Imagine that, for every question, you will have to pay ϵln1p dollars if the event you assigned a probability p occurs. Here, ϵ>0 is some sufficiently small constant (this assumes your strategy doesn’t fluctuate as ϵ approaches 0). Answer in the optimal way for that game, according to whatever decision theory you follow. (But choosing which questions to answer is not part of the game.)
p is the probability of the event that actually occured. You can’t submit p=1 without knowing what is true in advance. For example, suppose you need to predict who wins the next US presidential election. You assign probability 0.6 to Biden, 0.3 to Trump and 0.1 to Eliezer Yudkowsky. Then, if Biden wins, p=0.6. But, if Yudkowsky wins then p=0.1.
Imagine that, for every question, you will have to pay ϵln1p dollars if the event you assigned a probability p occurs. Here, ϵ>0 is some sufficiently small constant (this assumes your strategy doesn’t fluctuate as ϵ approaches 0). Answer in the optimal way for that game, according to whatever decision theory you follow. (But choosing which questions to answer is not part of the game.)
Eh? You’d perform best in that game by just submitting p = 1 for every question
Was it meant to be{ ϵln1pif event happens ϵln11−potherwise , or something like that?
p is the probability of the event that actually occured. You can’t submit p=1 without knowing what is true in advance. For example, suppose you need to predict who wins the next US presidential election. You assign probability 0.6 to Biden, 0.3 to Trump and 0.1 to Eliezer Yudkowsky. Then, if Biden wins, p=0.6. But, if Yudkowsky wins then p=0.1.
A “yes” wrt my guess would have been kind here.
This is a very confusing thing to say because I absolutely can.