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Research note Partial single-peakedness: An extension and clarification

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  • Scott Feld
  • Bernard Grofman

Abstract

Niemi (1969), in an important but neglected paper, found that when orderings were drawn from a simulation based on the impartial culture, the greater the proportion of voter orderings that were single-peaked (a condition he called partial single-peakedness), the more likely was there to be a transitive group ordering. Niemi also found that the likelihood of transitivity increased with n, group size — approaching one as n grew large. Niemi's simulation was restricted to the case of three alternatives. Also, he provided no theoretical explanation for the results of his simulation. Here we provide a theoretical explanation for Niemi's results in terms of a model based on the idea of net preferences, and we extend his results for the general case of any finite number of alternatives, m, for electorates that are large relative to the number of alternatives being considered. In addition to providing a rationale for Niemi's (1969) simulation results, the ideas of net preferences and opposite preference we make use of have a wide range of potential applications. Copyright Martinus Nijhoff Publishers 1986

Suggested Citation

  • Scott Feld & Bernard Grofman, 1986. "Research note Partial single-peakedness: An extension and clarification," Public Choice, Springer, vol. 51(1), pages 71-80, January.
    • Handle: RePEc:kap:pubcho:v:51:y:1986:i:1:p:71-80
    DOI: 10.1007/BF00141686
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    References listed on IDEAS

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    1. Richard D. McKelvey & Richard E. Wendell, 1976. "Voting Equilibria in Multidimensional Choice Spaces," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 144-158, May.
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    6. Riker, William H., 1980. "Implications from the Disequilibrium of Majority Rule for the Study of Institutions," American Political Science Review, Cambridge University Press, vol. 74(2), pages 432-446, June.
    7. Kuga, Kiyoshi & Nagatani, Hiroaki, 1974. "Voter Antagonism and the Paradox of Voting," Econometrica, Econometric Society, vol. 42(6), pages 1045-1067, November.
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    9. Niemi, Richard G., 1969. "Majority Decision-Making with Partial Unidimensionality," American Political Science Review, Cambridge University Press, vol. 63(2), pages 488-497, June.
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    11. Gehrlein, William V. & Fishburn, Peter C., 1976. "The probability of the paradox of voting: A computable solution," Journal of Economic Theory, Elsevier, vol. 13(1), pages 14-25, August.
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    Cited by:

    1. Nicholas R. Miller, 2019. "Reflections on Arrow’s theorem and voting rules," Public Choice, Springer, vol. 179(1), pages 113-124, April.
    2. Michel Regenwetter & Bernard Grofman, 1998. "Approval Voting, Borda Winners, and Condorcet Winners: Evidence from Seven Elections," Management Science, INFORMS, vol. 44(4), pages 520-533, April.
    3. Scott L. Feld & Bernard Grofman, 1992. "Who's Afraid of the Big Bad Cycle? Evidence from 36 Elections," Journal of Theoretical Politics, , vol. 4(2), pages 231-237, April.
    4. Isaac Lara & Sergio Rajsbaum & Armajac Ravent'os-Pujol, 2024. "A Generalization of Arrow's Impossibility Theorem Through Combinatorial Topology," Papers 2402.06024, arXiv.org, revised Jul 2024.
    5. Riste Gjorgjiev & Dimitrios Xefteris, 2015. "Transitive supermajority rule relations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 299-312, October.
    6. James F. Adams & Ernest W. Adams, 2000. "The Geometry of Voting Cycles," Journal of Theoretical Politics, , vol. 12(2), pages 131-153, April.
    7. Scott Feld & Bernard Grofman & Nicholas Miller, 1988. "Centripetal forces in spatial voting: On the size of the Yolk," Public Choice, Springer, vol. 59(1), pages 37-50, October.
    8. Scott Feld & Bernard Grofman, 1988. "The Borda count in n-dimensional issue space," Public Choice, Springer, vol. 59(2), pages 167-176, November.

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