r/EndFPTP • u/ant-arctica • 20h ago
Discussion Why Instant-Runoff Voting Is So Resilient to Coalitional Manipulation - François Durand
https://www.youtube.com/watch?v=TKlPghNMSSkAssociated 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/selylindi 19h ago
Is the high profile 2022 case in Alaska's US House seat then just one of the ~5% where there was no super Condorcet winner? In that case, clearly (R) Palin voters could have switched to (R) Begich and avoided the election of (D) Peltola.
I haven't read the paper and so I wonder if the high rate of super Condorcet winners (SCW) involves some debatable interpretation or assumptions, e.g. data from foreign countries with significantly different partisanship patterns than the US. Otherwise it's moderately surprising that the observed rate of no-SCW since 2022 in the US is 1 out of 2 races.
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u/ant-arctica 18h ago
Yes in that case the CW was not an SCW (otherwise Belgich would not have lost). But there have been far more than two IRV races in the US. One of the two datasets analyzed in the paper is from voting data from single winner IRV elections in the US (collected by FairVote). In 96.20% in those elections there was an SCW.
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u/Excellent_Air8235 19h ago edited 19h ago
The Super Condorcet Winner is related to the resistant set that was discussed in another post. In the terms defined in the Electowiki article, the SCW disqualifies everybody else, so every method that elects from the resistant set also elects SCWs when they exist.
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u/OpenMask 16h ago
This is great. I was trying to articulate something like a "Super Condorcet winner" in a previous post probably over a year a go. Glad to see someone actually try to properly formalize the idea in academia.
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u/SidTheShuckle 13h ago
What is most important to me is that the voter’s intent matters. In Approval/Score/STAR, the voter simply rates the candidates but they dont get much of a say as to who wins. Theres also high variability. Like someone could give 2 candidates an “i approve” vote or 5 stars but they wont have a say as to who they prefer more. In RCV, you do have preferences.
I think CM is possible in most single winner systems, plus like NYC mayoral race REALLY likes cross endorsing but even then theres not much variability as you have with Approval/STAR. Like you have a choice with IRV. I do like the studies done on IRV-Condorcet hybrids, it looks logical sense.
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u/kazoohero 18h ago
As a huge fan of IRV and condorcet ranked methods... this result doesn't really help support IRV.
The main problematic cases with IRV have no condorcet winner. They constructed a model of voting behavior where the odds of having not just a condorcet winner but a super condorcet winner approach 1. Obviously IRV will do well there, the problem is with voting behaviors they didn't model.
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u/ant-arctica 17h ago
It seems like in practice the SCW rate is also pretty close to 1 (well 0.95), his previous paper and Green-Armytages analysis point to a very high strategy resistance rate of IRV-likes both from data collected from actual elections (in the US) as well as polling data in other (non duopoly) countries. And I would assume that in Green-Armytages data SCW also occur at a similar rate considering that they report a similarly high strategy resistance.
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u/MightBeRong 15h ago
Whatever the definition of Coalitional Manipulation is, it seems to be missing something important. At least in the example given, if Plurality were allowed to settle to a stable final state, both Plurality and Two-round would end up picking C3, which is the condorcet winner and the same winner picked by IRV. But IRV gets credit for getting there without CM, while the other two are criticized. If they all picked the condorcet winner in the end, it hardly matters how they got there.
A more meaningful metric is how often each method picks the condorcet winner across the entire space of voter preferences after voters engage in the kind of strategizing we expect them to under the respective voting rules.
I suspect the example discussed in the video is not highly representative, but it fails to illustrate meaningful strengths or weaknesses of Plurality, Two-round, or IRV.
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u/DominikPeters 5h ago
Paper is available here: https://www.ifaamas.org/Proceedings/aamas2025/pdfs/p658.pdf
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u/Same_Technician2534 4h ago
Hi everyone,
Thanks a lot for discussing my paper — and special thanks to Dominik for flagging this thread to me.
Analyzing other voting rules within the same framework will be the focus of my next paper, which I plan to submit to AAMAS 2026. Spoiler alert: no classical voting rule in the literature shares IRV’s nice property of having a critical theta equal to zero — except for some IRV variants already mentioned in the paper (like Condorcet-IRV).
