When I think of Aumann’s agreement theorem, my first reflex is to average. You think A is 80% likely; my initial impression is that it’s 60% likely. After you and I talk, maybe we both should think 70%. “Average your starting beliefs”, or perhaps “do a weighted average, weighted by expertise” is a common heuristic.
That’s just the modesty argument, which is of highly questionable effectiveness when talking to non-rationalists.
Anyway, thanks for re-posting—this is one of my favorite OB posts.
It’s awkward to talk about, but it is of highly questionable effectiveness in general. A 2000 rated chess player should very rarely Aumann much on the implicit opinion of a 1600; if you’re playing blitz you just assume it’s a blunder. (If you’re playing rapid you have more time; it’s like the difference between a real-time conversation and an internet discussion.) Sure, they’re both in the category “decent chess players”, and in far mode 400 rating points doesn’t feel like a big difference—and over the course of months it’s very surmountable—but during the game it’s really important to keep the strength difference in mind. This is why it’s really sad that “rationality” doesn’t (can’t) have a martial-arts-style belt system. Everybody prides themselves on their ability to think effectively about arbitrary topics and thus any claim of inequality is at best awkward and at worst lastingly offensive.
That’s just the modesty argument, which is of highly questionable effectiveness when talking to non-rationalists.
As a rationalist, I disagree and I am 170% certain of this fact. We should average our certainty and improve our Pareto-Efficiency until you agree with me.
That’s just the modesty argument, which is of highly questionable effectiveness when talking to non-rationalists.
Anyway, thanks for re-posting—this is one of my favorite OB posts.
It’s awkward to talk about, but it is of highly questionable effectiveness in general. A 2000 rated chess player should very rarely Aumann much on the implicit opinion of a 1600; if you’re playing blitz you just assume it’s a blunder. (If you’re playing rapid you have more time; it’s like the difference between a real-time conversation and an internet discussion.) Sure, they’re both in the category “decent chess players”, and in far mode 400 rating points doesn’t feel like a big difference—and over the course of months it’s very surmountable—but during the game it’s really important to keep the strength difference in mind. This is why it’s really sad that “rationality” doesn’t (can’t) have a martial-arts-style belt system. Everybody prides themselves on their ability to think effectively about arbitrary topics and thus any claim of inequality is at best awkward and at worst lastingly offensive.
As a rationalist, I disagree and I am 170% certain of this fact. We should average our certainty and improve our Pareto-Efficiency until you agree with me.
Point well-taken. :)