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A comment on What is ranked-choice voting and why is New York using it?. Parent comment

Re:What is ranked-choice voting and why is New York using it? by vitus on Tuesday June 22, 2021 @10:08PM (#27599977)
One important distinction to make is that RCV isn't the same as Instant Runoff Voting (IRV); rather, IRV is a specific (the most commonly championed, as far as I can tell) implementation of RCV, likely because it's the easiest to explain.

Note that all RCV implementations have limitations, per the oft-cited https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theore... which outlines a number of ostensibly desirable attributes then demonstrates that no RCV implementation can satisfy all of them.

But that's not to say that approval voting methods are flawless, either. One often cited desirable property is the Condorcet criterion, namely, if one candidate beats all others in head-to-head matchups, that candidate should be the winner. (There's a related Condorcet Loser criterion which is the inverse: if one candidate loses to all others in head-to-head matchups, that candidate should not be elected.)

Suppose we applied approval voting to a simplified view of the 2016 election. (Y to indicate approval, N to indicate disapproval)

- 48%: Partisan R. Trump (Y) > Stein (N) > Clinton (N)

- 48%: Partisan D. Clinton (Y) > Stein (N) > Trump (N)

- 3%: 3rd-party, very slight D lean. Stein (Y) > Clinton (Y) > Trump (N)

- 1%: 3rd-party, very slight R lean. Stein (Y) > Trump (Y) > Clinton (N)

Stein beats both Clinton and Trump in head-to-head matchups, 52% to 48%. But with an approval voting system (selecting Clinton with 51% approval), this fails the Condorcet criterion! (IRV is no better here, to be clear. And Condorcet methods have their own pathologies.)

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Re:What is ranked-choice voting and why is New York using it? by elihu on Tuesday June 22, 2021 @10:54PM (#27600276)
As far as I know, the label RCV as it's commonly used in the United States (and advocated most prominently by FairVote) usually means the same thing as IRV. Perhaps there are some minor differences in terms of specifying exactly what happens if a ballot doesn't rank all the candidates, or ranks two candidates equally. Perhaps using RCV to mean an exact system rather than a whole category of voting systems is imprecise, but I think that ship has already sailed.

It's also sometimes called alternative vote, and the Australians call it preferential voting.

I've wondered if IRV couldn't be substantially improved by using Borda count for the elimination step rather than eliminating the candidate with the least first-choice options. (I think there's an actual name for that system, but I don't remember what it is.)

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Re:What is ranked-choice voting and why is New York using it? by vitus on Wednesday June 23, 2021 @12:11AM (#27600707)
Oh, I agree that in the US, RCV is (unfortunately) often conflated with IRV.

> I've wondered if IRV couldn't be substantially improved by using ... rather than eliminating the candidate with the least first-choice options.

This is exactly the family of RCV systems -- IRV merely defines one implementation by which a winner is selected from a ranked ballot.

Borda count has its own pathologies, too -- the usual cited problem is that it fails independence of irrelevant alternatives.

https://en.wikipedia.org/wiki/Independence_of_irrelevant_alt...

(Further, Borda count fails the majority criterion, namely there are situations where a candidate is the first pick of a majority of the electorate, yet fails to win. Some proponents of Borda count argue this is a feature, not a bug.)

The wiki article for Borda count has a solid table of various voting systems and whether they satisfy various criteria:

https://en.wikipedia.org/wiki/Borda_count#Other_properties

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Re:What is ranked-choice voting and why is New York using it? by elihu on Wednesday June 23, 2021 @12:52AM (#27600916)
You're right that Borda count on its own isn't a great system. Though an RCV-style system that eliminates candidates on the basis of least-Borda count would be something else. It might be better than either normal IRV or plain Borda count on their own. (Though I still think I'd rather go with approval voting or STAR.)
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Re:What is ranked-choice voting and why is New York using it? by vitus on Wednesday June 23, 2021 @07:39AM (#27603287)
It sounds like you're referring to

https://en.wikipedia.org/wiki/Nanson%27s_method

and the related Baldwin's method, which, while being Condorcet methods, both fail monotonicity.

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Re:What is ranked-choice voting and why is New York using it? by elihu on Wednesday June 23, 2021 @06:09PM (#27611141)
I looks like what I was thinking of is Baldwin's method, actually. Failing monotonicity is still a problem, but it's actually pretty cool that it satisfies the Condorcet criterion. That seems like a pretty big step up from plain IRV.
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