Theory and Decision

, Volume 50, Issue 4, pp 305–332 | Cite as

Instability and Convergence Under Simple-Majority Rule: Results from Simulation of Committee Choice in Two-Dimensional Space

  • David H. Koehler


Nondeterministic models of collective choice posit convergence among the outcomes of simple-majority decisions. The object of this research is to estimate the extent of convergence of majority choice under different procedural conditions. The paper reports results from a computer simulation of simple-majority decision making by committees. Simulation experiments generate distributions of majority-adopted proposals in two-dimensional space. These represent nondeterministic outcomes of majority choice by committees. The proposal distributions provide data for a quantitative evaluation of committee-choice procedures in respect to outcome convergence. Experiments were run under general conditions, and under conditions that restrict committee choice to several game-theoretic solution sets. The findings are that, compared to distributions of voter ideal points, majority-adopted proposals confined to the solution sets demonstrate different degrees of convergence. Second, endogenous agenda formation is a more important obstacle to convergence than the inherent instability of simple-majority rule. Third, if members maximize preferences in respect to agenda formation, a committee choice that approximates the central tendency of the distribution of voter preferences is unlikely. The conclusion is that the most effective way to increase the convergence of majority choice is to restrict the role of individual preferences in agenda formation: identification of proposals to be voted up or down by a committee.

majority rule spatial voting models computer simulation rational choice committee choice convergence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bartholdi, J.J., Narasimhan, L.S. and Tovey, C.A. (1991), Recognizing majority rule equilibriumin spatial voting games. Social Choice and Welfare 7: 183-197.Google Scholar
  2. Davis, O.A., DeGroot, M. H. and Hinich, M. J. (1972), Social preference orderings and majority rule. Econometrica 40: 147-157.CrossRefGoogle Scholar
  3. Feld, S. L., Grofman, B. and Miller, N. R. (1988), Centripetal forces in spatial voting: on the size of the yolk. Public Choice 59: 37-50.CrossRefGoogle Scholar
  4. Feld, S.L., Grofman, B. and Miller, N.R. (1989), Limits on agenda control in spatial voting games. Mathematical Modeling 12: 405-416.CrossRefGoogle Scholar
  5. Ferejohn, J.A., Fiorina, M. P. and Packel, E.W. (1980), Nonequilibrium solutions for legislative systems. Behavioral Science 25: 140-148.Google Scholar
  6. Ferejohn, J.A., McKelvey, R.D. and Packel, E.W. (1984), Limiting distributions for continuous state markov voting models. Social Choice and Welfare 1: 45-67.CrossRefGoogle Scholar
  7. Koehler, D.H. (1990), The size of the yolk: Computations for odd and even numbered committees. Social Choice and Welfare 7: 231-245.CrossRefGoogle Scholar
  8. Koehler, D.H. (1992), Limiting median lines frequently determine the yolk: A rejoinder. Social Choice and Welfare 9: 37-41.CrossRefGoogle Scholar
  9. Koehler, D.H. (1996), Committee choice and the core under supramajority rule: Results from simulation of majority choice in 2-dimensional space. Public Choice 87: 281-301.CrossRefGoogle Scholar
  10. McKelvey, R.D. (1976), Intransitivities in multidimensional voting models and some implications for agenda control. Journal of Economic Theory 12: 472-482.CrossRefGoogle Scholar
  11. McKelvey, R.D. (1986), Covering, dominance, and institution free properties of social choice. American Journal of Political Science 30: 283-314.Google Scholar
  12. Miller, N.R. (1980), A new solution set for tournaments and majority voting. American Journal of Political Science 24: 68-96.Google Scholar
  13. Packel, E.W. (1981), A stochastic solution concept for n-person games. The Mathematics of Operations Research 6: 349-362.CrossRefGoogle Scholar
  14. 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: 49-74.Google Scholar
  15. Stone, R.E. and Tovey, C.A. (1992), Limiting median lines do not suffice to determine the yolk. Social Choice and Welfare 9: 33-35.CrossRefGoogle Scholar
  16. Tovey, C.A. (1991), A polynomial-time algorithm for computing the yolk in fixed dimension. Mathematical Programming 57: 259-277.CrossRefGoogle Scholar
  17. Weisberg, H.F. (1992), Central tendency and variability. Newbury Park, CA: Sage.Google Scholar
  18. Wilson, R.K. (1986), Forward and backward agenda procedures: Committee experiments on structurally induced equilibrium. Journal of Politics 48: 390-409.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • David H. Koehler
    • 1
  1. 1.David H. Koehler, Department of Public Administration, School of Public AffairsAmerican UniversityWashington DCUSA

Personalised recommendations