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Location: Any country or state that uses RCV. One that has used it for a while and worked out the kinks would be preferable. Edit for clarity: I am talking about the “instant runoff” kind of RCV in a single winner election.

If a candidate is last in the first round, but after the second round would have more votes than some other candidates, are they brought back into the equation?

Example: Alice, Bob, Carol, Dan, Ed. 100 votes Alice- 30 Bob- 20 Carol- 20 Dan- 18 Ed- 12

Ed gets dropped. Round 2 Alice- 30,
Bob- 28, Carol-22, Dan- 20

Dan gets dropped. Of his original 18 votes, 17 have Ed as the second choice. So if that were to be counted, Ed would have his original 12 first place plus 17 of Dan’s second votes for 29, putting Ed above all but Alice. Or is it that Ed is out, never to return, and we look at Dan’s third choice on those ballots, plus the next choice on any “Ed” ballots that had Dan second? Ed and Dan are out, no coming back.

I know the bringing back in would get complicated. Any Ed votes that went to say Bob would be taken away after round 2. But it should be nothing a computer could not handle.

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    Re "nothing a computer could not handle". Having a close relative working at the Australian Electoral Commission (incl. recent elections), I can say that the votes are counted entirely by hand, with all the re-distribution of preferences processed on pieces of paper. The individual ballots are never scanned. Almost a month after the election, the count is not finished yet. At least, that's for the lower house, where there are 6-10 candidates per ballot and a single winner. Senate counting with up to 100+ candidates and multiple winners is more complicated.
    – Zeus
    Jun 17, 2022 at 2:09
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    @Zeus this is done to try and prevent certain types of electoral fraud. I could see a system where a computer does the "fast count" to get a result quickly, but the manual slow count is still done to verify that nobody has messed with the computer or there was some kind of error caused by cosmic rays.
    – Turksarama
    Jun 17, 2022 at 3:25
  • @Turksarama, yes, this is one of the reasons usually put forward, but it's easily avoidable by using open/certified counting software (the algorithm itself is trivial, even for IRV). The main problem with fully-digital voting is avoided by having a physical paper ballot, which can always be counted by hand in case of a dispute. The only problem is the trust to the database of scanned/digitised ballots, but it's not any greater than the problem of trust to manual count. Yet, you need to digitise ballots even for "fast count" on a computer, and this is the slowest process.
    – Zeus
    Jun 17, 2022 at 7:42
  • ...IRL, the "fast count" (in Australia) is also done by hand, it's just restricted to the two leading candidates (so called "two-party preferred" count).
    – Zeus
    Jun 17, 2022 at 7:47

3 Answers 3

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It depends on the counting method used.

In "instant run-off" voting, Ed is eliminated, and so the 17 votes that place Ed second would need to be redistributed to their third choice.

However in Condorcet voting methods, you set up head-to-head battles. If Ed is everyone's second choice, then he would beat all the other candidates in a head-to-head and so could be the Condorcet winner. In Borda count, Ed is again not eliminated, and his second place votes might let him score highly.

The difficulty in Condorcet methods is that there may be no single winner (eg Ed might beat Dan, Dan beats Carol, but Carol beats Ed) The counting method has to deal with breaking this kind of impasse. In general, it is a consequence of Arrow's theorem that there is no method of counting that deterministically finds a winner, and is always manifestly fair in every possible combination of votes.

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    As applied by jurisdictions that adopt it, ranked choice voting almost always means instant runoff voting and not Condorcet ranking of outcomes - something that no jurisdiction to my knowledge has adopted with the moniker of ranked choice voting.
    – ohwilleke ♦
    Jun 16, 2022 at 16:52
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    Sure, nearly all systems that use ranked voting go for some variant of instant run-off. But that's not what "ranked voting" means, and Borda count or (for example) or minimax condocet methods are forms of "ranked voting"
    – James K
    Jun 17, 2022 at 5:31
  • "... but Condorcet cycles are just a form of tie, which all voting methods need to deal with anyway, and cycles are very unlikely with the ballot distributions found in real-world elections, so don't worry about them."
    – endolith
    Jun 17, 2022 at 12:54
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    @JamesK How is that an issue? That's their primary feature, not a bug. How is it unclear that the most-preferred candidate is the optimal social choice? If you use score ballots that show strength of preference, there may be a more highly-liked candidate than the most-preferred candidate, but again, with realistic distributions of ballots, that is rare.
    – endolith
    Jun 18, 2022 at 12:15
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    @JamesK Yes, if you use score ballots to get that extra information, as I said, you can make a better choice, but with ranked ballots, that information doesn't exist, so electing the Condorcet winner is the obvious minimum bar for any ranked voting method. In most realistic elections, the Condorcet winner and Utility winner are the same candidate anyway.
    – endolith
    Jun 19, 2022 at 19:08
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No, and this is the fundamental flaw in the instant runoff tabulation method that's promoted so heavily in the US.

Advocates claim that it makes it safe to list your honest favorite as your first choice, because if they don't make it, your vote will transfer to your second choice, but this is only true in the contrived examples used to market this system.

In reality, voting honestly for your true favorite may backfire, getting your second favorite eliminated first, and then your vote cannot transfer to them.

In this way, you can still help the "greater of two evils" win if you "vote your conscience", which means you have "wasted your vote".

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I just now discovered this recent question and it looks like there are some good answers.

I would like to point to a few documents that I have written about this subject in the context of me politikking in Vermont. The first paper is (still) on the way to publication in Constitutional Political Economy.

The Failure of Instant Runoff Voting to accomplish the very purpose for which it was adopted - An object lesson in Burlington Vermont

Precinct Summability

Five different templates for plausible legislative language implementing Ranked-Choice Voting

Letter to governor that make the Progs really mad at me

Finally this is a Scientific American article from 2004 co-authored by Nobel laureate and Harvard prof, Eric Maskin.

I may come back to this and try to address the question more specifically.

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  • Negative votes from FairVote or CES apologists are a badge of honor for me.
    – robert bristow-johnson
    Jul 25, 2022 at 0:53

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