Discrimination: A quick math puzzle

2012-08-22 00:29

Someone in a discussion recently conceded that people in meetings will often ignore a woman’s idea, but react positively to the same idea if a man offers it. This is moderately well studied. He then went on to point out that if this didn’t happen, things might not be better; after all, it wouldn’t be “twice as many people are talking and being listened to”, the meeting would still have the same amount of time and pick up the same number of ideas.

This is not correct. Normally, ideas are weighted by applicability, appeal, or otherwise in terms of how people feel about them. But if you start weighing something else instead, that falls by the wayside.

Here’s a way you can sort of explore this. Take a deck of cards, and deal them out face up, two at a time. From each pair, take the left card, and sum the totals of the cards (A=1, J=11, Q=12, K=13). Your sum is likely to be in the rough neighborhood of 182; the average card’s value is 7, and you have 26 of them.

Now, what if instead of taking the left card, you always took the higher card? I get an average of about 238-239.

And now for the illustration. Deal the cards two at a time. If one card is red and one is black, take the red card. Otherwise take the higher card. What do you end up with? I seem to see an average of around 211. You still get some benefit from being selective when you have a red-red or black-black comparison, but the rest of the time, you’re back in random-choice territory.

Now, some people might argue that that’s okay, because men are better than women and give better ideas. That’s a stupid thought, but the beauty of the test is: It doesn’t matter. Let’s say we cheat. Take out all the red 1, 2, and 3 cards, and all the black J, Q, and K cards. It should be pretty obvious that the average of all the red cards is higher, right?

Well. If you select randomly, you get a total around 139 (lower because there’s fewer cards). If you pick the higher card, you get 178. And if you prefer red, but pick the higher card in red-red or black-black pairs? 172.

What, you say? Selecting consistently from a set with higher averages still hurts you? Why, yes. Yes it does.

Discrimination hurts your chances, and the beauty is, it does so even if you are right about the respective merits of the two groups. It really is important to try to be fair.

Peter Seebach

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