Social Choice and Welfare

, Volume 15, Issue 4, pp 559–562

The number of weak orderings of a finite set

  • Ralph W. Bailey

DOI: 10.1007/s003550050123

Cite this article as:
Bailey, R. Soc Choice Welfare (1998) 15: 559. doi:10.1007/s003550050123


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≤15, 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.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Ralph W. Bailey
    • 1
  1. 1.Economics Department, University of Birmingham, Birmingham B15 2TT, UK (e-mail: R.