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DanielLC comments on St. Petersburg Mugging Implies You Have Bounded Utility - Less Wrong
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I have an unbounded utility function, but my priors are built in such a way that expected utility is the same regardless of how you calculate it. For example, if there was a 2^-n chance of getting 2^n/n utility and a 2^-n chance of getting -2^n/n utility (before normalizing), you could make the expected utility add to whatever you want by changing the order. As such, my priors don't allow that to happen.
This has two interesting side effects. First, given any finite amount of evidence, my posteriors would follow those same laws, and second, pascal's mugging and the like are effectively impossible.
Edit: fixed utility example
Interesting. But it has been a while since I studied divergent series and the games that can be played with them. So more detail on your claim ("make the expected utility add to whatever you want by changing the order.") would be appreciated.
It seems that you are adding one more axiom to the characterization of rationality (while at the same time removing the axiom that forces bounded utility.) Could you try to spell that new axiom out somewhat formally?
Expected utility can be thought of as an infinite sum. Specifically, sum(P(Xn)*U(Xn)). I'm assuming expected utility is unconditionally convergent.
Take the serieses 1+1/2+1/3+1/4+... and -1-1/2-1/2-1/4-... Both of those diverge. Pick an arbitrary number. Let's say, 100. Now add until it's above 100, subtract until it's below, and repeat. It will now converge to 100. Because of this, 1-1+1/2-1/2+... is conditionally convergent.
Yes, I understand conditional and unconditional convergence. What I don't understand is how you get conditional convergence from
I also do not understand how your "priors don't allow that to happen".
It almost seems that you are claiming to have unbounded utility but bounded expected utility. That is, no plausible sequence of events can make you confident that you will receive a big payoff, but you cannot completely rule it out.
I just noticed, that should have been 2^-n chance of getting 2^n/n utility and a 2^-n chance of getting -2^n/n
Anyway, 2^-n*2^n/n = 1/n, so the expected utility from that possibility is 1/n, so you get an unbounded expected utility. Do it with negative too, and you get conditionally converging expected utility.