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The number of weak orderings of a finite set

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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≤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.

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Received: 29 May 1995 / Accepted: 22 May 1997

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Bailey, R. The number of weak orderings of a finite set. Soc Choice Welfare 15, 559–562 (1998). https://doi.org/10.1007/s003550050123

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  • DOI: https://doi.org/10.1007/s003550050123

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