New York City is currently undergoing their first experience of using ranked-choice voting, otherwise known as preferential voting, in a major election. It is being used for the primaries for the mayor of New York City along with other local offices.

The Democratic mayoral primary will effectively decide the election, with whoever wins almost certainly going on to win the general election.

At the moment only the first preference votes have been counted, and even those aren’t complete, because we’re waiting on absentee votes. No preference distribution will be conducted until the final first preference count is in. This is different to Australia, where interim preference distributions are usually available from election night.

I don’t have any special insight into New York City politics or the candidates, but I do know a lot about preferential voting, and I think a lot of the analysis has been looking at the wrong questions. So here I thought I would lay out the key questions that need to be answered to know which outcomes are most likely.

- What proportion of preferences are exhausting before they reach the top three candidates, and what proportion exhaust before reaching the top two?
- How do preferences from other candidates split between the top three (Adams, Wiley and Garcia)?
- How do preferences from other candidates split between the top two (Adams and either Wiley or Garcia)?

On the **latest figures**, these are the votes for the leading candidates:

- Eric Adams – 31.7%
- Maya Wiley – 22.3%
- Kathryn Garcia – 19.5%
- Andrew Yang – 11.7%
- Others – 14.8%

Yang cannot overtake Garcia, let alone Wiley. I am confident of that. I am also confident that Adams will certainly come in the top two at the end of the count, and will likely still be in first place when the first preference count is concluded. I won’t venture opinions about whether his vote is likely to go up or down as the count continues.

But it is entirely possible that Garcia could close the 2.8% gap between her and Wiley off the 26.5% of the vote cast for minor candidates. This makes things more complicated. If the top two was clear, there would be less variables to consider.

So we need to determine which of the other two candidates (Wiley or Garcia) is likely to make the final count, and how they will do against Adams.

**Exhaustion rates**

You can’t understand how hard it will be for Wiley or Garcia to win without knowing how many preferences are exhausting.

It is wrong to think of this contest as a race to 50%. You don’t need a majority to win. You just need the most votes at the end. So it is more of a race to see if any other candidate can catch Adams, or if he can hold on to his lead. If no-one overtakes him, he wins. Adams will have an easier time winning if more preferences exhaust, since that leaves fewer votes for someone else to catch him.

There are thirteen candidates in the race, and voters may number up to five preferences. In theory it’s possible for voters to number five candidates and skip all of the viable candidates, but that’s not that likely. Voters will usually preference at least one of the viable contender high up – it’s rare that someone will vote just for a bunch of low-profile and low-polling candidates.

But voters are not required to number five preferences. Adams will have a much better chance if large numbers of voters have just chosen to mark a first preference. I would argue that is the key metric that will decide the race.

If we want to be technical, there are three different exhaustion rates we need to consider:

- Votes that exhaust before reaching the final three (out of 26.5% of the total vote cast for the other ten candidates)
- Votes that exhaust before reaching Adams or Wiley (out of 46.0%)
- Votes that exhaust before reaching Adams or Garcia (out of 48.8%)

**How preferences split between the top three**

Okay, so there are 26.5% of the votes cast for Andrew Yang and the nine candidates below him. How do they preference between Adams, Wiley or Garcia?

It’s not so simple as to say Garcia needs a certain proportion of the vote, since Adams will be taking some (probably many) of these votes. He doesn’t need them yet, but any votes that flow to him won’t have a say in deciding between Wiley or Garcia.

Garcia is 2.8% behind Wiley. So she needs 2.8% more than Wiley, after factoring in exhaustion rates and the proportion of the vote for Adams. If 40% of those 26.5% of the electorate exhaust, and 40% of the remainder vote for Adams, then Garcia needs to win 64.7% of the remaining votes to overtake Wiley and make it to the final two. Increase those two variables, and Garcia’s challenge gets even harder.

Exhaustion rate

20%

40%

60%

20%

40%

60%

Adams preferences

25%

25%

25%

40%

40%

40%

Garcia target

58.8%

61.7%

67.6%

61.0%

64.7%

72.0%

**How preferences split between the top two**

This is simpler to model, but we need to do it twice.

Wiley is currently 9.4% behind Adams. So she needs to lead on the remaining count by 9.4% (of the total vote) to win. 46% of the vote has gone to candidates other than the top two. If no preference were to exhaust, Wiley would need 27.7% of the vote, or 60.2% of the preferences available. As the exhaustion rate rises, that task becomes more difficult.

Exhaustion rate

0%

25%

40%

50%

60%

75%

Wiley target

60.2%

63.6%

67.0%

70.4%

75.5%

90.9%

It’s slightly harder still for Garcia. There is a slightly larger pool of preferences (48.8% of the total vote) including Wiley’s votes, but Wiley also has a larger gap to close (12.2% of the total vote).

Exhaustion rate

0%

25%

40%

50%

60%

75%

Garcia target

62.5%

66.7%

70.8%

75.0%

81.3%

100.0%

That’s right, if 75% of preferences from Wiley, Yang and others exhaust before flowing to Adams and Garcia, then Garcia would need to win every single remaining preference to tie the result.

I don’t have any data beyond the data that has been published, and I haven’t tried to do any analysis of likely trends. Other people who know more about NYC politics. But you should be targetting your analysis at answering these variables, and that will then inform judgements about who is likely to win.