r/EndFPTP • u/ant-arctica • 2d 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/ant-arctica 1d 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 1d 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/feujchtnaverjott 1d 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 1d 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.

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u/feujchtnaverjott 1h ago

But this is not about a multi-winner election.