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Tuesday, December 5, 2023

# Ranked Choice Voting Reveals the Weird Math of Elections

On the first day of class, Daniel Ullman—a mathematician at George Washington University—has his students run an exercise. Ullman presents a hypothetical three-way election, with candidates designated as A, B, and C vying for the win. Then he gives his students 99 voter profiles. This one prefers A over B and B over C. The next one wants A over C and C over B. And et cetera, 99 times.

Then the class runs three different kinds of elections—a “plurality,” in which whoever gets the most votes wins; a “Condorcet,” with successive head-to-head matchups; and “ranked choice,” in which voters can indicate their order of preference and a winner gets calculated through successive tallies.

You can guess what happens in Ullman’s exercise. Each method of voting results in a different winner. None of the methods is wrong. Nobody cheated. But still: same votes, different counting, different winners. That seems bad, right? But as a mathematician, Ullman knows better than most that numbers don’t always add up to truth. “I make the data close,” he says, describing how he designed those 99 made-up voter profiles to show how different, good-faith math can change the future. “Elections are easy when they’re landslides. If all the voters agree, we don’t have to worry about these issues. But when elections are close, these things matter. And elections being close is very common in the US.”

The fact is, democracy only promises to reach for a more perfect union—not an actually perfect one. For decades, a field of study called social choice theory has tried to find new ways of rocking the vote that rocked even harder. Finicky electioneers have tinkered with the ways big groups of people can express their preferences (Approval votes! Quadratic votes! Judgment votes!) in a fair, equitable, feasible way—to make sure the “winner” is actually the winner. Ranked choice voting is the latest popular approach, maybe even better than the plurality-type winner-take-all elections most Americans know best (for some values of “better,” anyway). It’s how New York City is choosing a Democratic candidate for mayor right now, and if that election goes well, ranked choice voting may be the way you cast your next ballot, too.

If your goal for democracy is to get the greatest amount of participation from voters—creating the most representative sample of the body politic—then elections are the survey mechanism for capturing their true desires. But elections are also a cost-benefit proposition. The cost to the voter is the time it takes them to figure out whom to vote for and actually do the voting—by mail or in person. (In some places that cost is higher than in others, in longer lines or fewer options for, say, early or by-mail voting, and higher for certain kinds of people, often poor people and people of color.) The benefit is getting a policy enacted, or a desirable person in a position of representative authority. A good system would reduce the costs, making it easier to vote, and it’d increase the benefits, making a vote more reflective of the desires of the voter and, ideally, converting those desires into laws or action.

So while Americans are most familiar with plurality votes, that kind of ballot might not most accurately reflect their desires. That’s especially true if the election has a bunch of people on a ballot, not either-or but a panoply of options. In the version of ranked choice voting used in New York—also sometimes called an instant run-off—if nobody gets more than 50 percent of the votes on the first tally, the candidate with the fewest votes gets eliminated and their first place votes go to whoever those voters ranked second. Then there’s another round of counting. As the attenuated San Francisco mayoral election of 2018 showed, it can take a while.

This could be good! Proponents say that it gives more people a sense that they chose the winner in some form, even if the winner’s not their first choice. “There’s something that feels bad about electing a politician and that person only received 30 percent of support from voters,” says Stephen Pettigrew, director of data sciences at the Program on Opinion Research and Election Studies at the University of Pennsylvania. “Ranked choice voting kind of solves that problem. It ensures that whoever ends up getting the office has in some fashion received more than half of support.” It’s supposed to chill out negativity and aggression in campaigns, too, because candidates might want to avoid alienating another candidate’s diehard stans. And it might even open up elections to a wider range of ideologies, giving third-party candidates—libertarians, Greens, anarchists, whatever—a window of opportunity as everyone’s third choice. It could likewise prevent an opposition candidate from acting as a spoiler when two other candidates might split an electorate.

Look at it this way: Imagine a 2000 presidential election in which Ralph Nader’s voters could have listed Al Gore as their second choice. Or, more proximately, look at the math in Georgia’s 2020 presidential and Senate elections, where some election experts think ranked choice would have given at least one of the Republican Senate candidates (running against a Democrat and a Libertarian) a win.

