Polya Urn Model Dissolves The Gender War

Now listen, you queer, you stop calling me a crypto-Nazi or I’ll sock you in the goddamn face and you’ll stay plastered.

—William Buckley1

I’m not sure whether the two sexes are about to stage World War III over gender issues or if I’m in some sort of gender bubble but, for whatever reason, I’ve been hearing about gender issues daily for the past six or so weeks and, as part of a gender, I have some thoughts on it. These thoughts revolve around the notion of boys clubs and general irritation at the idea that I’m somehow in the wrong for being a manly guy who likes to do manly things, and those manly things happen to be math and computers.

You see, friend, I’m part of a number of male-dominated communities, of boys clubs, and — to my perpetual dismay — I find myself surrounded by discussions where some naive progressive yells something like, “Hey, look at all these men here. It’s all men. Where are the women? Therefore, sexism.” And I’m thinking something like, “Hey, fuck you. I’m not a fucking sexist. Take your agenda elsewhere and let me read about category theory in peace.”

But then I had idea. What if boys clubs are like Polya’s urn? And, if you don’t know what Polya’s urn is, don’t worry, because I’m about to tell you. There’s this urn, right, a big fucking urn, and it’s got two balls in it, like one of those lottery contraptions, a blue one and a red one. Here’s the thing about this urn, though. When you draw a blue ball from it, you have to put two blue balls back in. When you draw a red ball, you put two red balls back in.

Now, the notable thing about this urn is that small changes in initial conditions lead to big changes in the long run. If your first draw is blue, it’s pretty likely that all the subsequent draws will be blue, too.

What if male-dominated sites like, let’s say Reddit, are like this? The Reddit founders were two men, Alexis Ohanian and Steve Huffman. Given that men are more likely to have male friends, they’re like the balls in Polya’s urn. They’re in the urn, convincing a friend to sign up is like picking a ball out of the urn and throwing two more back in, and Reddit’s current male-dominance is the long-run outcome of this sort of process. Men invite men, therefore men and not sexism. QED.

Hey, look Ma! My model predicts boys clubs without positing sexism anywhere.

Or, you know, there’s the whole compelling narrative that men and women have different preferences, with men more likely to be interested in things, like computers, and women more interested in people. Oh, and hey, before you go screaming “But that’s sexist. Men and women are the same in every way,” here’s some empirical validation with massive effective sizes.

1. A Google search for both “quotes about men” and “quotes about women” return these pages. Both are filled with quotes about how great women are and what brutes men are.

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