One of my favorite things about Bob Wilson, co-winner of today's prize, is how gentle a giant he is, how modest yet understatedly charismatic and funny. This rare recording gives a sense.
"I'm here to today to argue that sequential equilibrium [his own invention with Kreps] -- which you said ... in 1982 completed the answer to the questions that Luce and Raiffa raised in 1957 -- well, MY stance was that that was a mild disaster!
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"Sequential equilibrium turned out to have enormous flaws. And the revelation of those flaws has, I think, been actually opening up what the real challenge is for game theory in terms of establishing what its foundations are.
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Now I realize there are all these applications, this rich domain of applications. But it's been UNSETTLING to me that game theory went off down track of technical devices, more and more elaborate technical devices, without establishing foundations.
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And the foundations have remained opaque. They're clear up to a certain point—I would take the point of view up until the point of sequential equilibrium. And then I want to suggest that there's a lot more to do."
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Here @O_Goss_ reviews some of that work. Bob won primarily for his foundational work on auctions and mechanism design, as well as their applications.
But his separate work just on foundations of game theory would be a stellar career all by itself.
We look at a society where people update their opinions according to the _DeGroot model of updating_. It says you decide what to think tomorrow by taking a weighted average of what you and your friends think today.
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Despite its simplicity and strong assumptions, DeGroot's model has been a surprisingly helpful workhorse in networks.
We ask: suppose initial estimates are centered at the truth θ and conditionally independent.
Do we get a "wisdom of crowds" in the long run? More precisely...
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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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