robert bristow-johnson > Sent: Thursday, January 21, 2010 6:49 AM > but breaking it down to piles regarding every conceivable permutation > of candidate preference is *still* breaking it down to a finite > number of piles. for 3 candidates, that number is 9. if you or > Kathy say it's 15, then you're wrong (and it's your slip that's > showing). for 4 candidates the number of necessary piles is > 40. > for N candidates, the number of piles necessary, P(N) is > > N-1 > P(N) = SUM{ N!/n! } > n=1 > > not > > N-1 > P(N) = SUM{ N!/n! } > n=0
I do not intend to comment on your formula, but I calculate the numbers of possible unique preference profiles for increasing numbers of candidates (N) as follows: N Unique Preference Profiles 2 4 3 15 4 64 5 325 6 1,956 7 13,699 8 109,600 9 986,409 10 9,864,100 11 108,505,111 12 1,302,061,344 13 16,926,797,485 14 236,975,164,804 15 3,554,627,472,075 16 56,874,039,553,216 17 966,858,672,404,689 18 17,403,456,103,284,400 19 330,665,665,962,404,000 20 6,613,313,319,248,080,000 Where there are large numbers of candidates, the maximum possible number of unique preference profiles will be limited by the number of voters. Thus if there are 10,000 valid votes and 12 candidates, the maximum possible number of preference profiles would be 10,000 and not 1,302,061,344. In practice the actual number of preference profiles would be even lower, as significant numbers of voters would record identical patterns of preferences. Thus in the Meath constituency for the Dáil Éireann election in 2002 with 14 candidates (236,975,164,804 possibilities), there were 64,081 valid votes, but only 25,101 unique preference profiles. The Minneapolis STV (RCV) ballots were all hand sorted to unique preference profiles for each precinct and hand counted. This was unnecessary but feasible as the voters could not record more than three preferences (rankings), no matter the numbers of candidates. I understand the full preference profiles, probably at precinct level, will be published on the City website, but they are not there yet. James Gilmour No virus found in this outgoing message. Checked by AVG - www.avg.com Version: 9.0.730 / Virus Database: 271.1.1/2636 - Release Date: 01/21/10 07:34:00 ---- Election-Methods mailing list - see http://electorama.com/em for list info