State University. Photocopy.Google Scholar
Owen, Guillermo. 1971. Political Games. Naval Research Logistics Quarterly 18:345–54.CrossRefGoogle Scholar
Owen, Guillermo. 1972. Multilinear Extension of Games. Management Science 64–79.Google Scholar
Owen, Guillermo. 1982. Game Theory. New York: Academic Press.Google Scholar
Packel, Edward W. 1981. A Stochastic Solution Concept for n-Person Games. Mathematics of Operations Research 6:348–62.CrossRefGoogle Scholar
Plott, Charles R. 1967. A Notion of Equilibrium and Its Possibility under Majority Rule. American Economic Review 57:787–806.Google Scholar
Riker, William.1980. Implications from the Dis equilibrium of Majority Rule for the Study of Institutions. American Political Science Review 74:432–46.CrossRefGoogle Scholar
Riker, William. 1982. Liberalism v. Populism. New York: W. H. Freeman.Google Scholar
Schofield, Norman. 1978. The Theory of Dynamic Games. Review of Economic Studies 45:575–94.10.2307/2297259CrossRefGoogle Scholar
Schofield, Norman, Grofman, Bernard, and Feld, Scott L.. 1985. The Core and the Stability of Group Choice in Spatial Voting Games. University of California, Irvine. Typescript.Google Scholar
Shapley, Lloyd. 1977. A Comparison of Power Indices and a Non-symmetric Generalization (Paper P–5872). Santa Monica, CA: Rand Corporation.Google Scholar
Shapley, Lloyd, and Owen, Guillermo. 1985. The Copeland Winner and the Shapley Value in Spatial Voting Games. University of California, Irvine. Typescript.Google Scholar
Shepsle, Kenneth A. 1979. Institutional Arrangements and Equilibrium in Multidimensional Voting Models. American Journal of Political Science 23:27–59.CrossRefGoogle Scholar
Shepsle, Kenneth A., and Weingast, Barry R.. 1982. Institutionalizing Majority Rule: A Social Choice Theory with Policy Implications. American Economic Review 72:367–72.Google Scholar
Shepsle, Kenneth A., and Weingast, Barry R.. 1984. Uncovered Sets and Sophisticated Voting Out-comes with Implications for Agenda Institutions. American Journal of Political Science 28:49–74.CrossRefGoogle Scholar
Straffin, Philip D. Jr. 1977. Homogeneity, Independence, and Power Indices. Public Choice 30: 107–18.CrossRefGoogle Scholar
Straffin, Philip D. Jr. 1980. Topics in the Theory of Voting. Cambridge, MA: Birkhauser.Google Scholar
Straffin, Philip D. J., and Grofman, Bernard. 1984. Parliamentary Coalitions: A Tour of Models. Mathematics Magazine 54:259–74.CrossRefGoogle Scholar
Tullock, Gordon. 1981. Why So Much Stability? Public Choice 37:189–202.CrossRefGoogle Scholar
Wilson, Rick, and Herzberg, Roberta. 1984. Voting Is Only a Block Away: Theory and Experiments on Blocking Coalitions. Paper presented at the annual meeting of the Public Choice Society, Phoenix, AZ.Google Scholar
Wuffle, A., Feld, Scott, Owen, Guillermo, and Grofman, Bernard. N.d. Finagle's Law and the Finagle Point: A New Solution Concept for Two-Candidate Competition in Spatial Voting Games without a Core. American Journal of Political Science. Forthcoming.Google Scholar
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