This week I came across a real world example of an uncertainty that became more polarised—an event caused the outcome to be more likely to go to one extreme or the other, and less likely to be middling. I realised it when someone asked if I thought David Davis’s resignation was a good thing or a bad thing. Let me explain…

Shortly after Theresa May engineered her cabinet to collectively endorse her white paper on leaving the EU, the minister responsible for ensuring the UK’s exit, David Davis, resigned. I appreciate that events have moved fast since then, and continue to do so, but for the sake of discussion let’s keep it narrow: a briefly-united cabinet followed by a departing minister.

The uncertainty we’re considering is around how hard a Brexit we’re likely to end up with. As Nico Lategan has explained (which I’ve referenced before) we can describe this as our degree of sovereignty, with the scale on the x-axis running wider than “soft Brexit” to “hard Brexit” (not withstanding that these are very rough descriptions anyway). Further to the left is annexation, like Crimea under Russia, and further to the right is complete isolation, like North Korea. No-one seriously wants either of those; soft Brexit and hard Brexit are between those two extremes.

But while prominent Leave supporter Davis was in the cabinet, tacitly endorsing the paper, there was some likelihood that we’d get a soft-ish Brexit. That is roughly what May’s paper suggested. I like using probability distributions for picturing this kind of thing. The probability distribution here would look something like this:

But with Davis out of the cabinet I’d guess there is more opportunity for Brexiteer rebellion from her own party, and less chance of a compromise. This means the resulting degree of sovereignty is less likely to fall in the middle. The probability distribution shifts to something a bit more like this:

Whether you think this change is good or bad depends on your point of view. As a Remainer I would rather we stay in the EU, and the chances of that are increased a bit, which is good. But the chances of a very strong separation are also increased. There is a smaller chance of something in the middle. So if I can’t get everything I want there’s less of a chance I’ll get close to what I want, and I think that’s bad.

Overall, then, for me Davis’s resignation is a bad thing, as seen through the lens of how hard a Brexit we may get. You may see things differently. Another Remain supporter may look at the increased chance of remaining very close to, or in, the EU and be motivated to exploit the opportunity. A Leave supporter may be happy with an increased chance of a clearer separation, albeit via the route of some rebellion or upset. A Russian president may judge things with another scale of measure entirely—the stability of the UK government, say, or the strength of the UK government on the world stage.

But the real point of this discussion is to exercise a tool for thinking about this.