A photo finish in New York's mayoral race?

Tuesday's ranked-choice election will be the largest in U.S. history

Next Tuesday, New York City is on track to conduct the largest ranked choice election in U.S. history. This breaks the previous record, which was also in New York, when over 900,000 votes were cast in the 2021 primaries (see the Electoral Innovation Lab analysis of that election).

Set to take place next week are Democratic and Republican primaries for mayor, as well as a variety of other offices. In the Democratic mayoral contest, many candidates are making good use of the key feature of ranked-choice voting: the ability to elect a candidate acceptable to the majority. But not everyone is on board.

Candidates are arranged on a spectrum

The most prominent candidate is Andrew Cuomo, a former governor with considerable name recognition, both because of his past tenure and because his father Mario was a beloved figure in New York state politics. However, Cuomo the Younger also has a checkered record: harsh maneuvering in Albany that included partnering with Republicans, poor handling of the COVID epidemic, credible accusations of sexual harassment of 11 women leading to his resignation, and hostile relations with New York City. He is positioning himself as a moderate focusing on public safety and housing affordability. He's a mixed bag, to say the least. But for months before voters started tuning in, he had a strong lead in opinion surveys. Lately his lead has diminished.

Cuomo's seeming polar opposite is Zohran Mamdani. Mamdani is a third-term state assemblyman and a Democratic Socialist. If elected, he promises to pursue an ambitious platform that includes free bus transit, increases in the minimum wage, public child care, rent freezes, and city-owned grocery stores. He has run a surprisingly effective social media campaign complete with catchy TikToks. Mamdani has now become the most plausible candidate to defeat Cuomo.

Somewhere between them is Brad Lander, the city comptroller. Lander seemed frankly kind of boring to me. But he is well-liked in the city. And he got headlines last week while he was accompanying a man to his immigration hearing. The man was taken by ICE agents, and the agents arrested Lander. Lander was soon released, but not before Mamdani held a press conference to support him.

Ranked-choice voting and strategic alliances

Mamdani’s appearance to boost Lander was a natural consequence of the fact that the two have cross-endorsed one another. They are in effect asking voters to view them as running together, or at least approving of one another as candidates. They want voters to rank both of them highly on Tuesday. Voters get to make five choices, and a Mamdani/Lander alliance is helps both of them against Cuomo. Presumably, if one of them wins, the other will play a key role in the new city government.

In ranked-choice voting as conducted in New York, voters can rank up to five candidates for mayor in descending order of preference. If their first choice finishes last, then the vote transfers to their second choice, and so on. This “instant runoff” process continues until there are two finalists left and one is the majority winner.

In 8 polls taken since Memorial Day, median first-choice support is at Cuomo 41%, Mamdani 30%, and Lander 8.5%. If all of Mamdani and Lander’s supporters did as they were asked by their favorites, the combined result would be Cuomo 41%, Mamdani 39%, a margin of Cuomo +2.0 +/- 1.6 points (median +/- SEM). That’s a race on a knife edge.

In this scenario, voters’ alternative choices will be the deciding factor. Mamdani and Cuomo are playing very different games. Continuing his strategic approach, Mamdani endorsed New York City Council Speaker Adrienne Adams, elevating her fundraising ability and possibly getting some voters to rank her above Cuomo. Adams has not returned the favor, and so far has declined to endorse Mamdani. Similarly, minor candidate Jessica Ramos has endorsed Cuomo, but he hasn’t endorsed Ramos.

A Single-Axis Theory

These four candidates are mostly acting as if they are all sitting along a single axis of polarization:

It is not necessarily the case that voters will act the same way. New York City is a diverse and complex place, containing specific groups with particular interests that they may wish to see pursued. But based on my research team’s analysis of past elections, most voters may end up acting as if they are somewhere on this axis as well.

For example, a Lander voter might mark their ballot as follows:

1. Lander

2. Mamdani

3. Adams

4. Cuomo

Alternatively, they might also mark their ballot like this:

1. Lander

2. Adams

3. Mamdani

4. Cuomo

Both of these orderings would be consistent with the diagram above.

