The outside view technique is as follows:

You are given an estimation problem f(x)=?. x is noisy and you don't know all of the internals of f. First choose any set of functions F containing f. Then find a huge subset G of F such that g in G has that for all y in Y, g(y) is (say) bounded to some nice range R. Now find your probability p that x is in Y and your probability q that f is in G. Then with probability p*q f(x) is in R and this particular technique says nothing about f(x) in the remaining 1-p*q of your distribution.

Sometimes this is extremely helpful. Suppose you have the opportunity to bet $1 and you win $10 if a < f(x) < b. Then if you can find G,Y,R with R within (a,b) and with p*q > (1/10), you know the bet's good without having to bother with "well what does f look like exactly?".

Obvious pitfalls:

• Depending on f and G, sometimes p is not much easier to estimate than f(x). If you do a bad job estimating p and don't realize it, your bounds will be artificially confident. This IMO is what is happening when we pick any-reference-class-we-want F and then say the probability f is in G is equal to the number of things in G divided by the number of things in F.
• Estimate the wrong quantity. For example, instead of estimating the EV of a bet, estimate the probability you lose. You will establish a very nice bound on the probability, but the quantity you care about has an extra component which is WinPayoff*WinProbability, and if WinPayoff is greater order of magnitude than the other quantities, your bound tells you little.
• Mis-estimate q. It feels to me like this rarely happens, and that often it's the clarity of q's estimation that makes outside view arguments feel so persuasive.

What does this mean for continued investigation of the structure of f? It crucially depends on how we estimate p. If further knowledge about the structure of f does not affect how we should estimate p, then changing our estimate of the R*(p*q) component of f(x) based on our inside view is a bad plan and makes our estimate worse. If further knowledge about the structure of f does affect how we should estimate p, then to keep our R*(p*q) component around is also invalid.

So I see 3 necessary criteria to show that investigating the structure of f or the specifics of x won't help our estimate of f(x) much based on an outside view G,Y,R:

• An argument that 1-p*q is small.
• An argument that we cannot estimate the probability that f is in G much better given further knowledge of the structure of f.
• An argument that we cannot estimate the probability that x is in Y much better given further knowledge of the specifics of x.