[EM] number of ways to vote a ranked ballot.

Rob LeGrand honky1998 at yahoo.com
Mon Apr 30 13:31:23 PDT 2001

Martin wrote:
> Ok, if there are n candidats then there are n! ways to vote a fully 
> ranked ballot, and {int(e x n!)} ways to vote a truncated ballot, or 
> {int((e-1) x (n!) - 1)} ways if you count votes like A>B>C(>D) as 
> equivalent to A>B>C>D. All this I've found out by reading around 
> websites and such.
> However, I can't seem to find anywhere which says how many ways there 
> are to vote a ranked ballot which allows draws in arbitrary places, and 
> I can't see any way to work it out. Any maths/stats people here know 
> what the answer is, or where I might find out?

I haven't been able to figure out a simple general formula, but here are my
results for up to 6 candidates:

candidates:          1    2    3    4    5    6
possible ballots:    1    3   13   75  541 4683

Rob LeGrand
honky98 at aggies.org

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