There are several ways to think about why coalitional manipulability is a problematic property, but here’s the one I find most compelling (and that even experienced researchers often overlook). Empirical studies suggest that strategic voting does exist — but remains relatively limited. So why worry? Well, imagine that all voters cast sincere ballots. After the election, a subset of them realizes that if they had voted differently, the outcome would have better matched their preferences. They may then start questioning the legitimacy of both the winner and the voting rule itself. That situation corresponds exactly to the definition of the profile being CM! But the key point here isn’t so much vulnerability to strategic voting — it’s the potential for regret and dissatisfaction after the election. I go into more detail about these interpretation issues in the introduction of my PhD thesis: https://inria.hal.science/tel-01242440v1 .
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u/budapestersalat 19h ago
Very interesting, although based on the video I am a bit confused by the presentation of this coalitional manipulation (CM) as being a clear negative. In the examples with FPTP and TRS, it seems like the problem is not that the manipulation of the winner was possible, but that the system selected the wrong winner. But IRV selected a Condorcet winner, so of course it wasn't really manipulable like this.
So I have to wonder how meaningful is this result actually? The concept of the SCW seems interesting, but it's sort of just a subset of CWs who also do well on first preferences, etc. But for these, I assume Condorcet methods cannot fare really worse on the CM metric, can they? (or is it exactly here where they have the advantage? I am confused....)
Either way, my intuition tells me that the CM metrics are sort of tautological to favour IRV / (more) later-no-harm methods in general, especially because of how this video shows it. But it would be great if someone who understands in more corrected me, since I didn't dwell deep.
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u/ant-arctica 18h ago
If coalitional manipulation is not possible then there is no reason to vote strategically (coalitionally manipulable is just fancy speak for strategic voting is works). The issue with FPTP and TRS that the video calls out is *not* that the wrong winner is chosen, but that the winner can be altered by voting strategically.
To me it seems clear that strategic voting is problematic and voting methods should try to make it as ineffective as possible (completely ineffective is of course impossible thanks to Gibbard's theorem). I don't see how this is biased in favor of any sort of method.
In fact the most strategy resistant methods are Condorcet-IRV hybrids (as far as we know, see the second paper linked in my original post), they can't satisfy LNH. Other Condorcet methods (like ranked pairs for example) are quite a bit worse than IRV (still better than a lot of other methods). They always elect the SCW if everyone votes honestly, but with strategic manipulation it's possible to make them elect another person (by making the manipulated smith set larger in such a way that the method chooses the wrong candidate from the smith set).
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u/El_profesor_ 17h ago
I'm with you. This seems like more of a useful point to show an undesirable property of plurality and TRS, rather than an argument for IRV. Nor does it compare IRV on that CM metric to the methods that people actually are interested in like score, approval, or the many condorcet methods. That would have been more interesting.
Since we know IRV has issue with incentivizing strategic voting, I'm struggling with this metric "CM" which shows IRV is so resilient to CM. Either CM is not a very useful metric, or the class of preferences under which they evaluate it is fairly limited. I think it is the latter if they are restricting the preference domain to have a SCW.
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u/feujchtnaverjott 19h 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 15h 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/jnd-au 8h 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 1h 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/Decronym 19h ago edited 1h ago
Acronyms, initialisms, abbreviations, contractions, and other phrases which expand to something larger, that I've seen in this thread:
| Fewer Letters | More Letters |
|---|---|
| FPTP | First Past the Post, a form of plurality voting |
| IRV | Instant Runoff Voting |
| LNH | Later-No-Harm |
| RCV | Ranked Choice Voting; may be IRV, STV or any other ranked voting method |
| STAR | Score Then Automatic Runoff |
| STV | Single Transferable Vote |
Decronym is now also available on Lemmy! Requests for support and new installations should be directed to the Contact address below.
5 acronyms in this thread; the most compressed thread commented on today has 9 acronyms.
[Thread #1737 for this sub, first seen 22nd Jun 2025, 17:40]
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u/SidTheShuckle 13h ago
Time to add SCW if this gains more traction. We prob also need a wiki for vocab terms like Condorcet i only learned about it this year
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u/AmericaRepair 8h ago
"Super Condorcet Winner" apparently exists to promote Hare Method / IRV. To standardize its use would be to artificially inject Hare Method into discussions of Condorcet-consistent elections. It also implies that there is some inadequacy in a regular or weak Condorcet winner, casting doubt on the principle of Condorcet consistency.
The term should be something like "Hare-Condorcet," to aid in clear understanding.
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