Skip to main content
SpringerLink
Log in

Centripetal forces in spatial voting: On the size of the Yolk

  • Published:
Public Choice Aims and scope Submit manuscript

Abstract

The yolk, the smallest circle which intersects all median lines, has been shown to be an important tool in understanding the nature of majority voting in a spatial voting context. The center of the yolk is a natural ‘center’ of the set of voter ideal points. The radius of the yolk can be used to provide bounds on the size of the feasible set of outcomes of sophisticated voting under standard amendment procedure, and on the limits of agenda manipulation and cycling when voting is sincere. We show that under many plausible conditions the yolk can be expected to be small. Thus, majority rule processes in spatial voting games will be far better behaved than has commonly been supposed, and the possible outcomes of agenda manipulations will be generally constrained. This result was first conjectured by Tullock (1967).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Banks, J.S. (1985). Sophisticated voting outcomes and agenda control. Social Choice and Welfare 1 (4): 295–306.

    Google Scholar 

  • Chamberlin, J.R., and Cohen, M.D. (1978). Toward applicable social choice theory: Comparison of social choice functions under spatial model assumptions. American Political Science Review 72 (4): 1341–1356.

    Google Scholar 

  • Cox, G. (1987). The uncovered set and the core. American Journal of Political Science 31 (2): 408–422.

    Google Scholar 

  • Davis, O., DeGroot, M.H., and Hinich, M. (1972). Social preference orderings and majority rule. Econometrica 40 (January): 147–157.

    Google Scholar 

  • Denzau, A.T, and Mackay, R.J. (1983). Gatekeeping and monopoly power of committees: An analysis of sincere and sophisticated behavior. American Journal of Political Science 27 (November): 740–776.

    Google Scholar 

  • Farquarson, R. (1970). Theory of voting. New Haven, CT: Yale University Press.

    Google Scholar 

  • Feld, S.L., and Grofman, B. (1986). Partial single-peakedness: An extension and clarification. Public Choice 51: 71–80.

    Google Scholar 

  • Feld, S.L., and Grofman, B. (1987a). Informal constraints on agendas. Presented at the Annual Meeting of the Public Choice Society, Tucson, AZ, 27–29 March.

  • Feld, S.L., Grofman, B. (1987b) Necessary and sufficient conditions for majority winner in n-dimensional spatial voting games: An intuitive geometric approach. American Journal of Political Science 31 (4): 709–728.

    Google Scholar 

  • Feld, S.L., and Grofman, B. (1988a). Ideological consistency as a collective phenomenon. American Political Science Review, forthcoming.

  • Feld, S.L., and Grofman, B. (1988b). Majority rule outcomes and the structure of debate in one-issue-at-a-time decision making. Public Choice, forthcoming.

  • Feld, S.L., Grofman, B., Hartley, R., Kilgour, M., Miller, N., and Noviello, N. (1987). The uncovered set in spatial voting games. Theory and Decision, 23: 129–156.

    Google Scholar 

  • Feld, S.L., Grofman, B., and Miller, N. (1989, forthcoming). Limitations of agenda manipulation in the spatial context. Mathematical Modelling.

  • Ferejohn, J.A., Fiorina, M., and Packel, E.W. (1980). Nonequilibrium solutions for legislative systems. Behavioral Science 25 (March): 140–148.

    Google Scholar 

  • Ferejohn, J.A., McKelvey, R.D., and Packel, E. (1984). Limiting distributions for continuous state Markov models. Social Choice and Welfare 1: 45–67.

    Google Scholar 

  • Grofman, B., Owen, G., Noviello, N., and Glazer, A. (1987). Stability and centrality of legislative choice in the spatial context. American Political Science Review 81 (2): 539–553.

    Google Scholar 

  • Koehler, D.H. (1988). Legislative structures and legislative choice: A computer simulation of sequential majority decisions. Presented at the Annual Meeting of the Public Choice Society, Tucson, AZ, 27–29 March.

  • Krehbiel, K. (1984, January). Obstruction, germaneness and representativeness in legislatures. Social Science Working Paper 510: 1–37. California Institute of Technology.

    Google Scholar 

  • McKelvey, R.D. (1976). Intransitivities in multidimensional voting models and some implications for agenda control. Journal of Economic Theory 12: 472–482.

    Google Scholar 

  • McKelvey, R.D. (1979). General conditions for global intransitivities in formal voting models. Econometrica 47: 1085–1111.

    Google Scholar 

  • McKelvey, R.D. (1986). Covering, dominance, and institution free properties of social choice. American Journal of Political Science 30 (2) (May): 283–315.

    Google Scholar 

  • McKelvey, R.D., and Niemi, R.G. (1978). A multistage game representation of sophisticated voting for binary procedures. Journal of Economic Theory 18: 1–22.

