The number of weak orderings of a finite set
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- Bailey, R. Soc Choice Welfare (1998) 15: 559. doi:10.1007/s003550050123
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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.