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In Search of the Uncovered Set

Published online by Cambridge University Press:  04 January 2017

Nicholas R. Miller
Nicholas R. Miller*
Affiliation:
Department of Political Science, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250. e-mail: [email protected]
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Abstract

This paper pursues a number of theoretical explorations and conjectures pertaining to the uncovered set in spatial voting games. It was stimulated by the article “The Uncovered Set and the Limits of Legislative Action” by W. T. Bianco, I. Jeliazkov, and I. Sened (2004, Political Analysis 12:256—78) that employed a grid-search computational algorithm for estimating the size, shape, and location of the uncovered set, and it has been greatly facilitated by access to the CyberSenate spatial voting software being developed by Joseph Godfrey. I bring to light theoretical considerations that account for important features of the Bianco, Jeliazkov, and Sened results (e.g., the straight-line boundaries of uncovered sets displayed in some of their figures, the “unexpectedly large” uncovered sets displayed in other figures, and the apparent sensitivity of the location of uncovered sets to small shifts in the relative sizes of party caucuses) and present theoretical insights of more general relevance to spatial voting theory.

Type
Research Article
Information
Political Analysis , Volume 15 , Issue 1 , Winter 2007 , pp. 21 - 45
Copyright
Copyright © The Author 2006. Published by Oxford University Press on behalf of the Society for Political Methodology 

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References

Bianco, William T., Jeliazkov, Ivan, and Sened, Itai. 2004. The uncovered set and the limits of legislative action. Political Analysis 12: 256–78.CrossRefGoogle Scholar
Bräuninger, Thomas. 2007. Stability with restricted preference maximizing. Journal of Theoretical Politics. Forthcoming.Google Scholar
Enelow, James M., and Hinich, Melvin J. 1983. On Plott's pairwise symmetry condition for majority rule equilibrium. Public Choice 40: 317–21.CrossRefGoogle Scholar
Feld, Scott L., Grofman, Bernard, and Miller, Nicholas R. 1988. Centripetal forces in spatial voting games: on the size of the yolk. Public Choice 59: 37–50.CrossRefGoogle Scholar
Feld, Scott L., Grofman, Bernard, and Miller, Nicholas R. 1989. Limits on agenda control in spatial voting games. Mathematical and Computer Modelling 12: 405–16.CrossRefGoogle Scholar
Ferejohn, John A., McKelvey, Richard D., and Packel, Edward W. 1984. Limiting distributions for continuous state Markov voting models. Social Choice and Welfare 1: 45–67.CrossRefGoogle Scholar
Godfrey, Joseph. 2005. Computation of the Shapley-Owen index in two dimensions. Paper presented at Voting Power & Procedures (VPP) Workshop, Warwick University, Coventry, UK, July 20-22, 2005.Google Scholar
Grofman, Bernard, Owen, Guillermo, Noviello, Nicholas, and Glazer, Amihai. 1987. Stability and centrality of legislative choice in the spatial context. American Political Science Review 81: 539–52.CrossRefGoogle Scholar
Hartley, Richard, and Marc Kilgour, D., 1987. The geometry of the uncovered set. Mathematical Social Sciences 14: 175–83.CrossRefGoogle Scholar
Hug, Simon. 1999. Nonunitary actors in spatial models. Journal of Conflict Resolution 43: 479–500.CrossRefGoogle Scholar
Koehler, David H. 1990. The size of the yolk: Computations of odd and even-numbered committees. Social Choice and Welfare 7: 231–45.CrossRefGoogle Scholar
Koehler, David H. 1992. Limiting median lines frequently determine the yolk: A rejoinder. Social Choice and Welfare 9: 37–41.CrossRefGoogle Scholar
McKelvey, Richard D. 1976. Intransitivities in multidimensional voting models and some implications for agenda control. Journal of Economic Theory 12: 472–482.CrossRefGoogle Scholar
McKelvey, Richard D. 1979. General conditions for global intransitivities in formal voting models. Econometrica 47: 1085–1112.CrossRefGoogle Scholar
McKelvey, Richard D. 1986. Covering, dominance, and institution free properties of social choice. American Journal of Political Science 30: 283–314.CrossRefGoogle Scholar
Miller, Nicholas R. 1980. A new solution set for tournaments and majority voting. American Journal of Political Science 24: 68–96.CrossRefGoogle Scholar
Miller, Nicholas R., Grofman, Bernard, and Feld, Scott L. 1989. The geometry of majority rule. Journal of Theoretical Politics 1: 379–406.CrossRefGoogle Scholar
Owen, Guillermo, and Shapley, Lloyd S. 1989. Optimal location of candidates in ideological space. International Journal of Game Theory 18: 339–56.CrossRefGoogle Scholar
Penn, Elizabeth Maggie. 2006. Alternate definitions of the uncovered set and their implications. Social Choice and Welfare 27: 83–7.CrossRefGoogle Scholar
Plott, C. R. 1967. A notion of equilibrium and its possibility under majority rule. American Economic Review, 57: 787–806.Google Scholar
Schofield, Norman. 1978. Instability of simple dynamic games. Review of Economic Studies 45: 575–594.CrossRefGoogle Scholar
Schofield, Norman. 1999. The heart and the uncovered set. Journal of Economics Suppl 8:79–113.CrossRefGoogle 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. 1984. Uncovered sets and sophisticated voting outcomes with implications for agenda institutions. American Journal of Political Science 28: 49–74.CrossRefGoogle Scholar
Stone, Richard E., and Tovey, Craig A. 1992. Limiting median lines do not suffice to determine the yolk. Social Choice and Welfare 9: 33–5.CrossRefGoogle Scholar
Tovey, Craig A. 1990. The almost surely shrinking yolk. Monterey, CA: Naval Postgraduate School.Google Scholar