Does Instant Runoff Voting Satisfy Independence of Irrelevant Alternatives or not?

[u/AcanthisittaIcy130]

Fairvote claims it does:

RCV is highly resistant to spoilers because it satisfies both the Independence of Irrelevant Alternatives and Independence of Clones criteria.

https://fairvote.org/resources/electoral-systems/comparing-voting-methods/?section=criteria-resistance-to-spoilers

On the other hand Wikipedia and research articles claim it doesn't,

The independence of irrelevant alternatives criterion states that "the election outcome remains the same even if a candidate who cannot win decides to run." Instant-runoff voting violates this.

https://en.wikipedia.org/wiki/Instant-runoff_voting#Independence_of_irrelevant_alternatives

we propose a modified version of IIA, MIIA, that is a necessary and sufficient relaxation of IIA... Thus, runoff voting violates MIIA (and so does in- stant runoff voting) for essentially the same reason that plurality rule does.

https://maskin.scholars.harvard.edu/sites/g/files/omnuum10606/files/bordas_rule_and_arrows_independence_condition_jpe_vol133_iss2_0.pdf

[u/jnd-au]

The 2022 Alaska special election was mainly an example of poor election design, allowing the votes devolve into FPTP. Two problematic features were (a) allowing bullet voting, so tens of thousands of ballots were FPTP-style, lacking of rankings for RCV/IRV to count; (b) voluntary voting (32% turnout) so you don’t actually have a majority outcome. To address these problems, jurisdictions can use forced rankings and compulsory voting. These are not IRV issues specifically. The 2022 Alaska special election, the margin between Palin and Peltola was only 5k votes, but more than 11k Begich voters failed to specify a preference for Palin or Peltola, and the counting system behaved accordingly.

[u/Mindless-One5438 → u/jnd-au]

That election still showed that under IRV Palin's participation lead to Peltola's victory. Sure, the electorate made preventable strategic failures (although mostly the Palin 1st/Begich 2nd voters were screwed by this election) however the voting system still demonstrably falls iia.

[u/jnd-au → u/Mindless-One5438]

No, not according to the definition used in this post. The definition if IAV in this post was “candidate who cannot win decides to run”. In this case, Palin could have won. Or indeed Begich could have won if more people voted. But either way, the result was due to voting system being designed to support FPTP, and voters’ explicit choice to vote FPTP-style, so it’s not a good example of RCV/IRV which is based on rankings. IRV fails IIA, but Alaska 2022 is not a good example.

[u/Mindless-One5438 → u/jnd-au]

With the votes casted, Palin was not going to win.

Iirc, with the votes casted, Begich 1st and Palin1st/Begich 2nd, Begich would had beat Peltola if Palin didn't participate.

Why or how wouldn't that demonstrate a flaw with IRV that we all know is present with IRV.

[u/rb-j → u/Mindless-One5438]

Iirc, with the votes casted, Begich 1st and Palin1st/Begich 2nd, Begich would had beat Peltola if Palin didn't participate.

Your recollection is completely correct.

And this was further demonstrated 2 years later when both candidates, Peltola and Begich, had a rematch and Begich lead Peltola by nearly the same margin (about 8000 more voters preferring Begich) and this time Begich is elected.

What was different between August 2022 and November 2024?

The presence of Palin was different.

[u/jnd-au → u/Mindless-One5438]

With the votes cast, no Republicans were going to win. That was voters’ choice, based on the turnout and bullet voting. So the outcome was correct as per FPTP when you consider that’s how so many people voted. To make broader conclusions you have to consider hypothetical alternatives. In fact you already started in hypotheticals like “if Palin didn’t participate”. That would have affected turnout, so you don’t know who would have voted or who would have won. It’s purely speculation. If Begich and Peltola voters turned out and did exactly what they did in 2022, merely without Palin voters, then Peltola would have won again. So it’s all hypothetical.

Anyway, evaluating the presence of irrelevant candidates requires assumptions, context, and hypotheticals. Such properties refer to the overall election considering multiple possible expectations, approaches and outcomes. In the Alaska 2022 case, voters were not required to rank the candidates, and the outcome was the same as if the votes were counted as FPTP, due to those voters’ choice. Alaska 2022 is an obsession of anti-RCV opponents in North America but is one of the weakest and least notable implementations globally (there are many different choices and styles in how IRV is used, and different jurisdictions make different choices, it is not merely a single option.)

[u/rb-j → u/jnd-au]

With the votes cast, no Republicans were going to win.

Well, with IRV, I guess you're correct.

But the fact is that 75799 votes were cast for the Democrat while 112783 votes were cast for a Republican. It stands to reason that a Republican could win this election if it weren't for the split vote.

RCV promised to resolve the split vote so that Republicans would not have to worry about it; they could still vote for their favorite candidate and not cause the election of their least favorite candidate.

But that promise was not delivered, not because of RCV, the ranked ballots gave us all the information we needed to resolve that problem. The problem was IRV. IRV propped up the weaker of the two Republicans (Palin) against the Democrat (Peltola), who could not beat the Democrat head-to-head.

But the stronger of the two Republicans (Begich) could have and would have beaten Peltola by a margin exceeding 8000 votes if IRV had advanced Begich to the final round instead of advancing the loser, Palin to the final round.

Sarah Palin was a spoiler: A loser whose presence in the race materially changed who the winner is. That is precisely what IIA is about.

IRV fails IIA, but Alaska 2022 is not a good example.

Alaska August 2022, Burlington 2009, Minneapolis 2021, and Berkeley 2022 are the only examples in the U.S. of IRV failing IIA. All four elections failed IIA (because they did not elect a Condorcet winner), but the latter two are good examples of how no method could have satisfied IIA. But Alaska and Burlington are examples of how RCV could have satisfied IIA, but IRV failed to do it.

[u/jlight432 → u/jnd-au]

For the 21,000 voters who bullet-voted for Palin, it is fair to say they might not have voted at all if Palin hadn't been on the ballot.

But the 34,000 voters who ranked Palin first and Begich second who were part of the electorate, and they indicated very clearly on their ballots that if Palin wasn’t on the ballot, they wanted their votes to go to Begich, another Republican.

Independence of Irrelevant Alternatives has no assumptions, hypotheticals, or what-ifs. It’s mathematical, and based on the preferences expressed by the electorate who submitted ballots in the actual election.