Excellent insights! Once again, thank you Kristofer for your wisdom. Richard Fobes The VoteFair guy On 2/10/2022 5:15 AM, Kristofer Munsterhjelm wrote: > On 09.02.2022 20:51, Richard, the VoteFair guy wrote: >> In the new "Hare clustering MAM-based PR, and a tie problem" thread, >> Kristofer Munsterhjelm wrote: >>> .... It's based around the idea of making a >>> number of virtual constituencies (one for each seat), and >>> then trying to allocate voters to each so that the case for >>> the winner (according to the Ranked Pairs method run in >>> that constituency) is as strong as possible, i.e. the >>> choice of winner or winning order is as justified as >>> it can be. >>> ... >>> Then both Kemeny and RP, in the absence of ties, calls an election by >>> producing the social ordering that maximizes its respective score >>> function. That is, Kemeny chooses the one whose sum of consistent >>> pairwise victories is maximized, and RP the one whose largest pairwise >>> victory is maximized, and among these, the one whose next largest >>> pairwise victory is maximized, and so on. >> >> Kristofer, what you're describing sounds similar to the STV version of >> VoteFair Representation ranking: >> >> https://electowiki.org/wiki/VoteFair_representation_ranking#STV_version > > It is, sort of, but I would say that there are some differences. > > - Your method is house monotone. Since the first seat is chosen with a > Condorcet method, it must therefore fail Droop proportionality, see > https://electowiki.org/wiki/Left,_Center,_Right. > > - The deweighting method seems a bit ad hoc, where it tries to reduce > the influence of voters who got the candidate they wanted, but uses a > heuristic to determine just who that is. In contrast, my method doesn't > make up its mind about who the first group of voters (who deserve the > first candidate) is, until it's done finding a candidate for that group; > and once it has done so, it knows exactly who they are. > > Your method seems more consistent with the Droop quota than the Hare > quota, as in: mine tries to find a group of voters, then remove them, > while yours tries to find a group of voters and then reweight them (like > ordinary STV). > > My method could be made Droop-style, and this would (I think) help > attenuate the tie problems. Instead of the LP step choosing a Hare quota > that's consistent with the defeat magnitudes locked in, it would choose > to magnify a group of voters' weights so that a Droop quota becomes a > majority. Then the mutual majority criterion of original RP (that Kemeny > also passes, by the way) would translate directly to the Droop > proportionality criterion. > > Let's say every voter's weight is 1 before we do reweighting, and there > are v voters in total. Then the Droop quota is v/(s+1), so suppose > everybody in this Droop quota gets a weight w, and everybody else > retains the weight of 1. Then we have > wv/(s+1) = 1/2 (wv/(s+1) + (v - v/(s+1))) majority blowup > which gives the solution w=s. > > So the LP would set: let each voter's weight be between 1 and s, so that > the total weight distributed is exactly 2sv/(s+1), and set the weights > so that the given pairwise preference's strength is maximized. This is > an additive weights solution, similar to Warren STV. Presumably > multiplicative weights (like Meek) are also possible, but this post is > already long enough :-) > > This attenuates tie problems because now the unweighted ballots have > some say in breaking the tie; the chance of a tie would be low even with > very small virtual constituencies because (in effect) the ballots who > are not participating help drag the outcome in their direction. > >> I added this section to Electowiki recently because there is growing >> interest in using STV to elect city councils, yet STV is overly >> simplistic, and has flaws similar to IRV flaws (especially ignoring >> valid ranking data that's very relevant). >> >> This STV version of VoteFair Representation ranking extends the two-seat >> version of it that I designed for partisan elections. The result is an >> STV-like non-partisan method. >> >> Of course it's based on the Kemeny method rather than Ranked Pairs. >> That's my bias for the reason you mention, namely that locking in a >> pairwise win can block additional info. This is similar to the way IRV >> blocks lower-ranked preference info from being looked at. > > Well, if you're willing to pay the NP tax, then Ranked Pairs can also be > made to optimize its particular metric. > > As for Kemeny vs RP, I would say that "taking into account every > candidate" sounds good, but if it's not done with proper insight, the > method can get confused about how much information is available to each > candidate. > > That's how Borda gets its teaming incentive: by cloning A, you make the > "weight of evidence" that's about A stronger, relative to the other > candidates, and so the method gets pulled in the direction of A. Because > Kemeny takes the sum of preferences, it's also vulnerable to this sort > of confusion. And sure enough, it's not cloneproof. > > In any case, the idea of my method is to generalize Condorcet methods > like RP to proportional representation in a way that's clearly based > around that Condorcet method and not on a candidate elimination method > (like IRV-based STV is). It doesn't *completely* satisfy this as winners > are still eliminated after winning, and so probably isn't monotone, but > there are no remnants of IRV left. And unlike Schulze STV etc., it's > polynomial time -- barely. > > (Now there's a thought: don't eliminate any candidates, but skip past > already elected candidates when choosing the winner for the kth > constituency based on its RP social ordering. It would probably still be > non-monotone, but it should be better behaved.) > > -km >