Instant-Runoff Ranked-Choice Voting Elects Wrong Winner in Alaska
Alaska recently started using an alternative voting system that is commonly called Ranked-Choice Voting (RCV). This is a bit of a misnomer; the better term is Instant-Runoff Voting (IRV). I’ll explain this more in a subsequent post; for now, just be aware that they’re the same thing, but I will call it IRV. If you’re unfamiliar with it, there’s lots of information on the Web, but in a nutshell, it asks voters to rank the candidates in order of decreasing preference, and then applies a somewhat complex ballot tabulation procedure, which I’ll explain with an example below.
There was a special election on August 16th, 2022 to fill a Congressional seat, between Mary Peltola, Nick Begich, and Sarah Palin, that was conducted using IRV. FairVote, a prominent organization promulgating IRV, released this statement afterwards, with these facts:
73% of ballots ranked at least two candidates
Of those who ranked Begich first (and excluding those whose second choice was a write-in), 50% ranked Palin second and 29% ranked Peltola second
Of those who ranked Peltola first (with the same exclusion), 63% ranked Begich second and 5% ranked Palin second
Of those who ranked Palin first (with the same exclusion), 57% ranked Begich second and 6% ranked Peltola second
These additional facts are known:
Peltola won 40.2% of the first-choice votes
Palin won 31.3% of the first-choice votes
Begich won 28.5% of the first-choice votes
Here is the way an IRV election is tabulated, using this election as an example. No candidate won over 50% of the first-choice votes, so the candidate with the fewest first-choice votes — Begich, in this case — is eliminated. Then the ballots that have Begich first and also list a second choice are transferred to that second choice. That adds 14.3% (50% of 28.5%) to Palin’s total and 8% (29% of 28.5%) to Peltola’s, giving Peltola 48.2% to Palin’s 45.6%. (There might be a little slop in these numbers since I’m using percentages, which have already been subject to rounding, rather than raw numbers of ballots, but they’re close enough for our purposes). Thus the winner was Peltola.
Let’s compare that result against what has long been considered the gold standard of voting systems: the Condorcet criterion. This asks us to imagine that the voters have been presented separately with every pair of candidates, and says that the winner should be the person who would have won the most of these head-to-head contests.
We can use the ranked-choice ballots from this election to get a good idea of who would have been the Condorcet winner. 73% of the ballots ranked at least two candidates and can therefore be treated as ranking all three; the remaining ones we’ll initially treat as ranking the first choice over the other two, but not ranking the two remaining. Under those assumptions we get the following numbers:
Begich > Palin 53.8%
Begich > Peltola 46.3%
Peltola > Begich 42.1%
Peltola > Palin 48.5%
Palin > Begich 33.3%
Palin > Peltola 45.6%
This already shows Begich as the winner. If we assume, not unreasonably, that the second and third choices of those voters who didn’t specify any would have been in the same proportions as those of the voters with the same first choice, then we get these numbers:
Begich > Palin 65.7%
Begich > Peltola 56.8%
Peltola > Begich 43.2%
Peltola > Palin 50.7%
Palin > Begich 34.3%
Palin > Peltola 49.3%
Here Begich’s win is more dramatic. I emphasize that these numbers are just projections, based on the data we have, of what might have happened in an ideal Condorcet election where every voter ranks every candidate, and the truth is likely to be somewhere between them; but they clearly indicate that Begich would have won such an election by a solid margin.
This election, in short, is a disaster for IRV, failing as it did to elect the clear Condorcet winner. And I think it’s an instructive disaster, because these numbers don’t seem to me to be atypical results for a scenario in which a relatively moderate candidate joins an election against two opposite candidates given a fairly polarized electorate. What we see, very clearly, is that IRV can’t pick the moderate unless they can draw more first-choice support than one of the more extreme candidates. And as this example shows, that’s true even if the electorate clearly prefers the moderate overall.
Let me now turn to a different alternative voting system called Approval Voting (AV). If you don’t know how it works, my previous post provides an introduction (I think it will be of interest even to experts). How would this election have come out if it had been conducted using AV?
We can’t say for sure, because AV ballots are different from those of ranked-choice systems like IRV; they ask voters a different question. Instead of asking for a ranking of the candidates, they ask voters to give a thumbs-up or thumbs-down on each candidate independently.
So to say how the election would have come out under AV, we would need to know what fraction of second-choice votes in this election would have translated to thumbs-up votes in an AV election. There’s no way to determine that with certainty. What we can do is game out a few scenarios and see what outcome seems most plausible.
For example, if we assume that 70% of the second-choice votes for all three candidates would have converted to thumbs-up, we get these numbers:
Begich 58.7%
Peltola 47.3%
Palin 42.7%
And here’s what we get if only 40% of the second-choice votes converted:
Begich 45.8%
Peltola 44.2%
Palin 37.8%
For Peltola to win, the conversion rate has to be under 34.5% — barely over 1 in 3.
Can we get a sense of what conversion rate seems most plausible? Let’s consider the question facing a voter whose first choice would be Peltola, and who was trying to decide whether to vote for or against Begich. There are two possible outcomes in which their ballot could have changed the result, but the winner was not Peltola: either they voted for Begich and he won, or they voted against him and Palin won. AV asks them to decide which of these outcomes is the most unpalatable, and choose the other one. So if they can live with Begich but strongly disprefer Palin, they have a pretty strong reason to give Begich the thumbs-up. Similar reasoning applies to those whose first choice would be Palin.
Looking at the IRV results, what we see is that of those voters whose first choice was Peltola or Palin and who cast a second-choice vote, those votes were overwhelmingly for Begich. This suggests that at least a substantial fraction of the electorate felt fairly strong opposition to the candidate at the other end of the spectrum from their first choice. I can’t be sure that that circumstance would would imply a 70% conversion rate, though it seems entirely possible; but it’s hard to see it much under 50%. As we saw above, that’s easily large enough for Begich to have won.
In all probability, I conclude, Begich would have won this election had it been conducted using AV.
So in summary, here we have a real-world example of an election in which AV outperforms IRV — and I didn’t have to dig to find it, either. While it’s always dangerous to draw conclusions about a voting system based on one election, at this point I think the burden of argument is on IRV proponents to explain why this example is atypical. To me it seems likely to represent a common scenario.
I gather that IRV is catching on faster than AV, as more and more electorates try it out (though a few are trying AV instead). I have mixed feelings about that. I’m glad they’re considering alternatives to our existing choose-one system, which tends toward polarization and makes it very hard for third parties to get a foothold; but based on the above example, I think AV actually solves the problem, where IRV promises change but doesn’t deliver.
I’ll have more to say on AV vs. IRV in subsequent posts.