Peaks and valleys, too clever by half
It’s often said that “a little knowledge is a dangerous thing”. On this view, there’s a “bad valley” - a level of knowledge that’s actually harmful. That’s because small amounts of knowledge are supposed to lead to big increases in overconfidence.
No doubt there are situations where more knowledge is harmful. But it seems to me to be an untypical situation. Usually, the more knowledge, the better. Being somewhat literate is better than being illiterate. Knowing some French when you’re in France is better than knowing none. And so on.
Similarly, there is a common misconception about the Dunning-Kruger effect. According to this misconception, the Dunning-Kruger effect says that the most incompetent are more confident than people of average competence. Only the most competent have a confidence level that starts to match that of the least competent. So again we see this “valley”; this time of lower confidence.
But in fact, the Dunning-Kruger effect just says that people’s confidence is more or less independent of their actual competence. So there is no valley, but just a boring straight line (more or less).
Here’s yet another counter-intuitive claim:
I think Biden winning by a razor-thin margin is the least likely scenario. Likelier that either the bottom drops out for Trump and Biden wins handily, or Trump ekes it out again.
It seems that our prior should be different. If we think that one candidate is somewhat more likely to win, then our prior should plausibly be that the most likely outcome is that they will win by a narrow margin. And that the further away an outcome is from that peak, the less likely it is.
That is, that the prior distribution is unimodal rather than bimodal.
Of course, there might be evidence that the distribution is different in the Biden vs Trump case. Maybe there is some mechanism that either propels Trump to victory, or makes “the bottom drop out” for him. Though my intuition is to be sceptical of that, unless I get much more detailed evidence. We tend to put too much credence in these kinds of inside-view explanations. By default I would stick to the outside view - to the unimodal prior. If so, there’s again no valley.
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Another claim you often hear is that there’s a “narcissism of small differences” in politics. That people who are fairly close on the political spectrum, yet disagree a bit, hate each other more than those who are further away. Again, there’s a supposed valley, this time of political sympathy:
But again, this seems like a relatively uncommon pattern. Usually, left-wing parties cooperate with other left-wing parties, and right-wing parties cooperate with other right-wing parties. And they express more sympathy for parties that are closer to them. On that view, political sympathy is rather a monotonically decreasing function of political distance.
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These claims are all counter-intuitive and thought-provoking. It’s counter-intuitive that a little knowledge is harmful, that the least competent are most confident, and that those who are politically closest are the most bitter enemies. This makes these claims seem clever, and gives them a bit of bite. The incorrect version of the Dunning-Kruger effect is more interesting than the correct version. So people who’ve misunderstood it is more likely to put it in a PowerPoint. And so it spreads.
Relatedly, these claims all have an inside-view character. The outside view supports the alternative and simpler theories - that the more knowledge the better, that political sympathy decreases with political distance, etc. So our prior should be that they are correct. We could of course have reason to move away from that prior, if we obtained sufficiently firm evidence. But more often than not, we aren’t given such firm evidence, but only smart-sounding just so-stories. And we’re too inclined to believe in such just so-stories - and too inclined to believe in the inside view. So we should be more sceptical of them.