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Note--A Note on Majority Rule under Transitivity Constraints

Author

Listed:
  • J. M. Blin

    (Northwestern University)

  • A. B. Whinston

    (Northwestern University)

Abstract

In a recent paper [Bowman, V. J., C. S. Colantoni. 1973. Majority rule under transitivity constraints. Management Sci. 19 (9, May) 1029-1041.] Bowman and Colantoni have described an optimization model which they relate to problems of majority voting in the theory of social choice. Their optimization model was a linear integer programming problem. The purpose of this note is to indicate that an alternative view may be more useful viz. formulating the problem as a quadratic assignment type. We have discussed this in detail elsewhere [Blin, J. M., K. S. Fu, K. B. Moberg, A. B. Whinston. 1973. Optimization theory and social choice. Proceedings of the Sixth Hawaiian International Conference on Systems Science. Supplement on Urban and Regional Systems: Modelling Analysis and Decision Making. University of Hawaii.] and will limit ourselves here to some brief comments.

Suggested Citation

  • J. M. Blin & A. B. Whinston, 1974. "Note--A Note on Majority Rule under Transitivity Constraints," Management Science, INFORMS, vol. 20(11), pages 1439-1440, July.
    • Handle: RePEc:inm:ormnsc:v:20:y:1974:i:11:p:1439-1440
    DOI: 10.1287/mnsc.20.11.1439
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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.
    5. 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.
    6. Jean-Marie Blin, 1976. "Assignment Models in Voting Theory," Discussion Papers 237, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. 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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