The average course size that students experience is bigger than the average course, because by definition the big courses have more students experiencing them ("the class size paradox.")
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When you go to the gym and look around, you feel relatively bad because the very frequent gym-goers are oversampled in your looking around, whereas the never-gym-goers are not sampled at all and don't make you feel (relatively) better.
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This is the assertion that "your friends are more popular than you are."
Why? Simplest way to see it: some people have no friends. But because they appear in nobody's friendship circles, they're not making anyone else feel unpopular.
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The selection effect that applies to these friendless (a.k.a. degree zero) people also applies to other people: the more friends you have, the likelier you are to be represented in people's friendship circles. So popular people are oversampled as friends. Hence the paradox.
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Still, what is the paradox exactly, as a quantitative statement?
Scott Feld, who coined the term and made the paradox famous, had one way of formalizing it. It isn't my favorite way, but it's a classic, and worth meeting first.
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A short thread on an obvious selection effect with some big consequences.
The social networks that are huge and very powerful now are the ones that grew the fastest. All else equal, these tend to be those with compelling products, but also another crucial thing:
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Being willing to make most trade-offs in favor of growth during a crucial period, which often was pretty long.
That process isn't pretty: it involves being willing to manipulate users and operate as many viral loops as possible, as long as they don't have a *growth* downside
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There's also a large, and maybe more important, effect on corporate culture: the people who grow most powerful and influential at the company during this period are the ones who were willing to give up a lot of other things for growth.
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Here's what she does: "I consider decision-making constrained by considerations of morality, rationality, or other virtues. The decision maker has a true preference over outcomes, but feels compelled to choose among outcomes that are top-ranked" by a "virtue/duty" preference.
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A question that people ask sometimes is, "What is your favorite paper in topic X written since y?"
It recently struck me that the reason I don't ever give a good answer is that it's a bit like the question, "What is your favorite beam in this building?"
It seeks assessment at the wrong level, both in terms of how most of us experience science, and in terms of what's important for its progress.
But it can take a while to see that!
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This was inspired by this @KevinZollman thread, which I like a lot because it says a similar thing at a different level (and in a different field).