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The number of weak orderings of a finite set

Author

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  • Ralph W. Bailey

    (Economics Department, University of Birmingham, Birmingham B15 2TT, UK)

Abstract

The number of Arrovian constitutions, when N agents are to rank n alternatives, is p(n)p(n)N, where p(n) is the number of weak orderings of n alternatives. For n\leq15, p(n) is the nearest integer to n!/2(log2)n+1, the dominant term of a series derived by contour integration of the generating function. For large n, about n/17 additional terms in the series suffice to compute p(n) exactly.

Suggested Citation

  • Ralph W. Bailey, 1998. "The number of weak orderings of a finite set," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(4), pages 559-562.
    • Handle: RePEc:spr:sochwe:v:15:y:1998:i:4:p:559-562
    Note: Received: 29 May 1995 / Accepted: 22 May 1997
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    Cited by:

    1. Hanna Bury & Dariusz Wagner, 2009. "Group judgement with ties. A position-based approach," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 4, pages 9-26.
    2. Campbell, Donald E. & Kelly, Jerry S., 2004. "Social choice rules with vetoers," Economics Letters, Elsevier, vol. 82(2), pages 245-248, February.
    3. Echenique, Federico, 2007. "Counting combinatorial choice rules," Games and Economic Behavior, Elsevier, vol. 58(2), pages 231-245, February.
    4. Hanna Bury & Dariusz Wagner, 2009. "Group judgment with ties. A position-based approach," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(4), pages 7-26.
    5. Cascón, J.M. & González-Arteaga, T. & de Andrés Calle, R., 2019. "Reaching social consensus family budgets: The Spanish case," Omega, Elsevier, vol. 86(C), pages 28-41.
    6. Rico, Noelia & Vela, Camino R. & Díaz, Irene, 2023. "Reducing the time required to find the Kemeny ranking by exploiting a necessary condition for being a winner," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1323-1336.

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