Rank with cutoff runoff 2.0
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A ranked ballot is submitted with a support cutoff, where unsupported candidates can also be ranked. The top two supported candidates are put head-to-head in a majoritarian runoff based on the rankings. The loser of the runoff is eliminated, and the process repeats until one candidate remains.
Does anybody see an obvious or non-obvious issue here? I’m sure there is something. I think it satisfies independence of clones, but I think it’s probably not Condorcet compliant. However, it could easily be made Condorcet or Smith (or Landau) compliant by first restricting to the chosen set.
I can imagine a seemingly unlikely “stair-case” situation where the top supported candidate is consistently defeated in successive runoffs, but restricting to the chosen set first might mitigate some of that kind of thing.
score-stratified-condorcet [10] cardinal-condorcet [9] ranked-condorcet [8] score [7] approval [6] ranked-bucklin [5] star [4] ranked-irv [3] ranked-borda [2] for-against [1] distribute [0] choose-one [0]
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Top two, by what measure?
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@jack-waugh quantity of support, I’m sorry I could have said “approval” and “approved” but I have a philosophical aversion to the connotation of the word.
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It seems odd to consider for elimination first, the candidates supported by the most count of voters. Why not start with the bottom two?
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@jack-waugh that’s something that crossed my mind as well, you might be right about that. The reason I went there was that I was thinking of clone candidates at the top. I figured an “elimination from the top” would force the top supported “faction” to effectively (not exactly) indicate a single “top” representative, who would be put head-to-head with the second top-supported faction’s top choice.
I think it’s really similar to IRV, but there are fewer moving parts. Another thing I thought about was just Landau//IRV, which in itself is fairly similar but has a more finalizing mechanism earlier in the runoff sequence.
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If either of these systems is F-balanced, the obvious candidate for an antivote would reverse the rankings and put the support cutoff at the corresponding place. And I think that does indeed provide balance. This is assuming that if equal-ranking is permitted at the bottom (sludge), it is also permitted at the top (cream).
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@cfrank, I think that ideal systems do not force a voter to find and conspire with her faction in order to have political power.
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@jack-waugh that makes sense, and I do think that kind of balance does work out. If two ballots have rankings reversed and the corresponding inverse support cutoff placed between the same two candidates, I think the net result of both ballots is neutral. This does mean that balance becomes generally less meaningful as there are more candidates who aren’t consistently supported or unsupported.
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@jack-waugh ah yes, I didn’t mean that the factions would literally conspire to support only or mostly a single candidate, or even that they would recognize themselves. What I meant is that if there are two clones with top support, they can’t crowd out the election, because the one who loses the runoff will get eliminated, and the other will still have to beat out the next top-supported candidate. This is what enables independence of clones, but I think it could also work from the bottom-up like you mentioned.
For example, if a plurality faction supported two clones A and A’, and conspired to rank A>A’, this ultimately would amount to them having supported only A. The remaining top faction might have candidate B as their top support, and A would need to beat B in a majoritarian rank runoff in order to win.
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@cfrank said in Rank with cutoff runoff 2.0:
I think the net result of both ballots is neutral.
To prove that, we can consider absolute scores for support and pairwise scores for preferences.
Antivotes support complementary sets of candidates. This just biases up all the support scores, which has no effect on the determination of the top (or bottom) two.
For each pair of candidates, antivotes balance in the preference score for that pair, so taken together, the two votes have no net effect on decisions based on preferences during the tally. QED
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Do you want to permit equal ranking everywhere?
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@jack-waugh yes, although perfect alignment of the support cutoffs becomes a priori less probable with more candidates, ignoring political spectrum forces.
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@jack-waugh I think it only makes sense to permit equal rankings between mutually supported or mutually unsupported candidates. If you’re indifferent between two candidates, there is no reason you should support one over the other. Every unsupported candidate must be ranked lower than every supported candidate.
It is possible I suppose to support every candidate, and also not to support any candidate. Between the two there isn’t any effective difference, since only the ranking will have any influence over the result. With either style somebody could indicate indifference between every pair of candidates, and in that case they might as well just not have voted.
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I think these are Condorcet compliant. If there is no Condorcet winner, the support aspect will determine the order of eliminations. But if there is a Condorcet winner, the order of the eliminations doesn't matter.
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@jack-waugh it is certainly Condorcet (or any other rank-criterion) compliant if the candidate pool is restricted according to the rankings even before the support-based runoff sequence begins.
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@cfrank said in Rank with cutoff runoff 2.0:
restricted according to the rankings
How does that work?
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@jack-waugh before considering the support aspect, you could just ignore all candidates who are not in the Smith or Landau set, for example. This is maybe peculiar though, since in principle it makes it possible that the winner is a candidate who doesn’t have much support at all. And this is perhaps a fair argument against the Condorcet criterion when certain additional information is provided.
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Unless I am mistaken, no restriction is necessary and the system will still find the Condorcet winner if there is one, just like Llull's last system. Any order of elimination would do this.
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@jack-waugh you’re right. No matter what, the runoff will eventually eliminate anybody who is not the Condorcet winner if one exists. It should also eliminate any Condorcet loser. It still leaves open the possibility of electing a candidate with low support, even if they are the Condorcet winner.
Maybe that’s fine? I’m sticking with the philosophy of “if people prefer something else, they should say so.” Aka, they should on the whole provide candidates that represent their preferences and fill the spectrum of feasible options, rather than relying on gamified quantifications of how much they prefer one thing over another.
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Moved from Single-winner by
SaraWolk