    Google Scholar 

  • Merrill, S. (1984). Comparison of efficiency of multicandidate electoral systems. American Journal of Political Science 28 (1): 23–48.

    Google Scholar 

  • Merrill, S. (1985, February). A statistical model for Condorcet efficiency based on simulation under spatial model assumptions. Presented at the Annual Meeting of the Public Choice Society, New Orleans.

  • Miller, N.R. (1977). Graph-theoretical approaches to the theory of voting. American Journal of Political Science 21 (November): 769–803.

    Google Scholar 

  • Miller, N.R. (1980). A new ‘solution set’ for tournaments and majority voting. American Journal of Political Science 24: 68–96.

    Google Scholar 

  • Miller, N.R. (1983). The covering relation in tournaments: Two corrections. American Journal of Political Science 27: 382–385.

    Google Scholar 

  • Miller, N.R., Grofman, B., and Feld, S.L. (1985). Cycle avoiding trajectories and the uncovered set. Paper presented at the Weingart Conference on Models of Voting, California Institute of Technology, 22–23 March.

  • Moulin, H. (1984). Choosing from a tournament. Social Choice and Welfare 3: 271–291.

    Google Scholar 

  • Niemi, R., and Wright, J.R. (1986). Voting cycles and the structure of individual preferences. Paper presented at the Annual Meeting of the Public Choice Society, Baltimore, MD.

  • Packel, E.W. (1981). A stochastic solution concept for n-person games. Mathematics of Operations Research 6.3 (August): 349–362.

    Google Scholar 

  • Plott, C.R. (1967). A notion of equilibrium and its possibility under majority rule. American Economic Review 57: 787–806.

    Google Scholar 

  • Rapoport, A., and Golan, E. (1985). Assessment of political power in the Israeli Knesset. American Political Science Review 79 (September): 673–692.

    Google Scholar 

  • Riker, W. (1982). Liberalism against populism: A confrontation between the theory of democracy and the theory of social choice. San Francisco: Freeman.

    Google Scholar 

  • Schofield, N. (1978). Instability of simple dynamic games. Review of Economic Studies 45: 575–594.

    Google Scholar 

  • Schofield, N., Grofman, B., and Feld, S.L. (1988). The core and the stability of group choice in spatial voting games. American Political Science Review 82 (1): 195–211.

    Google Scholar 

  • Shepsle, K.A. (1979). The role of institutional structure in the creation of policy equilibrium. In D.W. Rae and T.J. Eismeir (Eds.), Public policy and public choice VI: 96–111. Beverly Hills: Sage.

    Google Scholar 

  • Shepsle, K.A., and Weingast, B.R. (1984). Uncovered sets and sophisticated voting outcomes with implications for agenda institutions. American Journal of Political Science 28 (February): 49–74.

    Google Scholar 

  • Tullock, G. (1967). The general irrelevance of the general impossibility theorem. Quarterly Journal of Economics 81: 256–270.

    Google Scholar 

  • Wuffle, A, Feld, S.L., Owen, G., and Grofman, B. (1988). 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.

Download references

Author information

Authors and Affiliations

  1. Department of Sociology, State University of New York at Stony Brook, 11794, NY

    Scott L. Feld

  2. School of Social Sciences, University of California, 92717, Irvine, CA

    Bernard Grofman

  3. Department of Political Science, University of Maryland, 21228, Baltimore County, MD

    Nicholas Miller

Authors
  1. Scott L. Feld
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bernard Grofman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nicholas Miller
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

We are indebted to Helen Wildman, Sue Pursche, Cheryl Larsson, and Maggie Grice of the staff of the Word Processing Center, School of Social Sciences, UC Irvine, and to Gerald Florence and Deanna Knickerbocker of the Center for Adçced Study in the Behavioral Sciences for typing numerous early drafts of this manuscript from hand-scribbled copy, to Cheryl Larsson and Deanna Knickerbocker for preparing the figures, and to Dorothy Gormick for bibliographic assistance. A very early version of a portion of this paper was presented at the Weingart Conference on Formal Models of Voting, California Institute of Technology, 22–23 March 1985. Another earlier version of this paper was presented at the Annual Meeting of the Public Choice Society, Tucson, Arizona, 27–29 March 1987. We are indebted to participants at those sessions for helpful comments. This research was partially supported by NSF Grant #SES 85-06396 to the second-named author, NSF Grant #SES 85-09680 to the third-named author, and NSF Grant #BNS 8011494 to the Center for Advanced Study where the second-named author was a Fellow in 1985–86.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Feld, S.L., Grofman, B. & Miller, N. Centripetal forces in spatial voting: On the size of the Yolk. Public Choice 59, 37–50 (1988). https://doi.org/10.1007/BF00119448

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00119448

Keywords

Search

Navigation