From: Arthur Keller <arthur_at_kellers_dot_org>

Date: Thu Apr 29 2004 - 13:00:45 CDT

Date: Thu Apr 29 2004 - 13:00:45 CDT

At 1:42 PM -0400 4/29/04, David Mertz wrote:

*>On Apr 29, 2004, at 12:25 PM, Arthur Keller wrote:
*

*>>Since ranked preference voting says: A, B, C is different than B,
*

*>>A, C, there are more than 6 possible vote combinations for 3
*

*>>candidates. (ABC, ACB, BAC, BCA, CAB, CBA are the full ones; also
*

*>>A, B, C, AB, BA, AC, CA, BC, CB, and no choices selected. Wow,
*

*>>that's 16 choices. Does someone have a formula in closed form for
*

*>>the number of possible rankings for n candidates?
*

*>
*

*>Well... you've already almost given it:
*

*>
*

*>for
*

*> M = Number of Candidates ;
*

*> N = Maximum number of slots ;
*

*> P(N/M) = Permutations of N out of M = M!/(M-N)! ;
*

*>
*

*>V(N/M) = Possible votes =
*

*>
*

*> /.---- \
*

*>| \ |
*

*>| / P(X/M) | + 1
*

*>| '---- |
*

*> \ X=1 to N /
*

*>
*

*>
*

*>You'll need to look at my ASCII art in a fixed font to see it right.
*

OK, I converted it to Courier. Since you like to have fun with math,

how about giving us a table for values of M from 1 to 10. Thanks.

Best regards,

Arthur

-- ------------------------------------------------------------------------------- Arthur M. Keller, Ph.D., 3881 Corina Way, Palo Alto, CA 94303-4507 tel +1(650)424-0202, fax +1(650)424-0424 ================================================================== = The content of this message, with the exception of any external = quotations under fair use, are released to the Public Domain ==================================================================Received on Fri Apr 30 23:17:23 2004

*
This archive was generated by hypermail 2.1.8
: Fri Apr 30 2004 - 23:17:29 CDT
*