[EM] number of possible ranked ballots given N candidates
Rob LeGrand
honky1998 at yahoo.com
Wed Dec 14 13:47:58 PST 2005
Paul Kislanko wrote:
> > > If equal ranknigs are allowed, it's N! + 2^N - 1
. . .
> No, it really is 2^N - 1, not 2^(N-1). It's the sum of the ways to
> select 1,2,...N-1 of N-1 choices for where an = sign can go.
Could you explain how you derived that formula? I don't think it gives
the correct result for N = 4. 4! + 2^4 - 1 = 39, but I think there are
73 possible rankings:
24 of the form A>B>C>D
12 of the form A=B>C>D
12 of the form A>B=C>D
12 of the form A>B>C=D
4 of the form A=B=C>D
4 of the form A=B>C=D
4 of the form A>B=C=D
1 of the form A=B=C=D
--
Rob LeGrand, psephologist
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/
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