The number of weak orderings of a finite set

Ralph Bailey ()

Social Choice and Welfare, 1998, vol. 15, issue 4, 559-562

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.

Date: 1998-08-06
Note: Received: 29 May 1995 / Accepted: 22 May 1997
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