I like this method, and would like to discuss the behavior with the simple three-candidate "center squeeze" scenario, as compared to IRV.
If IRV falls victim to center squeeze, then the centrist candidate is candidate C in QR. Thus, for them to win, two things must happen: B has a majority win over A, and C over B. If you locate the three in one-dimensional issue space, and label the median voter X, this means something like the following: ...----B-C-X--A-----... If C is at the median voter, then they cannot win unstrategically, because whichever of the other two candidates is closer to the median will win both first preferences and pairwise against the other one. Thus, C must be on the same side of the median as B, in order to give A "more room" to win the first preferences. Can a truly-centrist (median) candidate win strategically? If C voters know how the other two candidates will fall in first preferences, their best vote for electing C will be C>B>A, even if their honest preference is C>A>B. Note that this is fundamentally a dangerous strategy, as, in order to work, it depends on B beating A; and so if C does not beat B, it helps the worst candidate B win the election. Thus, the A>C>B voters can spitefully defend against this by announcing their intention to bullet-vote for A. This defense means nothing to the honest C>B>A voters, who still prefer B to A; but it does deter strategic C>B>A votes from honestly-C>A>B voters. Thus, if the A voters' threat is plausible, a truly-centrist candidate is still vulnerable to center squeeze, and cannot win. So really, the advantage of QR over IRV is not so much in traditional center squeeze, as in "clonelike center squeeze". That is, where IRV (like closed primaries) often elects the more-radical of two near-clones, QR generally elects the more-centrist one. (Note that "DNA" analysis misses this point because it never includes both C>B>A and C>A>B preferences in the same scenario. I like the "DNA" idea, but this is its weakness.) JQ 2010/5/22 Kevin Venzke <step...@yahoo.fr> > Hello, > > I realized that QR can be generalized for any number of candidates and > still retain LNHarm, Plurality, and resistance to the usual type of > burial strategy. To me this makes the method surprisingly good. > > The philosophy is to elect the candidate with the fewest first-preferences > (think center-squeeze here) who has a very specific majority beatpath > to the first-preference winner. > > Here is the new definition: > > 1. Rank the candidates. Truncation is allowed. Equal ranking is not > planned for (but we could come up with something). > 2. Label the candidates A, B, C, ... Z in descending order of first > preference count. > 3. Let the current leader be A. > 4. While the current leader has a majority pairwise loss to the very > next candidate, set the current leader to the latter candidate. (In > other words step 4 must be repeated until there is no loss or no other > candidates.) > 5. Elect the current leader. > > Proof of LNHarm satisfaction: Let's say you were voting B>Y (retaining > the meaning of the alphabetical ordering) and you consider changing > your ballot to B>Y>M. The sole effect this may have is to create a > majority for M>L, causing L to lose. You didn't rank L, so you didn't > harm any higher preferences. (And if you had ranked L, then adding the > M preference could not have created a majority M>L. Also note that > adding preferences cannot reverse or remove any majorities.) > > Who wins instead? Let's talk about burial. Typically the concern is that > voters for a strong candidate will rank a weak candidate insincerely > high in an effort to make a strong competitor lose. For example, you > would vote A>C to confuse the method into defeating B and electing A. > In QR your added C preference can only help elect a candidate who was > even weaker (in first preferences) than C. This makes burial a useless > strategy for the largest factions. > > Proof of Plurality satisfaction (a second advantage over MMPO): If X has > more first preferences than Y has votes total, then Y can't have a > majority win over anybody and can never be the current leader. > > Monotonicity: We still have an unusual monotonicity problem in that a > candidate who lacks a majority over the candidate previous to him in > first-preference order, may wish he had received fewer first preferences > in order to sit behind a candidate that he did defeat (and who can > still provide the necessary majority beatpath to the top). He may also > wish he received *more* first preferences. Is it a wash? > > In any case, getting additional second or third (etc) preferences can't > hurt a candidate. > > QR doesn't satisfy Condorcet(gross) (i.e. a candidate with a majority > over every other candidate is not guaranteed to win unless he is one > of the top two candidates in first-preference order) but it does satisfy > Condorcet(gross) Loser. > > It doesn't satisfy minimal defense in general. A candidate barred > according to minimal defense can only win if he places first (since he > will be unable to take the win from any other candidate) and he does > not lose by a majority to second-place. (If the latter candidate is the > majority's common candidate under minimal defense, then the barred > candidate will lose.) > > It doesn't satisfy SFC generally (because a majority win is only enforced > against one other candidate) but it does work when the involved candidates > place first and second in some order. (If the suspected sincere CW is > A, then A has a majority over B and wins immediately; if the suspected > sincere CW is B, then B takes the win from A and B cannot lose it to > anybody.) > > Fairly obviously it satisfies Majority Favorite and Majority Last > Preference. It doesn't satisfy Majority for Solid Coalitions due to the > possibility that the majority's first preferences are so fragmented that > none of their candidates place first or second, and the necessary > beatpath is not created (B>A). > > Due to this it doesn't satisfy Clone-Winner. It may not satisfy > Clone-Loser either, since cloning a candidate could adjust the first- > preference order to the benefit of the clones as well as to their > detriment. > > (It's conceivable that another way of ordering the candidates could > preserve all the properties plus clone independence, but I'm not very > optimistic at the moment.) > > It should be clear that the method doesn't satisfy Later-no-Help. If you > change D to D>C you could change the winner from B to D. > > What remains is the criterion I defined in my method generator to > differentiate IRV from QR, which says that the largest faction's last > choice is never elected. I'm not sure how to reformulate it for more > than three candidates. > > When we are dealing with scenarios in issue space, the general behavior > of IRV is to remove tiny center candidate(s) (as well as other > miscellaneous losers) until all that's left are two enormous flanks, and > then we pick the lesser evil. > > With QR we hope to see one flank knock out its counterpart and "reveal" > additional preferences. We'd like to see our finalists near the median, > not the flanks. This can fail (imagine that the subsequent candidate > is further from the median). But a criterion would be based on the goals > of this approach. > > The MMPO (Minmax(pairwise opposition)) approach is basically similar, > and more successful theoretically, but the lack of structure creates > unacceptable oddities and also strategic vulnerabilities. > > The DSC (Descending Solid Coalitions) approach is also kind of similar, > though its focus on solid coalitions makes it less sensitive to majority > opinions. (A pairwise preference of dissimilar factions is not likely to > be counted.) It does satisfy nice criteria though (monotonicity, > participation, clone independence). > > Thanks for any comments. Hopefully I haven't made any errors. > > Kevin Venzke > > > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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