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Majority Rule Under Transitivity Constraints

Author

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  • V. J. Bowman

    (Carnegie-Mellon University and The University of Pittsburgh)

  • C. S. Colantoni

    (Carnegie-Mellon University)

Abstract

In this paper we are concerned with imposing constraints directly on the admissible majority decisions so as to insure transitivity without restricting individual preference orderings. We demonstrate that this corresponds to requiring that majority decisions be confined to the extreme points of a convex polyhedron. Thus, transitive majority decisions can be characterized as basic solutions of a set of linear inequalities. Through the use of a majority decision function (which is not restricted to be linear) it is shown that constrained majority rule is equivalent to an integer programming problem. Some special forms of majority decision functions are studied including the generalized l p norm and an indicator function. Implications of an integer programming solution, including alternate optima and post optimality analysis, are also discussed.

Suggested Citation

  • V. J. Bowman & C. S. Colantoni, 1973. "Majority Rule Under Transitivity Constraints," Management Science, INFORMS, vol. 19(9), pages 1029-1041, May.
  • Handle: RePEc:inm:ormnsc:v:19:y:1973:i:9:p:1029-1041
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    File URL: http://dx.doi.org/10.1287/mnsc.19.9.1029
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    Cited by:

    1. Alfonso D'errico, 1994. "Una funzione ordinale di benessere sociale," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 17(1), pages 19-33, March.
    2. repec:spr:orspec:v:39:y:2017:i:3:d:10.1007_s00291-017-0477-z is not listed on IDEAS
    3. Tavana, M. & Kennedy, D. T. & Joglekar, P., 1996. "A group decision support framework for consensus ranking of technical manager candidates," Omega, Elsevier, vol. 24(5), pages 523-538, October.
    4. Michael Brusco & Hans-Friedrich Köhn & Stephanie Stahl, 2008. "Heuristic Implementation of Dynamic Programming for Matrix Permutation Problems in Combinatorial Data Analysis," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 503-522, September.

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