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One answer: If you have a selection process that compares a minority group against the general population for any metric which produces a well-defined ranking,
by Enginerrrd 5y ago
One answer: If you have a selection process that compares a minority group against the general population for any metric which produces a well-defined ranking, and then selects for the top X% of performers on that metric, then you will end up with a selected group that has a lower proportion of the minority group.
To put this in clearer language: If I have a bunch of 100-sided dice: 90 blue dice in one bucket, and 10 red dice in another, and I roll them all and select the top 10 numbers rolled, I'll have a greater proportion than 90% of blue dice, because there are more total dice rolls in that group.
- aaaaaaaaaaab 5y agoThis doesn’t sound right. Can you prove this?
- pandaman 5y agoI guess he is alluding to effects of rounding up/down in small samples but those cannot be biased in one direction. Nor are they certain to happen. If I toss 9 quarters and a nickel and count the fraction of tails that rolled on the nickel then it will be equal to 1/10 of all the tails only if all coins roll tails or all roll heads i.e. in 2 outcomes out of 1024. In half of the other cases nickel tails will be overrepresented and in in the other half - underrepresented. It's because you cannot roll a fraction of a tail.
- Enginerrrd 5y agoI just ran some monte carlo simulations. Turns out I was totally wrong, at least for a uniform distribution. I now suspect it's probably true for any distribution, but I can't prove it yet. It just seems really odd to me: It seems like because you get 9x the number of dice rolls for one group you would end up with a final distribution that favors the majority group, but that is obviously not the case. I need to wrap my brain around that one.