STAR-like method ("reverse STAR"?)
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Perhaps we can differentiate them like so:
star: top two runoff based on borda score and pairwise winner for the second round
dasgupta_maskin/one_by_one: 1/0.5/0 copeland with borda tiebreaker
reverse_star: 1/0/0 copeland with borda tiebreaker
black: simple condorcet with borda tiebreaker -
@culi In Borda, you can't skip ranks, but in reverse STAR (which could be called RATS), you can.
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@culi Well it isn't a Borda tie breaker, it is a Score tiebreaker. This method uses Cardinal ballots.
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This may be the fairest system I have ever heard of for a single winner.
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@jack-waugh Cool I'm not sure whether it is the absolute fairest but I like its balance of fairness (i.e. "one person one vote" or more accurately described as "everyone has equal voting power") and simplicity.
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@rob OK, I'll bite -- what do you think is fairer, and on what grounds?
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@jack-waugh My primary criteria for fairness is that each voter has equal pull. As you know, I've said the nearest to perfect example of this is voting for a number (such as temperature) and picking the median. If you translate that to single winner elections with a finite number of candidates, you want to make it "as Condorcet as possible." That is, you want to -- as much as possible -- ignore strength of preference. (because factoring in strength of preference incentivizes exaggeration, etc)
I have a suspicion, but I haven't confirmed it, that the "most Condorcet" method is the recursive IRV one I proposed. (https://www.votingtheory.org/forum/topic/276/recursive-irv) The deeper you recurse, the better. If you only do it one level deep, it is plain old IRV. Go one level deeper and it will make it Condorcet compliant. Go 3 or 4 levels deep, and, well, it will just keep getting more and more Condorcet-ish.
That said, this reverse STAR one is plenty good, simply by virtue of being Condorcet. A simple improvement (based on what I said above) would be to normalize the ballots of the members of the Copeland set prior to calculating scores, but that makes it more complicated and I think it is unnecessary.
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@jack-waugh said in STAR-like method ("reverse STAR"?):
@rob OK, I'll bite -- what do you think is fairer, and on what grounds?
You're saying it's the fairest. I think the onus is on you to justify that!
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Paul Cohen comments on this method (I had brought it to his attention (writing under my real name, William Waugh)). One can reply in the publication he uses if one is fast enough. After a certain timeout period, it becomes impossible to add a comment to a given article without supporting the publication with money. I don't know how many or few people read his posts.
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Maybe it should be called "LLull Then Score", abbreviated LLTS.
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@jack-waugh He doesn't seem to understand the basics.
He says "it seems quite likely that Condorcet scoring would only result in the continuation of two-party politics," but doesn't really give any reason for coming to this conclusion.
He previously noted "Consider that in a contest between only two candidates, it is unclear what advantage Condorcet voting might have, even over plurality voting." Well, yeah, of course. If only 2 candidates, making it ranked or Condorcet or anything else won't improve it.
But the point is that, under a better system (which could be this one, IRV, Approval, STAR, or whatever), the incentives change, especially in the long term. People more in the middle have far more incentive to run. There is less incentive to eliminate similar candidates via primaries or other party nomination mechanisms. Meaning it is far more likely to have more than two viable candidates.
Parties, and especially the two major parties, will remain an important force in political elections as long as there are plurality elections. Even if the current election is done via Condorcet, you can't 100% escape the influence of parties that are mostly incentivized due to the plurality elections that are still happening. But the more you have Condorcet elections (or STAR or IRV or whatever), the less the influence by the major two parties will be.
I believe this "vote splitting resistant" effect is strongest on Condorcet methods, but it is true for all of the above methods. If he doesn't understand how this would reduce two-party domination, I would suggest he needs to do some reading before he give hot-takes.
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@rob, yes, I started to argue with him in the same direction as yours, but instead of carrying the argument all the way through, I paused in the middle of it to see whether he was following me so far. He evidently has family trouble and has had to throttle his level of attention on my responses.
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@rob I repeat, however, that there is a time limit for appending comments.
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@jack-waugh yeah I started to reply there but it has a weird registration process that annoyed me. (it had a "register and post" button, but then complained I wasn't registered when I tried to use it). Also just an old site that looks like it's hardly used anymore. So I didn't bother.
Feel free to direct him here if you want to. (not that there's been a lot of activity here either)
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@toby-pereira said in STAR-like method ("reverse STAR"?):
You're saying it's the fairest. I think the onus is on you to justify that!
Compared to which alternative?
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@jack-waugh The "-est" suffix means compared to all alternatives.
But if you want a specific alternative to compare it to, I'd suggest recursive IRV, at a depth of at least 3.
All this hinges on a definition of "fair." To me the most fair method would give every voter equal influence on the outcome. But of course that's tricky to quantify as well.
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@jack-waugh said in STAR-like method ("reverse STAR"?):
This may be the fairest system I have ever heard of for a single winner.
