The Stopped Clock Problem

[Unusually for me, I actually wrote this and published it on Less Wrong first. I’ve never reverse-cross-posted something to my blog before.]

When a low-probability, high-impact event occurs, and the world “got it wrong”, it is tempting to look for the people who did successfully predict it in advance in order to discover their secret, or at least see what else they’ve predicted. Unfortunately, as Wei Dai discovered recently, this tends to backfire.

It may feel a bit counterintuitive, but this is actually fairly predictable: the math backs it up on some reasonable assumptions. First, let’s assume that the topic required unusual levels of clarity of thought not to be sucked into the prevailing (wrong) consensus: say a mere 0.001% of people accomplished this. These people are worth finding, and listening to.

But we must also note that a good chunk of the population are just pessimists. Let’s say, very conservatively, that 0.01% of people predicted the same disaster just because they always predict the most obvious possible disaster. Suddenly the odds are pretty good that anybody you find who successfully predicted the disaster is a crank. The mere fact that they correctly predicted the disaster becomes evidence only of extreme reasoning, but is insufficient to tell whether that reasoning was extremely good, or extremely bad. And on balance, most of the time, it’s extremely bad.

Unfortunately, the problem here is not just that the good predictors are buried in a mountain of random others; it’s that the good predictors are buried in a mountain of extremely poor predictors. The result is that the mean prediction of that group is going to be noticeably worse than the prevailing consensus on most questions, not better.

Obviously the 0.001% and 0.01% numbers above are made up; I spent some time looking for real statistics and couldn’t find anything useful; this article claims roughly 1% of Americans are “preppers”, which might be a good indication, except it provides no source and could equally well just be the lizardman constant. Regardless, my point relies mainly on the second group being an order of magnitude or more larger than the first, which seems (to me) fairly intuitively likely to be true. If anybody has real statistics to prove or disprove this, they would be much appreciated.

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