## Should Andrew Yang Wait to Concede?

Yesterday New York City held their mayoral primary elections. This was an exciting event for election system nerds (political scientists and public choice economists) because NYC is now using a form of ranked choice voting to determine the winner.

While this is not the first place in the US to use RCV (Maine, Alaska, and a handful of cities use it), it is still notable for a few reasons. First, this is America’s largest city. Second, there are a lot of viable candidates, which makes RCV especially interesting and useful.

Specifically, NYC is using a form of voting called instant runoff. There are currently 13 candidates, and voters indicate their top 5 in order. If no one has a majority (>50%) of the votes, then the rankings entered by voters come into play. And indeed that is what happened yesterday.

On the first round, only counting first place votes, Andrew Yang came in 4th with just under 12% of the votes. So last night he conceded.

But should Yang have conceded? Maybe not! Let’s explore how instant runoff works.

You can find lots of explainer pages out there for this election, but let me use a hypothetical example that I teach in my undergraduate public finance course. It’s called the “evil example” for good reason: it has 5 candidates, and any of them can win under 5 perfectly reasonable voting methods! I also tell my students the example is “evil” because under the most common voting method, simple plurality, the most “evil” candidate wins. It comes from Shepsle and Boncheck’s book Analyzing Politics.

In this example, there are five candidates (a-e) and six types of voters (I-VI, with the numbers under each telling us how many voters are in each group). For each Roman numeral group of voters, their preferences for the candidates a-e are listed in order. For example, the “I” voters like candidate “a” the best and candidate “b” the worst. The “I” voters are about 1/3 of the electorate (55 voters total). Notably, every other group (roughly 2/3 of the electorate) ranks candidate “a” as the worst candidate.

To use the “evil example” for instant runoff voting, first note that candidate “e” has the lowest number of first round votes (6 votes, from the V and VI voters). So in round 2, “b” gets 4 more votes and “c” gets 2 more votes. Candidate “d” is eliminated next, followed by candidate “b.” In the final round, it is “a” versus “c,” and of course “c” wins because 2/3 of the electorate (37 of 55 voters) really don’t like candidate “a.”

The nice thing about these “rounds” is that voters don’t have to come back to the polls, unlike other runoff elections you may have seen (for example, the recent Georgia Senate race). The calculations can be done in an instant, or roughly so, with any kind of modern computer, even for a large city like New York (though in reality we won’t know for a week or so, due to mail-in and absentee ballots still coming in — not quite an “instant,” but still faster than holding a second election).

So what does this have to do with Andrew Yang conceding? Note that in the hypothetical “evil example,” the winner under instant runoff (candidate “c”) only had 18% of the vote in the first round. That’s slightly more than Yang’s almost 12%, but the key is that this number doesn’t actually matter.

The frontrunner, Eric Adams, has almost 1/3 of the vote, just like candidate “a” in our hypothetical example! Will he win? We don’t know because, at this point, we don’t have any information on the rankings past voters’ top choice. I’m sure there are a few polls floating around out there, but this is really hard to poll. Remember, it’s 13 candidates (plus write-ins!), voters pick their top 5, plus this is the first time NYC voters have done this. If a pollster asked you how you intend to vote or how you actually voted after the fact, it’s doubtful voters could accurately express their preferences. And you’d need a really big sample. One of the major polling firms even admitted they just aren’t going to attempt exit polls.

Who will win? It all depends on the rankings. Maybe Eric Adams is like candidate “a” and everyone else ranked him last (or worse, not even in their top 5). Maybe Adams is ranked second by ~20% of voters, in which case he will win. But then again, it’s entirely possible that ~40% of voters placed Yang in second place on their rankings. Maybe he will win. And it’s not entirely crazy. Until mid-April, many polls had Yang in the lead, with the most voters preferring him as their first choice. So he clearly has a lot of support.

Some firms (bless them!) are trying to poll voters for their ranked choice preferences. One recent poll shows a final round between Adams and Yang, with Adams having the slight edge at 56-44. But given the many uncertainties about this election, and the new challenge of polling RCV, I’d say that is basically a tie. Though in that poll, Yang did have 20% in the first round.

Should Yang have conceded? Conceding is actually a weird thing. Candidates take it back all the time. It’s not really a formal legal action, it’s just a thing candidates do (no doubt some political scientist specializes in concessions and will tell me it is more nuanced than this — please do!). Perhaps Yang is looking at his first round vote total and seeing it much lower than the polls. Maybe that’s why he dropped out. But it’s entirely possible he will actually have a much better showing than his initial 11.7% indicates.

For the curious, here are the winners in the “evil example” under different voting methods (I’ll only briefly explain all these methods, you can investigate further yourself!):

• A wins under simple plurality
• B wins under plurality runoff (top 2 advance to final round)
• C wins under instant runoff
• D wins under Borda count (points assigned for each ranked position)
• E wins under the Condorcet method (beats all other candidates head-to-head)
• And finally, D and E tie under approval voting (that’s what the underlines in the chart indicate, whether votes approve of a candidate, and you can vote for as many as you like)