On the other hand, a Cuomo voter might mark their ballot as follows:

1. Cuomo

2. Adams

3. Lander

4. Mamdani

As it turns out, the vast majority of voters think this way.

Voters sit on the axis too

My students and I have analyzed hundreds of ranked-choice elections in the United States at the federal, state, and city level. Unsurprisingly, when it’s Democrats vs. Republicans, voters act like the candidates are all along a single axis, which might correspond to progressive-to-conservative.

But we have also found something somewhat unexpected: even in primaries and nonpartisan elections, voters still act as if the candidates are arranged on a single axis. On average, we find that in a three-candidate race, 90% of voters act as if this is true. And even in a four-candidate race, 85% act as if this is true. We furthermore found that these numbers are well above chance.

In effect, voters have a single shared cognitive space, in which everyone views the same two candidates as being at the ends of the axis, with others arranged at intermediate locations. In other words, voters almost all see the same landscape - they just place themselves at different places on it.

Mamdani and Lander’s efforts to shape the axis

Now think of the strategic actions of the candidates. In a sense, Mamdani and Lander are trying to make the axis look a little uneven, like this:

In this diagram, Adrienne Adams is evidently in quite a powerful position, since she’s close to the 50th-percentile (“median”) voter. Other candidates such as Scott Stringer may also be in a similar position.

Andrew Cuomo’s self-imposed isolation

Cuomo has taken no publicly visible actions to make common cause with any other candidate. This is strategically suboptimal. However, he is acting like a lot of polarizing candidates who don't see a benefit in a ranked choice system.

A recent example is Sarah Palin, who was initially hostile to ranked-choice voting in her failed Congressional bid in Alaska (though she eventually came around). And in 2015, when Republican rules made it possible for 30-40% of support to win the nomination, Donald Trump would probably not have been interested in ranked-choice voting. In this respect, Cuomo is like Palin and Trump.

As you can see, Sarah Palin eventually came around to ranked-choice voting. Click to read the whole story.

Then again, Cuomo has cultivated Black churches and has received some key endorsements from older Black leaders. She might play quite an important role in determining the outcome of the race.

Defects in New York’s system of voting

Ranked-choice voting is efficient by ensuring a majority winner in a single round of voting. On the other hand, this process causes the entire campaign to culminate on a single day.

Lack of deliberation. If voters tune in slowly, that leaves little time for deliberation. This year, the role of deliberation has become clear. Cuomo's support has eroded in parallel with voters paying more attention. A potential defect in this system is the difficulty of getting voters to focus on a few candidates, thereby evaluating their merits. If you believe the trends of the last few weeks arise from voters belatedly keying in to Andrew Cuomo’s past problems and Zohran Mamdani’s weaknesses, then you might think the current system does not provide time to focus on the most serious candidate.

One alternative is a system in which a primary first forces the field to get smaller, leading to consideration of a few candidates for the duration of a general election season. Imagine the top four finishers in an all-party primary advancing to the general election. Then, an intervening campaign season would allow the finishers to be examined for an extended period by voters.

Let’s call such a system “Top-N.” In Alaska, N=4. That’s not a magic number. My collaborators and I are doing simulations that suggest that many of the benefits of ranked-choice voting still ensue when N is smaller. Imagine N=3, and being able to examine Cuomo, Lander, and Mamdani at length. The eventual result might be quite different.

Sore losers can wreck the system. There’s another weird defect in New York’s system: the November election is actually a plurality election. So in the end, the city may not get a winner with majority support.

The general election will include the winner of the Democratic primary perennial Republican candidate Curtis Sliwa, and a number of minor parties. Indeed, Andrew Cuomo has not ruled out running again as an independent candidate even if he loses the primary. Similarly, Mamdani could run as the nominee of the Working Families Party. Giving Cuomo or Mamdani two bites at the same apple seems like a mess.

Can this system be fixed?

To me, this suggests several defects that can be fixed.

Sore-loser laws in other states forbid a defeated candidate in a primary to run again in the general election.

And of course there is the problem that Sliwa and minor-party candidates are pretty well left in the cold. An all-party primary could give factions a meaningful voice in choosing their elected officials.

In the meantime, all New Yorkers should get out and vote on Tuesday!