I’m way late to this party, but aren’t we ignoring something obvious? Such as imperfect knowledge of how likely Omega is to be right about its prediction of what you would do? If you live in a universe where Omega is a known fact and nobody thinks themselves insane when they meet him, well, then it’s the degenerate case where you are 100% certain that Omega predicts correctly. If you lived in such a universe presumably you would know it, and everyone in that world would pre-commit to giving Omega $100, just like in ours pizza-deliverers pre-commit to not carrying more than a small amount of cash with them.
There may be other universes where Omega is known to be right and do what he says he will do 80% of the time. Or ones where there are rumors of an omniscient Omega that always makes good on his word, but you assign them 80% probability of being true. And so on.
Given the $5000 expected payoff and the $50 expected cost for pre committing, you should do it if the probability of Omega being both right and trustworthy is greater than or equal to 0.01.
But, if you, knowing what you know about THIS universe, suddenly found yourself in the presence of some alien entity making the claim Omega makes in the above scenario, what kind of evidence would you demand for this claim before assigning a probability greater than 0.01?
It occurs to me that the dude in the robe and mask pretending to be Omega could up the ante to $1000000, and if I wouldn’t believe him more than 0.01% given a $10000 payoff, it probably wouldn’t matter to me what he offered as a payoff, because if he has enough delusions and/or chutzpah to make this claim in this universe, there’s no reason for him to balk at adding on a few extra decimal places. I’m not sure how to formalize that mathematically, though.
I’m way late to this party, but aren’t we ignoring something obvious? Such as imperfect knowledge of how likely Omega is to be right about its prediction of what you would do? If you live in a universe where Omega is a known fact and nobody thinks themselves insane when they meet him, well, then it’s the degenerate case where you are 100% certain that Omega predicts correctly. If you lived in such a universe presumably you would know it, and everyone in that world would pre-commit to giving Omega $100, just like in ours pizza-deliverers pre-commit to not carrying more than a small amount of cash with them.
There may be other universes where Omega is known to be right and do what he says he will do 80% of the time. Or ones where there are rumors of an omniscient Omega that always makes good on his word, but you assign them 80% probability of being true. And so on.
Given the $5000 expected payoff and the $50 expected cost for pre committing, you should do it if the probability of Omega being both right and trustworthy is greater than or equal to 0.01.
But, if you, knowing what you know about THIS universe, suddenly found yourself in the presence of some alien entity making the claim Omega makes in the above scenario, what kind of evidence would you demand for this claim before assigning a probability greater than 0.01?
It occurs to me that the dude in the robe and mask pretending to be Omega could up the ante to $1000000, and if I wouldn’t believe him more than 0.01% given a $10000 payoff, it probably wouldn’t matter to me what he offered as a payoff, because if he has enough delusions and/or chutzpah to make this claim in this universe, there’s no reason for him to balk at adding on a few extra decimal places. I’m not sure how to formalize that mathematically, though.