Direct Independent Condorcet Validation
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Do you think that Approval-seeded Llull adequately addresses the concern?
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@jack-waugh can you link me to that? I think the only way to address this concern fully would be to do a second, final, independent vote between two candidates, one of whom is the computed Condorcet winner if possible. The rationale is that this is the only possible way to actually test the status of the computed Condorcet winner. Unfortunately it isn’t a complete test, in that it only has a chance of refuting the computed Condorcet winner’s status and cannot confirm it, but at least it’s a test.
If the computed Condorcet winner wins the runoff as expected, that’s evidence supporting their computed status. Otherwise, if the computed Condorcet winner loses the runoff, that’s irrefutable evidence that they were not actually the honest Condorcet winner. For example, if this kind of head-to-head had been performed in Alaska 2022, it’s possible that the IRV winner could have actually beaten out the purported Condorcet winner head-to-head, and that would dismantle all arguments as to his status.
It doesn’t have to be score or approval per se either, any non-Condorcet method would work. More generally, we could have a Condorcet compliant method pitted against a Condorcet non-compliant method to select two front runners, and then do a second independent head-to-head vote.
Furthermore, secondary voting could be on a totally opt-in basis, where voters can choose to keep their preference as stated on their original ballot by default. That way, honest voters will never actually need to worry about the second round. Voters would be disallowed from revoking their ballots altogether, preventing strategic abstention.
A final interesting note is that any voters who choose to change their ballot essentially admit to having voted tactically.
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Approval-seeded Llull:
Ballots: voters classify each candidate as good or bad, and within each of those classes, they rank the candidates, with equal ranking permitted.
Tally:
First, the tally orders the candidates by how many "good" classifications they got from the voters. The candidate that got the most goes at the top.
Next, the tally compares the bottom two candidates on the list with regard to how many voters ranked one over the other minus how many ranked them in the opposite order. The loser of this comparison is stricken from the list.
The tally repeats the bottom-two comparisons until only one candidate remains; this is the winner.
Discussion:
Approval-seeded Llull is an hybrid rating-ranking system. The rankings are less tightly coupled to the ratings, as compared to how tightly they are coupled in STAR.
Why this might solve the problems you bring up:
There is no incentive to warp the ranking aspect for a strategic motivation coming from the rating aspect of the tally, nor vice versa (maybe?).
Example application to a real political controversy: Consider the 2024 US Presidential election. A voter would not have to classify Ms. Harris as "good" to rank her over Mr. Trump. They could receive the same rating but different rankings. Trump would have been less likely to win, I think, than he would have under STAR, because with STAR, voters who could not bring themselves to give Harris even a 1, on the grounds that she supports the elimination of every Arab in Gaza, would thereby be forced into not ranking her above Trump.
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@jack-waugh hm I quite like this in theory. I’m also recollecting that multi round systems tend to fail independence of clones. In principle, approval-seeded Llull could be made more robust by considering larger sets of the lowest-approved candidates and iteratively removing Condorcet losers.
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How large? What would be a good name for the resulting system? Would it address your original concerns equally so well as a second polling would?
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@jack-waugh I think I may have proved that the recursive bottom N runoff and ordinary bottom 2 runoff are equivalent: https://www.votingtheory.org/forum/topic/564/bottom-n-and-bottom-2-runoffs-are-equivalent
So actually it may make no difference, which would nice to know.
But I think maybe the concept of a second independent runoff is too complicated… I just got a bit hung up thinking about how the Condorcet winner as computed might not actually be the “real” Condorcet winner.
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A real runoff is not complex to understand, at least in principle. Do you think that actually running one could produce a more accurate result than would be produced by the best of systems (like approval-seeded Llull, for example) that perform "instant" runoff rounds of tallying, but do not require the voters to return for a second polling?
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@jack-waugh I agree it isn’t too complex to understand, it could also be made more convenient by setting defaults. I’m actually more concerned with failing independence of clones. But I’m not sure—is it even true that this kind of runoff actually would fail independence of clones? Only the Condorcet and score winners could be pitted against each other, and those are both (roughly) clone independent methods.
I think a real second runoff would only matter in cases where voters were employing tactics. Otherwise, probably we should elect the Condorcet winner (IMO).
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So, to make a more concrete proposal for how to narrow the field to two finalists, we could say collect Score-style five-star ballots, and present the Score winner as one finalist, and do something like Copeland to get the other finalist, who would be the calculated Condorcet winner if there is one, and would be otherwise pretty good as determined by Copeland-like techniques in the absence of a Condorcet winner.
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Or how about use the Score winner as one finalist, and the Minimax winner as the other.
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@jack-waugh exactly, that's the kind of thing I'm considering. Now I'm kind of puzzled though about whether a head-to-head between two winners of clone-independent methods can fail independence of clones. I actually don't think it's possible that the composite system fails independence of clones. FYI my preference for a Condorcet method would be Tideman's Bottom 2 Runoff (B2R), which I'm now certain is equivalent to BNR. For example, we could even pit the Approval winner against the B2R winner head-to-head. That would be a form of Approval-seeded Llull with a final independent head-to-head.
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If you're pitting the winners of two methods against each other, what do you do if it's the same candidate? Are they just the winner, or does there need to be a final head-to-head between two candidates?
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I suspect that the tightness of coupling between the rating part and the ranking part is a problem with these schemes. The first ballot should have separate sections (or "races" in the terms of bettervoting.com) for rating and ranking, if we want the absolute peak of accuracy.
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@toby-pereira I would say they are declared the winner if the methods coincide. Otherwise there may be potential clone issues. It’s also simpler that way. Although if we did have an unambiguous runner up, that would be preferred to validate any potential Condorcet winner status. For example, the second highest scorer.
But if we wanted the decision process to be consistent, that has the potential to cause a recursion of successive head to heads, say, if the two methods repeatedly coincide. Unlikely but still. That would probably be the “right” way to do it in this context.
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@jack-waugh I’m not sure, I think coupling encourages consistency, which is a prerequisite to honesty. The coupled structure is also simpler and more efficient. The score winner is not necessarily the Condorcet winner for instance, and need not be the winner of a Condorcet compliant method when the Condorcet winner doesn’t exist (e.g. B2R).
The same validation logic also works in a homologous sense for Smith compliance. I think it’s less flexible if for instance two divergent Smith compliant methods were pitted against each other in the absence of a Condorcet winner. In that instance though, the Condorcet winner could not be tested with the final head-to-head. I’m not sure about extending to particular special subsets of the Smith set in the same way, depending on the subset.
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@cfrank I honestly think that Trump and Harris deserve prison for life for supporting the killing of 17,000 Arab children. In a rating system, they both deserve the bottom rate. But on the ranking side, I would put Harris above Trump, because of his domestic fascist tendencies. Coupling would prevent honesty.
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@jack-waugh I see to an extent, but I would argue that your collapse of rankings is incompatible with the distinction by score. You prefer one to the other, even if they are both horrible, right?
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@cfrank Consider a score system with a range of 0 through 5 by 1. Giving Harris a 1 would raise her chances of beating, say, Stein, who gets a 5 from me.
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@jack-waugh but that’s always the tradeoff with score systems, which is why people bullet vote and/or min-max (translate to approval). I totally understand what you’re saying though.
I’m not saying the “Condorcet adversary” should be the score winner, just that they should be a strong alternative. Your approval-seeded Llull ballot could accommodate an approval winner as the Condorcet/Smith-method’s adversary, for example.
I think a “rank with approval cutoff” ballot makes sense. Then there could be the approval winner, and, say, the B2R (Smith compliant) winner, followed by an independent head-to-head.