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Majority Rule Under Transitivity Constraints

Author

Listed:
  • 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
    DOI: 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. Irène Charon & Olivier Hudry, 2010. "An updated survey on the linear ordering problem for weighted or unweighted tournaments," Annals of Operations Research, Springer, vol. 175(1), pages 107-158, March.
    3. Akram Dehnokhalaji & Pekka J. Korhonen & Murat Köksalan & Nasim Nasrabadi & Diclehan Tezcaner Öztürk & Jyrki Wallenius, 2014. "Constructing a strict total order for alternatives characterized by multiple criteria: An extension," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(2), pages 155-163, March.
    4. Akram Dehnokhalaji & Behjat Hallaji & Narges Soltani & Jafar Sadeghi, 2017. "Convex cone-based ranking of decision-making units in DEA," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(3), pages 861-880, July.
    5. Kelin Luo & Yinfeng Xu & Bowen Zhang & Huili Zhang, 2018. "Creating an acceptable consensus ranking for group decision making," Journal of Combinatorial Optimization, Springer, vol. 36(1), pages 307-328, July.
    6. 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.
    7. Michael J. Brusco & Douglas Steinley & Ashley L. Watts, 2022. "Disentangling relationships in symptom networks using matrix permutation methods," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 133-155, March.
    8. 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.

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