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Majority Decision-Making with Partial Unidimensionality


  • Niemi, Richard G.


A major dilemma for majority decision-making occurs when the summation of transitive individual preference orderings results in an intransitive social ordering. The problems posed by this phenomenon, which is known as the paradox of voting, can be seen in the following standard example.Suppose there are three individuals, one with each of the following preference orders of three alternatives: ABC, BCA, CAB. Under majority rule, A would defeat B, B would defeat C, and C would defeat A, so there is no majority winner.Most voting procedures, of course, yield a unique result whether or not the paradox occurs. But from this example it is apparent that when the paradox does occur, a majority of the voters prefer an alternative other than the one which is selected. Moreover, if a typical voting procedure is used, which of the alternatives is selected depends on the order in which the alternatives are voted on. Clearly these results have important implications, whether one is concerned with normative questions about majority rule or with the practical politics of legislative decision-making.In the burgeoning literature on the voting paradox, surely one of the most impressive and well-known findings is Black's and Arrow's demonstration that the paradox cannot occur if the set of individual preference orderings is single-peaked. Since single-peakedness implies that the individuals and alternatives can be arrayed on a single dimension, their finding has a meaningful substantive interpretation. Namely, complete agreement on a dimension for judging the alternatives ensures that majority voting will yield a transitive social ordering of the alternatives.

Suggested Citation

  • Niemi, Richard G., 1969. "Majority Decision-Making with Partial Unidimensionality," American Political Science Review, Cambridge University Press, vol. 63(2), pages 488-497, June.
  • Handle: RePEc:cup:apsrev:v:63:y:1969:i:02:p:488-497_26

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    Cited by:

    1. William Riker, 1987. "The lessons of 1787," Public Choice, Springer, vol. 55(1), pages 5-34, September.
    2. Peter Fishburn & William Gehrlein, 1980. "Social homogeneity and Condorcet's paradox," Public Choice, Springer, vol. 35(4), pages 403-419, January.
    3. R. Abrams, 1976. "The voter's paradox and the homogeneity of individual preference orders," Public Choice, Springer, vol. 26(1), pages 19-27, June.
    4. Achuthankutty, Gopakumar & Roy, Souvik, 2017. "Strategy-proof Rules on Partially Single-peaked Domains," MPRA Paper 82267, University Library of Munich, Germany.
    5. Adrian Deemen, 2014. "On the empirical relevance of Condorcet’s paradox," Public Choice, Springer, vol. 158(3), pages 311-330, March.
    6. Jansen, C. & Schollmeyer, G. & Augustin, T., 2018. "A probabilistic evaluation framework for preference aggregation reflecting group homogeneity," Mathematical Social Sciences, Elsevier, vol. 96(C), pages 49-62.
    7. Sven Berg, 1985. "Paradox of voting under an urn model: The effect of homogeneity," Public Choice, Springer, vol. 47(2), pages 377-387, January.
    8. Scott Feld & Bernard Grofman, 1986. "Research note Partial single-peakedness: An extension and clarification," Public Choice, Springer, vol. 51(1), pages 71-80, January.
    9. Richard Niemi, 1970. "The occurrence of the paradox of voting in University elections," Public Choice, Springer, vol. 8(1), pages 91-100, March.
    10. William Gehrlein & Peter Fishburn, 1976. "Condorcet's paradox and anonymous preference profiles," Public Choice, Springer, vol. 26(1), pages 1-18, June.
    11. Michel Regenwetter & James Adams & Bernard Grofman, 2002. "On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity," Theory and Decision, Springer, vol. 53(2), pages 153-186, September.

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