# The number of weak orderings of a finite set

Article

DOI: 10.1007/s003550050123

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

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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(*log*2)^{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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© Springer-Verlag Berlin Heidelberg 1998