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Kevin Dorst, Ph.D.

# How to Polarize Rational People

## An experiment showing how ambiguous evidence can pull reasonable people apart.

The core claim of this series is that political polarization is caused, in the main, by individuals responding rationally to ambiguous evidence.

To begin, we need a possibility proof: a demonstration of how ambiguous evidence can drive apart those who are trying to get to the truth. That’s what I’m going to do today.

​I’m going to polarize you, rational readers.

In my hand, I hold a fair coin. I’m going to toss it twice (…done). From those two tosses, I picked one at random; call it the Random Toss. How confident are you that the Random Toss landed heads? 50-50, no doubt—it’s a fair coin, after all.

​But I’m going to polarize you on this question. What I’ll do is split you into two groups—the Headsers and the Tailsers—and give those groups different evidence. What’s interesting about this evidence is that we can predict that it’ll lead Headsers to (on average) end up more than 50% confident that the Random Toss landed heads, while Tailsers will end up (on average) less than 50% confident. That is: Everyone (yourselves included) can predict that you’ll polarize.

The trick? I’m going to use ambiguous evidence.

First, to divide you: If you were born on an even day of the month, you’re a Headser; if you were born on an odd day, you’re a Tailser. Welcome to your team.

You’re going to get different evidence about how the coin-tosses landed. That evidence will come in the form of word-completion tasks. In such a task, you’re shown a string of letters and some blanks, and asked whether there’s an English word that completes the string. For instance, you might see a string like this:

P_A_ET

And the answer is: yes, there is a word that completes that string. (Hint: what is Venus?) Or you might see a string like this:

CO_R_D

And the answer is: no, there is no word that completes that string.

That’s the type of evidence you’ll get. You’ll be given two different word-completion tasks—one for each toss of the coin. However, Headsers and Tailsers will be given different tasks. Which one they’ll see will depend on how the coin landed.

The rule:

• For each toss of the coin, Headsers will see a completable string (like ‘P_A_ET’) if the coin landed heads; they’ll see an uncompletable string (like ‘CO_R_D’) if it landed tails.
• Conversely, for each toss, Tailsers will see a completable string if the coin landed tails; they’ll see an uncompletable string if it landed heads.

Here’s your job: Click on the appropriate link below to view a widget which will display the tasks for your group. You’ll view the first world-completion task, and then enter how confident you are (between 0–100%) that the string was completable. Enter “100” for “definitely completable," “50” for “I have no idea," “0” for “definitely not completable," and so on.

If you’re a Headser, the number you enter is your confidence that the coin landed heads on the first toss. If you’re a Tailser, it’s your confidence that the coin landed tails—so the widget will subtract it from 100 to yield your confidence that the coin landed heads. (If you’re 60% confident that the coin landed tails, that means you’re 100–60 = 40% confident that it landed heads.)

You’ll do this whole procedure twice—once for each toss of the coin. Then the widget will tell you what your average confidence in heads was, across the two tosses. This is how confident you should be that the Random Toss landed heads, given your confidence in each individual toss. And this average is the number that will polarize across the two groups.

Enough set up; time to do the tasks.

Welcome back. You have now, I predict, been polarized.

This is a statistical process, so your individual experience may differ. But my guess is that if you’re a Headser, your average confidence in heads was greater than 50%; and if you’re a Tailser, your average confidence in heads was less than 50%.

I’ve run this study. Participants were divided into Headsers and Tailsers. They each saw four word-completion tasks. Here’s how the two groups’ average confidence in heads (i.e. their confidence that the Random Toss landed heads) evolved as they saw more tasks:

The average confidence in heads of each group after seeing 0–4 independent word-completion tasks. Blue is Headsers; orange is T
Source: Kevin Dorst

Both groups started out 50% confident on average, but the more tasks they saw, the more this diverged. By the end, the average Headser was 58% confident that the Random Toss landed heads, while the average Tailser was 36% confident of it.

(That difference is statistically significant; the 95%-confidence interval for the mean difference between the groups’ final average confidence in heads is [16.02, 26.82]; the Cohen’s d effect size is 1.58—usually 0.8 is considered “large”. For a full statistical report, including comparison to a control group with unambiguous evidence, see the Technical Appendix.)

Upshot: The more word-completion tasks Headsers and Tailsers see, the more they polarize.

The crucial question: Why?

Getting a complete answer to this—and to why such polarization should be considered rational—will take us a couple more weeks. But the basic idea is simple enough.

​A word-completion task presents you with evidence that is asymmetrically ambiguous. It’s easier to know what to think if there is a completion than if there’s no completion. If there is a completion, all you have to do is find one, and you know what to think. But if there's no completion, then you can’t find one; but nor can you be certain there is none—for you can’t rule out the possibility that there’s one you’ve missed.

I polarized you by exploiting this asymmetry. Headsers saw completable strings when the coin landed heads; Tailsers saw them when it landed tails. That means that Headsers were good at recognizing heads-cases and bad at recognizing tails-cases, while Tailsers were good at recognizing tails-cases and bad at recognizing heads-cases. As a result, they polarize.

To preview where we’re headed: these ambiguity-asymmetries can be exploited. Fox News can spin its coverage so that information that favors Trump is unambiguous, while that which disfavors him is ambiguous. MSNBC can do the opposite.

So when we divide into those-who-watch-Fox and those-who-watch-MSNBC, we are, in effect, dividing ourselves into Headsers and Tailsers. As a result, we can be rationally polarized.