Sunday, 16 January 2011

This can't be an equilibrium

OK Cupid finds that women whose pictures generate high variance in rated attractiveness do better than those with the same average but lower dispersion. That's not too surprising: suppose that your rule is to send a message to any woman you rate a 5/5. A woman whose image generates a lot of 5s and a lot of 1s will do better than a woman whose image gets a 4 from everyone.

But Cupid also found, in regression analysis, the greater the number of 1/5 ratings, the more messages sent. 2s and 4s reduced total messages, and 5s increased them a fair bit. They chalk this up to game theory: if you think the woman you're rating highly won't be in too strong of demand, you'll send her a note. But if you think she'll have mass appeal, you'll not bother as your message will be lost in the swamp. As Yogi Berra might have put it "That woman's so cute, nobody asks her out anymore."

Two points to note. First, I have a hard time seeing this as an equilibrium now that this is a full information game. Once everyone knows that fewer messages are sent to the girls with mass-market appeal, they'll increase their likelihood of sending messages to those girls, right?

Second, I wonder what would happen if the regression were switched to have the dependent variable be "man sends a message" rather than "number of messages received by a woman". Run it as a probit. It's not completely implausible that some men send messages to women they've rated a one (so long as that rating isn't seen by her!), if he figures she'll be getting few invitations.

I can't disagree with OK Cupid's concluding advice:
But our advice can apply to anyone. Browsing OkCupid, I see so many photos that are clearly designed to minimize some supposedly unattractive trait—the close-cropped picture of a person who's probably overweight is the classic example. We now have mathematical evidence that minimizing your "flaws" is the opposite of what you should do. If you're a little chubby, play it up. If you have a big nose, play it up. If you have a weird snaggletooth, play it up: statistically, the guys who don't like it can only help you, and the ones who do like it will be all the more excited.
OK Cupid is big enough that there'll be a niche market in everything. Playing to the niche means that you're pre-screening for folks likely to be good matches rather than letting the screening happen after investments of time and effort.

I'm just lucky that that strategy worked for me in a non-online, much lower N environment back in '99 when this particular niche product found an interested match. Hi Susan!

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