Remember this is how it started.
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@rob said in STAR-like method ("reverse STAR"?):
To me the most fair method would give every voter equal influence on the outcome.
I am in emphatic agreement. I suspect the lack of this equality is a very key tool that the ruling class uses to keep the rest of us down. I do not know how to articulate the sufficient conditions for equality of influence. I believe that one of the necessary conditions, however, is Frohnmayer balance. Reverse STAR conforms to this. I believe that recursive application of Hare to a depth of three does not, although it may come quite close. I don't currently have a counterexample to display, but I don't see a proof that it conforms.
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@jack-waugh said in STAR-like method ("reverse STAR"?):
@rob said in STAR-like method ("reverse STAR"?):
To me the most fair method would give every voter equal influence on the outcome.
I am in emphatic agreement. I suspect the lack of this equality is a very key tool that the ruling class uses to keep the rest of us down. I do not know how to articulate the sufficient conditions for equality of influence. I believe that one of the necessary conditions, however, is Frohnmayer balance.
I haven’t seen a solid argument for why being “Frohnmayer balanced” automatically is better. There are many balanced methods that are terrible. But it, alone, shouldn't be the goal. A good method probably achieves it.
Vote splitting is the real enemy, and having it balanced (e.g. For and Against voting) doesn't eliminate vote splitting per se, but it tries to balance it between "clustering" vote splitting and "declustering" vote splitting. Clustering is what you get with plain old plurality, where you want to reduce similar candidates, incentivizing parties and primaries. For and against adds a declustering effect on top of that. But it's a fairly crude one, since it is still plurality.
As for recursive IRV, you could make it immediately Frohnmayer balanced simply by doing some sort of Borda count at the deepest level. I'd be willing to bet that, if you did, it would still converge to the same result. I will try it, though, it should be super easy to do.
I actually haven't “proven” anything regarding recursive IRV, but I do have it fully implemented now, thanks to a good bit of help from chatGPT, which made it so much easier. It's actually surprisingly fast, even when going way deeper than I'd expect is needed. I'd still like to build some sort of visualizer for it that's better than just a big dump of Json which is what I currently have.
However, although not a proof per se, I can walk through the logic a bit of why I think it is superior to anything else out there in terms of fairness. In general I will talk about it as if it recurses to Infinity, even though in practice, it should be completely unnecessary to go more than a couple levels deep for real world purposes.
First the background. We may all have different ideas of what fairness is, but to me it is all about removing vote splitting. Vote splitting is when irrelevant alternatives disproportionately draw votes away from relevant candidates. STAR, IRV, and Condorcet methods all attempt to remove irrelevant alternatives, but each have their flaws. With Condorcet methods, obviously there isn't always a Condorcet winner and that is the singular flaw (in that case, it “kicks the can down the road”, leaving you to find another way to settle who the winner is). With STAR, you're using score totals to guess what the irrelevant alternatives are, and that isn’t a lot more than a guess and is absolutely subject to vote splitting at stage one. With IRV you are using a process of elimination to estimate which are irrelevant. Since IRV depends on (inverse) plurality to determine who to eliminate, it also is subject to vote splitting at the elimination stage.
However, IRV, for all the complaints about it, does do one thing correctly, and that is that the process of elimination that it uses is always better than not using it, in terms of increasing the accuracy and resistance to vote splitting of the final result. That alone doesn't set it apart from other methods, but it just needs to be pointed out: process of elimination is always a good thing in terms of reducing the vote splitting effect, compared to using plurality directly.
And that last point is what recursive IRV taps into. If, in seeking a final winner, we get better results than plurality by using the process of elimination, why can’t we use the process of elimination to get better results than plurality for deciding who to eliminate? We’re always using plurality, but with each increased level of recursion, we are making it more indirect. The more indirect the usage of plurality, the better the result.
So recursive Irv, unlike every other voting method I know, can apply its effect over and over until we decide it's “good enough.” In that way, it’s analogous to how we address the computer science problem “binary representations of floating point numbers can never exactly represent certain numbers, like 1/3”. While true in theory, we can just add enough bits and the problem gets less and less significant. If 32 bit floats aren’t good enough, use 64 bit. If 64 bit isn’t good enough, use 128 bit. There is no limit to how many times you can increase the number of bits, and each time you, say, double them, the precision is increased by a predictable amount. It is a straightforward problem to increase the precision. While it has costs, obviously, you don’t need to reinvent anything if you need more precision, you just apply more of the same.
All my tests shows that recursive IRV will find a Condorcet winner, if they exist, very quickly. I’ve never seen it take more than one extra recursion level. But it doesn’t “seek out the Condorcet winner”, instead, finding the Condorcet winner is a byproduct of a process that makes the method more accurate, more resistant to vote splitting. But since that process still works in the absence of a Condorcet winner, we have something that never has to fall back on some ugly and imperfect kludge.
