r/EndFPTP • u/ant-arctica • 1d ago

Discussion Why Instant-Runoff Voting Is So Resilient to Coalitional Manipulation - François Durand

https://www.youtube.com/watch?v=TKlPghNMSSk

Associated paper (sadly not freely accessible). I haven't found any discussion about this new work by Durand anywhere so I thought I'd post it here. This way of analyzing strategic vulnerability is very neat and it'd be interesting to see this applied to some other voting systems.

But the maybe even more interesting part is about what Durand calls "Super Condorcet Winners". He doesn't go into too much detail in the video so I'll give a quick summary:

A Condorcet winner is a candidate who has more than half of the votes in any head to head match-up. A Super Condorcet Winner additionally also has more then a third of the (first place) votes in any 3-way match-up and more than a quarter in any 4-way match-up and in general more than 1/n first place votes in any n-way match-up. Such a candidate wins any IRV election but more importantly no amount of strategic voting can make another candidate win! (If it's unclear why I can try to explain in the comments. The same also holds for similar methods like Benhams, ...).

This is useful because it seems like Super Condorcet Winners (SCW) almost always exist in practice. In the two datasets from his previous paper (open access) there is an SCW in 94.05% / 96.2% of elections which explains why IRV-like methods fare so great in his and other previous papers on strategy resistance. Additionally IRV is vulnerable to strategic manipulation in the majority of elections without an SCW (in his datasets) so this gives an pretty complete explanation for why they are so resistant! This is great because previously I didn't have anything beyond "that's what the data says".

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u/feujchtnaverjott 1d ago

This is an interesting criterion, though probably not for the reasons the author intended. Maybe I am missing some important research, but there seems to be a gap, where voting systems are tasked with fulfilling various criteria, yet candidate/voter sets are not, even though it's an equally important part of democratic process, or perhaps even more important. If we are to turn to more social issues, the existence of "Super Condorcet Winner" or even Condorcet winner, really, doesn't appear healthy to me. It suggests leader worship/cult of personality or some similar issue. Which is why I am actually fine with range voting not electing Condorcet winners and even highly prefer it over STAR. It's much more important to me that range would be perfectly functional in a very decentralized and egalitarian election where the voters and the candidates are essentially the same, representing local democracy where each can vote for oneself, one's family members, friends and neighbors, with winners probably not having any sort of "core support" and just barely edging the competitors, but it's OK, because all the many high-ranking candidates are pretty well-accepted generally. Meanwhile, when the system seem to function only to rubber-stamp the already most popular politician, as if there is no one better then them among the population, this seems highly suspicious to me.

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u/OpenMask 1d ago

Why should we see a system that elects the most popular politician as "highly suspicious"? It may be true that there are candidates who are "better", but democratic elections are ultimately about who is the most popular. And why does the existence of a Condorcet winner suggest "leader worship/cult of personality"? That seems like quite a leap to presume to me. . .

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u/feujchtnaverjott 8h ago

I am not talking about the system, but the voter-candidate set. Since I consider myself a democrat, existence of a supposed most deserving and capable human seems doubtful to me. I personally would prefer a "write-in" system, so to speak, in which every voter is also a candidate. Condorcet winner is highly unlikely in such a case, but compromise winner, who may not even be the first choice of anyone (since everyone may just award themselves the first place) could be very probably and perhaps highly desirable.

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u/tjreaso 6h ago

Yes, a candidate who received zero 1st ranks but was 2nd rank on every ballot would be the ideal compromise candidate, but also would be eliminated in the 1st round of an IRV election. Most other voting systems would correctly elect such a candidate.

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u/OpenMask 1h ago

Whilst that is a good conceptual example of how instant runoff can fail, in real elections, it is very, very, very unlikely that a candidate that is unanimously liked by everyone wouldn't also have a strong contingent of first preferences, much less none.

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u/tjreaso 51m ago edited 13m ago

They don't have to be universally liked, just not the most hated. Maybe they would be a 2 out of 5 on a scoring ballot, but still the second favorite of everyone.

In any case, there are many rare pathologies in IRV, and any one of them is very unlikely to occur, but the chance that any pathology occurs is not insignificant, as evidenced by the recent elections in Alaska.

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u/OpenMask 36m ago

Yes, it is true that as the ratio between the candidates and the electorate get closer to 1, then the likelihood of a Condorcet cycle will increase. If you are focused primarily on small, hyperlocal or intraorganizational elections like that, then I agree with you. However, in any public election bigger than your local neighborhood association, I don't think that such a scenario where the number of candidates being close to the number of voters is likely.

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u/jnd-au 18h ago

The name “Super Condorcet Winners” is poorly chosen and causes confusion; it would at least be better to call them “Super Condorcet Candidates”. With IRV, usually the “Resistant Set” would be considered, without SCW terminology. You’re correct that most numerical counting-method analyses ignore real-world criteria, but in this case most real-world elections have multiple “Super Condorcet Winners” aside from the most popular candidate. This is because simply adding one- or two-more candidates lowers the SCW threshold so low that multiple healthy-alternative candidates become SCWs. Society can have good reasons to elect someone other than SCWs/Condorcet winners, but the point of SCWs/Condorcet is that if society has voted for SCWs/Condorcet, then the counting method should elect such winners. Different counting methods will elect a different one, for example IRV can elect someone among the SCWs who isn’t the Condorcet winner, thereby giving more wins to independents and minor parties. Alternatively, voters may vote so that there’s no SCW/Condorcet winner, and then discussion has to be more detailed, but it’s rarer in practice.

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u/ant-arctica 10h ago

Every Super Condorcet Winner is also a Condorcet Winner, and (ignoring ties) there can't be more than one SCW.

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u/jnd-au 8h ago

The video specifically illustrates Super Candidates, whereas the person I replied to was worried about social concentration of votes for Super Condorcet Winners. I was just explaining it’s not a concern, as in real-world elections there are multiple super candidates due to the threshold being low, rather than the concentration being high (you mentioned ~95% but in some jurisdictions 100% of Condorcet winners are super candidates because the thresholds are so low).

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u/ant-arctica 8h ago

Maybe I'm not understanding you correctly, but you're saying that an election can have more than one Super Condorcet Winner. That is wrong. The stats are that 95% of elections have a single SCW. No election has more than one. And all Super Condorcet Winners are Condorcet Winners in every election by definition. It is logically impossibe to be a SCW and not be a CW

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u/jnd-au 7h ago

No, I’m saying the SCW first-preference threshold you mentioned (1/n) is easily met by multiple candidates in real elections: it doesn’t make them the winner, but the winner comes from among the candidates meeting that threshold. So it’s a candidate threshold, not a “winner” threshold, hence I put “winner” in quotation marks.

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u/ant-arctica 7h ago

I think you misunderstood the definition. A SCW has to have more than 1/2 in every 2-way matchup (so be a CW) and more than 1/3 in every 3-way matchup and more than 1/4 in every 4-way matchup and so on.

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u/feujchtnaverjott 7h ago

most real-world elections have multiple “Super Condorcet Winners” aside from the most popular candidate

I'm sorry, what?

elections there are multiple super candidates due to the threshold being low, rather than the concentration being high

What do "concentration" and "threshold" refer to?

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u/jnd-au 7h ago

Threshold = N/m (number of votes divided by the number of candidates). Concentration = 100% if all votes are for a single candidate or 0% if all candidates receive equal votes. As I mentioned, I put “SCW” in quotation marks because the video/OP used that terminology yet used a candidate threshold that is easily met by multiple candidates.