​It’s September 21, 2020. Justice Ruth Bader Ginsburg has just died.  Republicans are moving to fill her seat; Democrats are crying foul.

​Fox News publishes an op-ed by Ted Cruz arguing that the Senate has a duty to fill her seat before the election. The New York Times publishes an op-ed on Republicans’ hypocrisy and Democrats’ options.

Becca and I each read both. I—along with my liberal friends—conclude that Republicans are hypocritically and dangerous violating precedent. Becca—along with her conservative friends—concludes that Republicans are doing what needs to be done, and that Democrats are threatening to violate democratic norms (“court packing??”) in response.

In short: we both see the same evidence, but we react in opposite ways—ways that lead each of us to be confident in our opposing beliefs.  In doing so, we exhibit a well-known form of confirmation bias.

And we are rational to do so: we both are doing what we should expect will make our beliefs most accurate.  Here’s why.

As we learn to live in the ‘new normal’, amidst the easing and tightening of local and national lockdowns, day-to-day decision-making has become fraught with difficulty. Here are some of the questions I’ve been grappling with lately:

• When would be a good time to visit friends and family members?
• Should I head out to the shop/ pub/ restaurant/ hairdresser this week?
• Would it be more sensible to stay home?

A year ago these questions had easier answers. I only needed to check in on my mood, bank balance, or general state of dishevelment. Now it’s far harder to weigh up the costs and benefits of going out and about. There’s so much more hanging on each decision. Is it worth taking the risk of picking up – or passing on – the virus? Of course, we will all settle on our own ways of balancing these concerns. But, in this post, I’m going to look at how our attitudes to risk depend on framing.

So far, I’ve laid the foundations for a story of rational polarization. I’ve argued that we have reason to explain polarization through rational mechanisms; showed that ambiguous evidence is necessary to do so; and described an experiment illustrating this possibility.

Today, I’ll conclude the core theoretical argument. I'll give an ambiguous-evidence model of our experiment that both (1) explains the predictable polarization it induces, and (2) shows that such polarization can in principle be profound (both sides end up disagreeing massively) and persistent (neither side is changes their opinion when they discover that they disagree).

With this final piece of the theory in place, we’ll be able to apply it to the empirical mechanisms that drive polarization, and see how the polarizing effects of persuasion, confirmation bias, motivated reasoning, and so on, can all be rationalized by ambiguous evidence.

Recall our polarization experiment.