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Vaniver comments on Negative and Positive Selection - Less Wrong
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I asked my father to read this and give his thoughts.
He says that positive selection only works well when you have a very good idea what you need to select for. If you're sending an athlete to the Olympics but the event he'll have to compete in will be chosen at random, you can't just choose the one with the best time on the 800 meter dash, because the event might end up being something like archery, fencing, or weightlifting. And you certainly wouldn't want to send a non-swimmer. If you need a generalist, seeing how well someone does at jumping through a wide variety of arbitrary hoops might really be the best test you can practically implement.
(Now I'm wondering just how good or bad the 800 meter dash actually is at predicting levels of success at unrelated sports. For example, could you tell the difference between an NHL-quality ice hockey player and one that plays on a minor league team just by looking at their times on the 800 meter dash?)
This (among other prior information) suggests to me that extreme levels of performance at different tests are probably negatively correlated, but I would not be surprised if there were events out there where extreme levels of performance on other tests are correlated with better (but not extreme) levels of performance on that test.
Unless you sample at random from the whole population, that's a Berkson's fallacy.
Upvoted for this link. I wish I had known this term back in the Amanda Knox days -- this fallacy (or rather, the reverse of it -- failing to take into account conditional dependence of a priori independent events) is a version of the main probability-theoretic error of that case.
This fallacy may also explain why people tend to assign 50% percent probability to the odds of the second child being a boy in the classic puzzle.
Thanks for the link! I think a careful statement of my claim avoids that fallacy.
The claimed data:
Stated carelessly, it seems likely to me that if I know you're an Olympic-level athlete, I'll have some estimate that you can play Olympic-level basketball; but then when you tell me that you're a Olympic-level wrestler, I can lower my probability estimate that you would be able to play Olympic-level basketball.
But if I condition on knowing you're an Olympic athlete, and then try to drop that condition without being careful, then I can get into trouble (this fallacy, specifically). So instead, let's start off with some (really low) probability that a person chosen uniformly at random can play Olympic-level basketball, and then update on the knowledge that they're an Olympic wrestler- we should increase our estimate based on their general level of athleticism, and then decrease our estimate based on their probable body shape. I think the effect of the body shape will be stronger than the effect of general athleticism, and so they will actually be negatively correlated.
I think my last statement in the grandparent- that extreme levels of performance on a specific test should correlate with better performance on some 'general athleticism' test- is true when you compare extreme individuals to random individuals, but less true (or perhaps not true) when comparing extreme individuals to good individuals. The NHL ice hockey player is probably not much more 'athletic' than a minor league hockey player, but probably is more 'hockey-shaped.'
But now that I've stated that last paragraph, I'm thinking of counterevidence- like the famous birth month effect for Canadian hockey players. Early training appears to have a huge impact on whether or not someone hits extreme levels of performance, but I think both NHL players and minor league players started early. So maybe it is biological talent that differentiates many of them. Hmm. I should probably stop speculating about sports.
If you put an Olympic-level wrestler on a college (American) football team, how well would they do? Michael Jordan did tolerably well during his year as a minor league baseball player.
Tolerably well for minor league, but remember that his father had envisioned him as a major league baseball player, so presumably he'd practiced and done well at the sport when he was younger. There are probably selection effects on Michael Jordan in particular to be good at baseball out of the set of NBA players; most never try to transition to baseball at all.