Those are the benefits. But of course, ranked choice also has costs. Technically it’s possible that voters who have made those decisions could try to game the system, to vote against their best interest or to try to tank someone they don’t like. (You could vote for someone you hated in slot two, let’s say, to try to eliminate someone you hated even more.) That means the system isn’t what election researchers call “monotonic.” It could introduce dishonesty (gasp!) into politics. “But this is theoretical,” says Victoria Powers, a mathematician at Emory University. “Who knows if this would actually happen in a real-life situation?”

More likely is the possibility that people just won’t get it. “The vast majority of voters, they don’t pay attention to politics. For some people, it’s already a lot to ask them to decide on just one person to represent them,” Pettigrew says. And just as ranked choice might open elections to candidates with nontraditional backgrounds or from underrepresented groups of people, you might guess that a more complicated ballot might make it harder for people with less education or less facility with the language of the instructions to vote. On a ranked choice ballot with more candidates than slots for a voter to rank, some proportion of voters could end up choosing people who eventually all get eliminated. Those ballots get “exhausted” before the final tally, which means in effect they don’t count. “That’s a little weird, too,” Pettigrew says.

But nobody’s sure about any of that. New York could be the place where they figure it out. So far only smallish, homogenous-ish places like San Francisco and Cambridge, Massachusetts, have used ranked choice. But NYC has more than 5 million potential voters from a vast range of socioeconomic and ethnic backgrounds, trying ranked choice voting in the real world. “Theoretically, people with lower socioeconomic status, with lower income, with less propensity to vote, are likely to be harmed by the complexity of the ballots,” says Jesse Clark, a postdoctoral researcher at the Election Innovation Lab at Princeton University who specializes in ranked choice. “That’s one of the things we’re going to be studying with New York City.” This election will be a huge data dump for election scientists, and they’re clamoring for it.

For example, once the primary in New York is over, Clark and his colleagues will be looking at exhausted ballots by the race of the voter—inferred, imperfectly but usefully, by the location of the vote. “The reason it hasn’t been studied in depth is, if you look at where ranked choice voting has been implemented, they were all pretty homogenous,” Clark says. “New York City is enticing for researchers because it’s so diverse. You just don’t see that in Maine, which used to be the whitest state in the country.” (He would know—Clark grew up in Maine, in one of the first congressional districts to use the method. It’s what got him interested in the system.)

Clark says he might even be able to finally quantify, once and for all, whether ranked choice elections make campaigns less nasty—using sentiment analysis, say, to tabulate how many mean words the candidates used in their ads. When I talked to Clark last week, he was optimistic. “They’re just starting to get negative, and it’s not even a week out,” he said then. “New York politics should be a lot meaner than that, in theory.”

He just needed to wait a couple minutes. Former presidential candidate Andrew Yang did indeed say that voters should consider ranking him first and another possible contender, New York sanitation commissioner Kathryn Garcia, second—but Garcia didn’t reciprocate. Opponents including Yang accused another candidate, Brooklyn borough president Eric Adams, of not actually living in the city of New York; Adams in turn suggested that Garcia’s and Yang’s decision to campaign on Juneteenth was racist, a sentiment decried by yet another candidate, Maya Wiley. Adams called Yang a “liar” and a “fraud.” New York—whattayagonnado, right?

To supporters of ranked choice voting, these are mere growing pains. “Part of it is letting all the actors in the political system adapt, letting candidates learn how to run and voters learn how to use these more expressive ballots,” says Nathan Lockwood, executive director of Rank the Vote, a national advocacy group. Satisfaction with ranked choice voting grows every time people use it, Lockwood says, and New York could be the beginning of a movement.

Most researchers think that even if ranked choice voting spreads across the country—amid Republican attempts to curtail other voting rights—it probably won’t be the key to ending polarization, or even increasing turnout. “We didn’t see more civil campaigns in Maine in the general election, because that’s just the way partisanship is set up right now. No diehard Republican is going to vote for, or even rank, the lefty independent, or vice versa,” Clark says. More people do seem to be voting for third party candidates—maybe as much as five percentage points. That might not sound like much, but election scientists usually see swings that big only when new demographic groups gain suffrage, or older ones die. Ironically, though, ranked choice voting also serves to consolidate the power of party elites. Who knows who would’ve won the Republican nomination in 2016 if Ted Cruz and Marco Rubio’s voters could have operated as a one-two bloc against Donald Trump? Like Ullman’s first-day-of-class eye opener, every election is a window onto a multiverse of parallel futures. It’d be nice if those elections better captured the will of the people. New York’s primary might be a big step toward finding out what kind of election system those people should use.