I don’t understand this post. Asking me to imagine that all utilities equal zero is like asking to imagine being a philosophical zombie. I’d do exactly the same as before of course.
That’s what I’d do too. If all utilities equal 0, then there’s no reason not to act as though utilities are non-zero. There’s also no reason to privilege any set of utilities over any other set. Firstly this means that if there’s any probability that utilities don’t really all equal zero (maybe EY’s proof is flawed, maybe my brain made an error in hearing the proof and it really proves something else entirely...) then the p-mass on “all utilities are 0” should have no effect on my decisions. If it actually is true, with probability 1 (which EY says doesn’t exist, but I’m not sure whether that’s true[*]), then I have no reason to behave differently, nor any reason to behave the same, so in some sense I “may as well” behave the same—but I can’t formalise this, because of course there’s no negative utility attached to “changing one’s behaviour”. I wonder if it can be got out of a limit—whether my behaviour in the limit as P(all utilities are 0) goes to 1 ought to define my behaviour when it equals 1 - but defining behaviour of limit to equal limit of behaviour is precisely what makes unbounded utility functions Dutch-bookable (as EY showed in Trust in Bayes).
So… I’d behave exactly as I do now, believing in utility functions, but I can’t justify that if I know for certain that all utilities are 0. Given that I haven’t thus far accepted the argument that ‘0 and 1 are not probabilities’, this is disturbing and confusing, hence maybe I should accept that argument; at least, updating on this has caused me to raise my probability estimate that 0 and 1 are not probabilities.
[*] If I were sure that ¬\exist X : P(X) = 1, then P(¬\exist X : P(X) = 1) = 1, in which case things break. A formal system can’t talk about itself coherently. (That ‘coherently’ is necessary, because Gödel numberings do allow PA to do something that looks to us like “talk about itself”, but you can’t conclude PA is talking about itself unless you have some metatheory outside PA, which ends up recursing to a skyhook.)
I don’t understand this post. Asking me to imagine that all utilities equal zero is like asking to imagine being a philosophical zombie. I’d do exactly the same as before of course.
I’m pretty sure that’s the entire point.
That’s what I’d do too. If all utilities equal 0, then there’s no reason not to act as though utilities are non-zero. There’s also no reason to privilege any set of utilities over any other set. Firstly this means that if there’s any probability that utilities don’t really all equal zero (maybe EY’s proof is flawed, maybe my brain made an error in hearing the proof and it really proves something else entirely...) then the p-mass on “all utilities are 0” should have no effect on my decisions. If it actually is true, with probability 1 (which EY says doesn’t exist, but I’m not sure whether that’s true[*]), then I have no reason to behave differently, nor any reason to behave the same, so in some sense I “may as well” behave the same—but I can’t formalise this, because of course there’s no negative utility attached to “changing one’s behaviour”. I wonder if it can be got out of a limit—whether my behaviour in the limit as P(all utilities are 0) goes to 1 ought to define my behaviour when it equals 1 - but defining behaviour of limit to equal limit of behaviour is precisely what makes unbounded utility functions Dutch-bookable (as EY showed in Trust in Bayes).
So… I’d behave exactly as I do now, believing in utility functions, but I can’t justify that if I know for certain that all utilities are 0. Given that I haven’t thus far accepted the argument that ‘0 and 1 are not probabilities’, this is disturbing and confusing, hence maybe I should accept that argument; at least, updating on this has caused me to raise my probability estimate that 0 and 1 are not probabilities.
[*] If I were sure that ¬\exist X : P(X) = 1, then P(¬\exist X : P(X) = 1) = 1, in which case things break. A formal system can’t talk about itself coherently. (That ‘coherently’ is necessary, because Gödel numberings do allow PA to do something that looks to us like “talk about itself”, but you can’t conclude PA is talking about itself unless you have some metatheory outside PA, which ends up recursing to a skyhook.)