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.
Well, all of the questions are binary so they either happen or don’t happen. They may not be sampled from some “objective” distribution, but you can still assign subjective probabilities to them. Just write how likely you think they are to happen.
What if all I can assign is a probability distribution of probabilities? Like in extraterrestrial life question. All that can be said is that extraterrestrial life is sufficiently rare to not find evidence of it yet. Our observation of our existence is conditioned on our existence, so it doesn’t provide much evidence one way or another.
Should I sample the distribution to give an answer, or maybe take mode, or mean, or median? I’ve chosen a value that is far from both extremes, but I might have done something else with no clear justification for any of the choices.
I am not a Bayesian, so I have philosophical objections to giving probabilities to things that are not a distribution you can sample from.
The survey just assumes that everyone is a Bayesian.
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.
Feel free to skip any question you object to answering. (Except the first one about the public data, that one you can’t skip.)
Well, all of the questions are binary so they either happen or don’t happen. They may not be sampled from some “objective” distribution, but you can still assign subjective probabilities to them. Just write how likely you think they are to happen.
What if all I can assign is a probability distribution of probabilities? Like in extraterrestrial life question. All that can be said is that extraterrestrial life is sufficiently rare to not find evidence of it yet. Our observation of our existence is conditioned on our existence, so it doesn’t provide much evidence one way or another.
Should I sample the distribution to give an answer, or maybe take mode, or mean, or median? I’ve chosen a value that is far from both extremes, but I might have done something else with no clear justification for any of the choices.