The problems with RCV’s “Majority” claim

One of the most popular arguments for instant runoff voting (IRV or single-winner Ranked Choice Voting) is that it guarantees a majority. It feels very intuitive, since all of the plurality elections that make us see the need for voting reform lack a majority winner. However, this argument has three major problems.

#1: It’s false

When voters fill out an IRV ballot, they’ll often forgo ranking every single one of the candidates. If, during tabulation, all of the candidates they ranked are eliminated, their ballots will become “exhausted” and have no effect on which of the remaining candidates is elected. It is common for this to prevent any candidate from receiving support from a majority of ballots in the final round. For example, in NYC’s Democratic mayoral primary Eric Adams won with support on just under 43% of ballots. More broadly, FairVote found that that this lack of a majority has occurred in 103 out of 289 (36%) of IRV elections in the US with three or more candidates.

It is worthwhile to distinguish between two types of exhausted ballots:

1. The voter ranked fewer candidates than were allowed by the ballot.
2. The voter ranked as many candidates as they could, but the ballot didn’t have enough room to rank each of the candidates.

For the purpose of evaluating IRV, the first type of exhausted ballot is completely benign and can’t possibly constitute a valid argument against IRV. Opting not to rank some of the candidates is like opting not to vote in a runoff election because you’re indifferent between the remaining candidates. You can’t ignore a voter’s preference when that preference doesn’t even exist.

However, the second type of exhausted ballot can pose a problem. For example, a voter may have one candidate who she hates and wants to prevent from winning, even if she’s largely indifferent between some of the other candidates. A limited number of rankings can deny this voter a voice in the final round, even though she strongly cares about the outcome of that round.

Stepping back from IRV, exhausted ballots and similar issues mean that no voting method can guarantee a majority. Condorcet methods don’t have exhausted ballots per se, but voters can still refrain from ranking either of the top two candidates and may not have enough room on their ballots to rank them all. Allowing voters to give two candidates the same ranking doesn’t solve the problem of a limited number of rankings either, since some voters will end up giving the top two candidates the same ranking. (This does mitigate the problem, however; candidates that a voter gives the same ranking to will be ones that the voter doesn’t have an extremely strong preference between.) This means that STAR cannot ensure a majority either.

Or consider the classic way of “ensuring” a majority: a separate runoff election. The problem with this is that the runoff will often have lower turnout. Consider the 2020 Georgia Senate election between Jon Ossoff and David Perdue. Ossoff won the runoff with 2,269,923 votes to Perdue’s 2,214,979 — but Perdue got 2,462,617 votes in the general election. Ossoff won legitimately, but it doesn’t feel like a real majority.

#2: Sometimes you get the wrong majority

Consider this example of a three-way election by RCV advocate Lee Drutman:

Let’s imagine a hypothetical 2020 presidential campaign between Elizabeth Warren, Donald Trump, and Michael Bloomberg. Let’s say that a month before the election, 40% of voters prefer Warren, 40% of voters prefer Trump, and 20% of voters prefer Bloomberg.

…

Let’s also assume that 75% of Bloomberg voters prefer Warren to Trump, so once Bloomberg is eliminated (as he would be once first preferences are counted), Warren picks up an additional 15%, which takes her over the top, thanks to Bloomberg supporters.

Warren wins with a majority over Trump. But this doesn’t mean she’d have a majority against Bloomberg. Bloomberg is the centrist here, and Drutman later posits that half of Trump’s supporters are “okay” with Bloomberg while assuming that none of them would be okay with Warren, so presumably there’s also plenty of Trump supporters who dislike both Bloomberg and Warren but still consider Bloomberg to be the lesser evil. Bloomberg has 20% first choice support. Add to that the half of Trump’s 40% who are okay with Bloomberg and other Trump voters who dislike him a little less than they despise Warren, and Bloomberg should easily have enough support to defeat Warren head-to-head.

IRV finds Warren’s majority over Trump, but it completely misses Bloomberg’s majority over Warren. Showing a majority doesn’t mean much when it’s the wrong majority.

#3: The concept of a majority winner isn’t all that meaningful outside of plurality elections

Under plurality, if a candidate gets over 50% of the vote, we can say with certainty that this election was not decided by the spoiler effect. A different candidate could not have won if some of the voters had been more strategic. In short, a candidate getting a majority under plurality means that no “funny stuff” was happening, giving the winner a meaningful form of additional legitimacy.

This goes out the window when votes get transferred away from a viable candidate, enough ballots get ignored in later rounds of tabulation, or (as happens in approval and STAR voting) voters show support for both of the top two candidates. You can still have situations in any voting method in which everything is as clean as it is with a majority winner under plurality (for example, this happens in an IRV election when a candidate wins in the first round), but there’s nothing special about a contrived majority.

IRV does not guarantee a majority, and, when it does yield a majority it does not necessarily yield the right majority. Moreover, the concept of a majority has little significance outside of plurality voting. Given this, is it possible to create a variant of the “RCV ensures a majority” argument that is correct and meaningful? Here are a few possibilities:

First, we could consider something like the mutual majority criterion — but IRV doesn’t actually satisfy it when there’s a limited number of rankings, and the real-world significance of this criterion is debatable.

Second, instead of looking for false promises of “ensuring” a majority we could measure the frequency at which different voting methods show the winner receiving a majority, i.e. support on over 50% of ballots. The big problem with this is that it loses the “no funny stuff” guarantee that you get with majorities under plurality. This metric can still give voting methods credit for finding the wrong majority. Also, it gives dubiously-deserved credit to approval voting in cases where a candidate exceeds 50%, and, if none of the voters who preferred the second-place finisher to the winner had voted for the winner, would have yielded a different outcome. However, this probably does do a good job of capturing how often different voting methods give the winner the mandate which comes from receiving a majority.

Third, we could consider how often different voting methods yield a winner who has more support than any other candidate on a majority of ballots. This is a bit less intuitive than the second option, but it avoids the problem of crediting IRV for finding the wrong majority and does a far better job of maintaining the “no funny stuff” guarantee of majorities in plurality elections. Basically, it can be interpreted as “How often does this voting method make an unambiguously correct decision in who it elects?” IRV should do relatively well here; it certainly beats plurality and approval voting on this metric, probably beats STAR, and should at least be competitive with Condorcet methods as well.

Overall, I prefer the third option; it’s reasonably well defined and has good continuity with the concept of a majority winner in a plurality election. But it’s not the most important metric out there — most notably, it fails to distinguish between cases in which a voting method elects the right winner in a way that doesn’t definitively prove the correctness of that winner and cases in which the voting method elects the wrong winner. Still, it offers RCV advocates a plausible argument which is at least related majorities, even if it falls short of being a guarantee.