OK James. As I said before, I agree with you that you were giving the total number of profiles *if* voters were allowed to rank all candidates, which they were not allowed to do in Minneapolis or elsewhere in the US public elections if I am right.
Further, I think that Robert is correct, that one could collapse the last N profiles into prior profiles if that is the system that is used (allowing ranking all candidates), although I do not think that gives any advantage, practically, to the counting process and may even complicate it. My formula provides the more practical number of how many profiles are allowed to be cast by voters and how many profiles are needed if one wants to count the number of votes cast for each profile and make IRV precinct-summable for an actual election. Obviously Condorcet counting methods are much simpler to make precinct-summable than IRV, requiring far fewer number of sums per precinct as the number of candidates increases. I think one thing that some election methods experts sometimes fail to consider are the election administration practicalities that are crucial to whether or not a method is functionally practical to provide public oversight over. I am fully aware that it is voting system technology, costs, and the increasing impracticality of manually auditing the election if the full range of preference profiles is allowed, if one is making an attempt to use paper ballots, that limits the number of choices a voter may fill out. I've studied this issue for 7 years now. Cheers, Kathy On Fri, Jan 22, 2010 at 4:08 AM, James Gilmour <[email protected]> wrote: > Kathy > I think my post made clear that I was referring only to "preference > profiles". I was not dealing with the situation where some > artificial, and highly undesirable, restriction had been placed on the > numbers of rankings the voters could mark. > > I think my comments about the counting procedure adopted in Minneapolis > should have indicated that I am well aware of the > restrictions that can be imposed. But note that in Minneapolis the > restriction was an artificial one imposed by the certified > counting machines available for use in the precincts. There is nothing in > the Minneapolis Election Ordinance that imposes such a > restriction. So when Minneapolis can obtain certified counting machines that > can deal with fully ranked ballots, there will be no > such restriction in practice. > > James > >> Behalf Of Kathy Dopp >> Sent: Friday, January 22, 2010 12:43 AM >> Subject: Re: [EM] IRV vs Plurality (back to the pile count controversy) >> >> >> James, >> >> Your formulas below are only correct in the case that voters >> are allowed to rank all the candidates who run for an >> election contest. That may be true in Australia, but is not >> true in the US where typically voters are allowed to rank up >> to only three candidates. >> >> I put the general formula that applies to *all* cases with n >> candidates and with r rankings allowed in my paper on IRV >> that I wrote a year or two ago: >> >> Realities Mar Instant Runoff Voting >> http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantR >> unoffVotingFlaws.pdf >> >> >> Because it's hard to write a summation, fraction formula, >> etc. here I'll let you look it up. It's on page 6 of the doc >> linked above. >> >> Cheers, >> >> Kathy >> >> >> >> > From: "James Gilmour" <[email protected]> >> > 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 D?il >> > ?ireann 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: 271.1.1/2637 - Release Date: 01/21/10 > 19:34:00 > > > -- Kathy Dopp Town of Colonie, NY 12304 phone 518-952-4030 cell 518-505-0220 http://utahcountvotes.org http://electionmathematics.org http://kathydopp.com/serendipity/ Realities Mar Instant Runoff Voting http://electionmathematics.org/ucvAnalysis/US/RCV-IRV/InstantRunoffVotingFlaws.pdf Voters Have Reason to Worry http://utahcountvotes.org/UT/UtahCountVotes-ThadHall-Response.pdf Checking election outcome accuracy --- Post-election audit sampling http://electionmathematics.org/em-audits/US/PEAuditSamplingMethods.pdf ---- Election-Methods mailing list - see http://electorama.com/em for list info
