No electoral voting method is perfect. The various methods of casting and counting ballots make different tradeoffs in terms of the simplicity or complexity of a method and its theoretical properties. Among all the possible voting methods, the widespread first-past-the-post or “plurality” method used in almost all US elections is among the absolute worst.
Many election reformers advocate for a ranked choice voting method known as “instant runoff voting” (IRV). (IRV is sometimes commonly referred to as simply “ranked choice voting,” but we will use the term IRV to avoid confusion with other ranked voting methods.) Like any voting method, instant runoff voting makes certain tradeoffs between desirable properties and simplicity. The August 2022 special election in Alaska for a U.S. House seat used IRV to elect the representative, and offers an opportunity to learn about some of the tradeoffs that various voting methods make.
Alaska 2022 special election
In that election, there were three candidates: Republicans Sarah Palin and Nick Begich, and Democrat Mary Peltola. After the first choice votes were tallied, no candidate had over 50% of the vote. So, the person with the least first-choice votes, in this case Nick Begich, was eliminated. Ballots listing Begich as the first-choice then went to the second choice. In the second round, because so many Begich first-choice ballots listed Peltola as the second choice, Mary Peltola was elected to the U.S. House of Representatives in the second round.
Mathematician Jeanne N. Clelland has published an excellent, rigorous study of the 2022 Alaska special election that compares outcomes under different voting systems.1 The main findings of the study are that:
- The election exhibited a phenomenon known as “Condorcet failure”. Based on the ballot rankings, Begich would have won a head-to-head contest against Palin, and he would have won a head-to-head contest against Peltola. However, he did not win the IRV election.
- A “Condorcet winner” in an election is a candidate who would win in a head-to-head contest against every opponent. While IRV often elects a Condorcet winner in an election (when one exists), it is not guaranteed, and Alaska’s 2022 special election was an example where IRV did not elect the Condorcet winner.
- The author looked at two other voting methods, and found that Approval Voting would likely have also elected Peltola, while a method called STAR voting (“Score Then Automatic Runoff”) would likely have elected Begich.
BTR-IRV result
I would have liked to see the author include a comparison of a tweaked IRV method known as Bottom Two Runoff IRV (BTR-IRV, sometimes pronounced “better IRV”). First given this name by Jan Kok in 2005 on a mailing list about voting systems, BTR-IRV is a slight tweak to the traditional IRV that has some desirable properties. The difference is that while traditional IRV in each round eliminates the lowest vote recipient, BTR-IRV instead in each round takes the two lowest vote recipients and matches them in a head-to-head runoff, eliminating the loser of the runoff while allowing the winner to advance to the next round. What is nice about BTR-IRV is that it avoids the possibility that a strong candidate with many second-choice votes is eliminated too early, like what arguably happened to Begich in the 2022 special election.
Jeanne Clelland’s study reports the vote tabulations in Table 6 of the paper, so we can do the vote analysis to see how BTR-IRV would have produced a different outcome from the Alaska 2022 special election. The vote tabulation from the paper is reproduced below.
The BTR-IRV method first needs to determine the bottom two candidates for the round 1 runoff. We can determine that by summing the first-choice votes each candidate received:
– Begich: 11,179 + 27,258 + 15,572 = 54,009
– Palin: 21,139 + 34,117 + 3,683 = 58,939
– Peltola: 23,647 + 47,429 + 4,727 = 75,803
The two bottom candidates in the first round are Begich and Palin. Thus, they face a bottom two runoff in the first round, based on their rankings across all ballots. This means that any ballot that expressed a preferences for Begich over Palin or Palin over Begich is counted, and the winner advances to the next round. In this case, the runoff would have yielded:
– Begich: (all ballots with Begich as first choice) + (Peltola ballots with Begich as second choice) = 54,009 + 47,429 = 101,438
– Palin: (all ballots with Palin as first choice) + (Peltola ballots with Palin as second choice) = 58,939 + 4,727 = 63,666
Begich easily wins the runoff in the first round and advances to the second round, while Palin is eliminated.
The final round is Begich against Peltola. We use the same calculation as before, giving each candidate their first-choice ballots, and then the Palin-first-choice ballots that listed the candidate as the second choice:
– Begich: 54,009 + 34,117 = 88,126
– Peltola: 75,803 + 3,683 = 79,486
In BTR-IRV, Begich is elected, and thus the “Condorcet winner” is elected.
Pretty much any method is better than the first-past-the-post widely used today. What is nice about the BTR-IRV method is that it is just a slight tweak to the IRV method already used in places like Alaska, but with the desirable property that if there is a Condercet winner in an election, that person will be elected. And that makes it worth discussing as part of electoral reform efforts.
- J.N. Clelland, “Ranked Choice Voting And Condorcet Failure in the Alaska 2022 Special
Election: How Might Other Voting Systems Compare?” submitted April 2024. Preprint
available at https://arxiv.org/abs/2303.00108. ↩︎