08 February 2010

"marriage supermarket"

Marginal Revolution | Alex Tabarrok | Revisiting the Marriage Supermarket

In comments to yesterday's post on the effects on dating style of a declining number of university men a number of people asked why a relatively small change in the sex ratio (m:w) from 50:50 to say 40:60 should make such a big difference.  In the Logic of Life, Tim Harford gave a characteristically excellent explanation.

Imagine, says Tim, a marriage supermarket. In this supermarket any man and woman who pair up get $100 to split between them. Suppose 20 men and 20 women show up at the supermarket, it's pretty clear that all the men and women will pair up and split the $100 gain about equally, $50,$50. Now imagine that the sex ratio changes to 19 men and 20 women. Surprisingly, a tiny change in the ratio has a big effect on the outcome.
I think Tabarrok's explanation is good; read the rest of his post for details. He does leave out Harford's point that woman can either accept a worse deal from their mates OR try to improve their own desirability. I'd bet that if you found two colleges with similar climates and academic standards but different gender ratios, women at the one with fewer men would spend more time at the gym, more money on clothes and more time preparing to go out.  Somebody get some grad students on that, pronto. I'll volunteer to do the field work at the campus with a paucity of men.

So I like the "marriage supermarket" explanation, but I think there's an even simpler one. A move from a 50-50 split to a 40-60 split is not "relatively small change" at all. Assume you have 100 students, 40 men and 60 women, and they all wanted to pair up in heterosexual relationships. (Assume also they are all equally desirable, since unequal distribution of desirability would only exacerbate the problems.)  In this case 20 women would be left without mates. That's a third of all the women. They would have to look for companions from the 40 men already paired off, which means 20 men would have the opportunity to have two women competing for them. That's half of all men.

Our instinct is to see a 40-60 split and think "oh, that's only 10 percentage points fewer men," but in this case it actually effects 50% of men, and therefore 50% of couples.

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