>> ballot to legally equivalent votes. The reduced set is this: >> >> A >> B >> C >> A>B >> A>C >> B>A >> B>C >> C>A >> C>B >> >> Note that this assumes a 2-rank ballot. > > no, it can be a 3-rank ballot where the voter declines to rate their > last choice. "3rd choice" is left unmarked. > >> It also assumes that majority vote isn't important. > > bullshit. it (the number of consequential ballot permutations) has > nothing to do with it (whether or not majority vote is important). > >> If it's important, as it would be in an IRV election under Robert's >> Rules, we have some more possibilities. They are all the three-rank >> permutations. >> >> A>B>C >> A>C>B >> B>A>C >> B>C>A >> C>A>B >> C>B>A >> >> >> Well, I won't speak about Kathy, but in terms of practical >> elections in the U.S., she's right. You did not state enough >> information to establish your reduced count, ... > > yes i did state enough information. may i remind you? i said that > there is *no* consequential difference in these two marked ballots > (in the case of N=3). there is no consequential difference between a > ballot marked A>B to one marked A>B>C . there is no election > scenario, whether it's IRV, Condorcet, Borda or any other method > using ranked ballots that will count those two ballots differently. > there is no need to separate the A>B and A>B>C into two piles.
OK. I understand now why you are confused Robert: 1. on the formula for the number of possible unique candidate orderings for any rank choice voting method you incorrectly assume that the number of possible ballot rankings that a voter may fill out is always equal to the number of candidates running for office and so you can collapse "N" of the rankings, but this simply is not the case in US IRV elections and it would just be unnecessarily confusing to collapse rankings for the special (and unusual) case when there are three candidates and three rankings, when a more general formula that always applies to all situations regardless of the number of candidates and allowed rankings could be used; and 2. on the fact that IRV and Condorcet must be reported similarly and counted similarly, because there are different methods available to count each one. With Condorcet, you can easily count it with an NxN matrix and you cannot count IRV that way at all generally (although I wouldn't put it past you to find an unusual special case where you could). With IRV, you can count it (albeit not easily depending on the number of candidates) with sorting into piles, but you cannot count Condorcet method that way. You can count either Condorcet or IRV by sorting into unique vote orderings, as I gave you the general formula for that works in all cases earlier. However that would be a very difficult and time-consuming way to count Condorcet since Condorcet is precinct-summable in the far simpler n x n matrix. It is the only way to make IRV precinct summable using the formulas I gave you earlier or you can look them up in my IRV report, unless you want to publicly report all voters' individual choices. Minneapolis chose to use the first method. I.e. The counting methods available and ideally used for Condorcet and IRV are different. -- 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