1. Voters can Prefer, Accept, or Reject each candidate. Default is
Accept.
2. Candidates with a majority of Reject, or with under 25% Prefer, are
eliminated, unless that would eliminate all candidates.
3. Tally "prefer" ratings for all non-eliminated candidates.
4. Find the leader in this tally, and add in "accept" ratings on
ballots that don't prefer the leader (if they haven't already been tallied).
5. Repeat step 4 until the leader doesn't change. The winner is the
final leader.

I earlier said that C would win in "PARFBC" in Chris's scenario. I was wrong, as Chris nicely pointed out to me privately: 43: A 03: A>B 44: B>C 10: C C is eliminated for having under 25% prefer, and so A wins. Honestly, I think that a scenario where the approval winner is eliminated on this basis is not very plausible. If 15 of the B>C voters switched to BC, then C would win. This switch would not stop B from winning if there were more A>B voters, so it's strategically safe; it's not hard to imagine that 1/3 of the honest B>C>A voters might vote like that either naively or strategically. 2016-11-09 10:09 GMT-05:00 C.Benham <cbenham@adam.com.au>: > *Envoyé le :* Lundi 7 novembre 2016 8h27 > *Objet :* [EM] Holy grail: PAR with FBC? > > Here's a new system. It's like PAR, but meets FBC, and deals with center > squeeze correctly in the few tricky cases where PAR doesn't. I'm > considering using the PAR name for this system, and renaming the current > PAR to something like "Old Par > <http://sr3.wine-searcher.net/images/labels/29/06/grand-old-parr-12-year-old-blended-scotch-whisky-scotland-10152906t.jpg>". > Meanwhile, the system below is temporarily called PARFBC > <http://wiki.electorama.com/wiki/PARFBC_voting>. > > > 1. Voters can Prefer, Accept, or Reject each candidate. Default is > Accept. > 2. Candidates with a majority of Reject, or with under 25% Prefer, are > eliminated, unless that would eliminate all candidates. > 3. Tally "prefer" ratings for all non-eliminated candidates. > 4. Find the leader in this tally, and add in "accept" ratings on > ballots that don't prefer the leader (if they haven't already been tallied). > 5. Repeat step 4 until the leader doesn't change. The winner is the > final leader. > > > > 43: A > 03: A>B > 44: B>C > 10: C > > No, PARHG (PAR Holy Grail) elects C here. > > > With default being "Accept", no candidate has a "majority of Reject" but > C has "under 25% Prefer" so is eliminated under rule 2. Then I suppose A > wins. > > If we assume that the truncators are giving "Rejects" to the > unrated/unranked candidates, then I suppose both A and B have a "majority > of Rejects" and so > none of the candidates are eliminated and then as you say C would win. (My > mistake was that I didn't notice B's "majority of Reject" so I thought that > C and > A would be eliminated). > > Have I now got this right? If so I'll correct my mistake on EM. > > Chris > > On 11/9/2016 5:07 PM, Jameson Quinn wrote: > > > > 2016-11-08 23:25 GMT-05:00 C.Benham <cbenham@adam.com.au>: > >> On 11/9/2016 8:35 AM, Michael Ossipoff wrote: >> >> (You wrote) : >> >> And it isn't clear to me that "wv-like strategy" is even something we >> should take if it was free. >> >> (endquote) >> >> In Benham, Woodall, ICT, & probably many or most pairwise-count methods, >> the CWs has no protection from burial, or even from innocent, non-strategic >> truncation. >> >> With wv-like strategy, truncation from one side can't take victory from >> the CWs & give it to the truncators' candidate. >> >> ...and plumping by the CWs's voters makes it impossible for burial to >> succeed. In fact, the mere threat of that plumping can deter burial. >> >> >> So to "protect" some candidate that some voters imagine is the sincere >> CW (when perhaps there is no sincere CW or some other candidate >> is the sincere CW) you want to have a "defensive truncation" strategy >> available* inside* a method with a very strong random-fill incentive? >> >> And you should add (and stress) that it needs plumping by *all *of the >> "CWs voters to make it impossible for burial to succeed", and not ,say, >> merely 93% of them (with the other 7% sincerely fully ranking): >> >> 43: A >> 03: A>B >> 44: B>C (sincere may be B or B>A) >> 10: C >> >> 100 ballots. C>A 54-46, A>B 46-44, B>C 47-10. Top Ratings A46 > B44 >> > C10. Approvals: C54 > A46 > B44. >> >> Here MDDTR (like MDDTA and WV and Margins and MMPO and Jameson's latest >> "holy grail") all elect the possibly burying voters' favourite, B. >> > > No, PARHG (PAR Holy Grail) elects C here. > > >> >> Viewing the ballots from the top, A is the strongest candidate (and >> possibly the sincere CW) and viewing the ballots from the bottom C is the >> strongest candidate. And electing B is simply a very bad (and flagrant) >> failure of Later-no-Help. And B is both pairwise beaten and positionally >> dominated by A. >> >> So I can't accept any method that in this scenario elects B. >> >> Chris Benham >> >> >> >> >> >> >> >> ---- >> Election-Methods mailing list - see http://electorama.com/em for list >> info >> >> > No virus found in this message. > Checked by AVG - www.avg.com > Version: 2016.0.7859 / Virus Database: 4664/13373 - Release Date: 11/08/16 > > >