[EM] number of possible ranked ballots given N candidates

[Rob LeGrand]

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/

__________________________________________________
Do You Yahoo!?
Tired of spam?  Yahoo! Mail has the best spam protection around 
http://mail.yahoo.com