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How to read those second-choice polls

Since so many candidates are running for president this year, people are spending a lot of time trying to figure out who can take votes from whom. And this has created a lot of interest in polls that ask supporters of each candidate who their 2nd choice is - particular in those conducted by Morning Consult, which updates its numbers quite frequently.

But there seems to be a lot of confusion about how to read these polls.
The standard mistake goes something like this. First, Morning Consult will publish its usual Second Choice Selections charts:

Then, someone will just compare these percentages to each other - directly - in order to decide who is taking the most voters from a given candidate. Here, for example, one might ask "Who has the largest number of 2nd-choice Bernie Sanders supporters?" And looking at the percentages, they might conclude that it is Elizabeth Warren rather than Joe Biden, since 34% is bigger than 26%.

What this analysis forgets is that Joe Biden has many more voters than Elizabeth Warren. This means that 26% of the Biden coalition represents a much larger number of voters than 34% of the Warren coalition. Here is what the charts above look like if you want to compare them directly:
This is just simple arithmetic: since 2nd-choice Sanders voters are 26% of Biden's coalition, and Biden's coalition represents 31% of all voters, then Biden-to-Sanders voters are (26% x 31% =) 8.1% of all voters. That's a larger absolute number of voters than Warren-to-Sanders voters, who are only 5.1% of the electorate.

But that's not all - now consider what happens if Sanders can actually win these 2nd choice swing voters. First, here's what the new numbers look like if Sanders wins all of the Warren-to-Sanders voters:
All things being equal, if Sanders captures his 2nd-choice voters from Warren, this leaves him trailing in second place by nearly four points. Compare that to what happens if Sanders takes the Biden-to-Sanders voters instead:
In this case, Sanders gets an 8.1% bump - and Biden loses 8.1% at the same time - which gives Sanders (30.1%) a more than seven point first place lead.

Bearing these numbers in mind, I remain skeptical about how useful these polls actually are:

  • For another, they don't take into account voter commitment. We know that a relatively high-number of Biden and Sanders supporters have their minds made up and will never transition to a second choice, whereas supporters of other candidates are far more fickle. This might suggest that Biden voters would be harder to move into the Sanders camp, even though more of them say he would be their second choice if they did move - but perhaps 2nd-choice Sanders supporters are less committed to Biden than the rest of his coalition is? We just don't know.
  • And for another, the second-order effects of crossover voting are very difficult to account for: for example, if Sanders takes away some voters from Biden, do other Biden voters flee the sinking ship and rally behind Warren?
  • Finally, why are we talking about competing for Biden and Warren voters as an either/or proposition? Can't Sanders vie for both, for example by stressing how preferable his health care plan is?

Nevertheless, if we are going to use the polls, we need to read them correctly. When you do the simple arithmetic, targeting Biden voters gives Sanders a potential seven point lead, while targeting Warren voters puts Sanders, at best, down by four points. In other words, the Biden strategy does eleven points better than the Warren strategy and gives you first place rather than second. This is the exact opposite of the popular misreading of these polls where you simply compare the percentages suggests, but that's how math works.