I’ve been watching elections for many years and in that context I learnt a slogan (can’t remember the source) that’s applicable to many other areas of life. Mathematically it’s rather obvious and trite, but it’s one of those things that’s worth fixing in your brain because it’s an easy mistake to make in an reflective moment. Just because you have no idea what’s going to happen doesn’t mean it’s going to be close.
Put like this the maxim seems obvious, but the point can easily be lost. For example, let’s say you’re watching an election somewhere. There’s no polling, but you can think of a bunch of good arguments for either side winning. Say it’s generally a safe Yellow party seat but Purple has a strong candidate while Yellow’s candidate has recently been embroiled in a scandal. Also there has recently been a redistricting that favours Purple, but new voter laws favour Yellow. In my experience, under these conditions many people default to thinking the result is going to be close, conflating the uncertainty of the result with a prediction that there will be a small margin. This is wrong though- just because there are reasons to think it could be either outcome doesn’t mean it’s going to be close.
We might state this as:
There is a distinction between the kind of uncertainty that arises because you don’t have enough information, and the kind of uncertainty that arises because the process itself is on a knife edge, and with very little intervention could go either way.
Or more formally, there is a difference between a process that is uncertain because it’s median predicted result is near the tipping point, and a process that is uncertain because, whatever it’s median predicted result, the error bars are very large. Although we talk about the ‘median predicted result’ here, to be clear that the maxim can apply to categorical results so long as there is some notion of ‘closeness’. For example, the winner of a battle.
The distinction bears some similarities with, but is ultimately distinct from, that between Knightian uncertainty and quantifiable risk. Sometimes we have good reasons to think a result will be close, even in the absence of quantifiable information. Sometimes even when there is a quantifiable information, the error might be large.
I’ve found this is a useful maxim to keep in mind when analysing everything from elections, to competitions, to product launches, to wars and revolutions
DePonySum 