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Majority cycles in a multi-dimensional setting


  • Laurent Vidu

    (G.E.M.M.A. - C.R.E.M.E. Université de Caen, 14032 Caen Cedex, FRANCE)


We consider a set of alternatives (electoral platforms, bills, etc. ...) defined as a Cartesian product of k finite discrete sets. We assume that the preferences of the individuals (voters) are marginally single-peaked and separable. The main result of this paper states that the pairwise majority relation satisfies these two properties but that it might exhibit several cycles. This result is important when related to classical problems of multi-dimensional decisions such as logrolling and vote trading. We relate our result with a continuous version of it (McKelvey, 1976).

Suggested Citation

  • Laurent Vidu, 2002. "Majority cycles in a multi-dimensional setting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 373-386.
  • Handle: RePEc:spr:joecth:v:20:y:2002:i:2:p:373-386
    Note: Received: March 21, 2000; revised version: April 12, 2001

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    Cited by:

    1. Munda, Giuseppe, 2009. "A conflict analysis approach for illuminating distributional issues in sustainability policy," European Journal of Operational Research, Elsevier, vol. 194(1), pages 307-322, April.
    2. Giuseppe Munda, 2012. "Choosing Aggregation Rules for Composite Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 109(3), pages 337-354, December.

    More about this item


    Majority cycles; Multi-dimensionnal vote; Logrolling and vote trading; McGarvey's theorem.;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making


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