Old OB repost: Share likelihood ratios, not posterior beliefs

Will_Newsome

http://www.overcomingbias.com/2009/02/share-likelihood-ratios-not-posterior-beliefs.html

By Anna Salamon and Steve Rayhawk

Indubitably intriguing snippet:

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.

But sometimes, not only is the best combination not the average, it's more extreme than either original belief.

http://www.overcomingbias.com/2009/02/share-likelihood-ratios-not-posterior-beliefs.html

By Anna Salamon and Steve Rayhawk

Indubitably intriguing snippet:

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.

But sometimes, not only is the best combination not the average, it's more extreme than either original belief.

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.

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.

10Will_Newsome15y

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.