AlephNeil comments on St. Petersburg Mugging Implies You Have Bounded Utility - Less Wrong

10 Post author: TimFreeman 07 June 2011 03:06PM

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Comment author: CarlShulman 07 June 2011 05:58:50PM 0 points [-]

However, if the subject takes them into account, it's very likely that the subject will lose, in the sense that the subject's estimated utility from all of these infinite expected utility bets is going to swamp utility from ordinary things.

The point of mixed strategies is that without distinctions between lotteries with infinite expected utility all actions have the same infinite (or undefined) expected utility, so on that framework there is no reason to prefer one action over another. Hyperreals or some other modification to the standard framework (see discussion of "infinity shades" in Bostrom) are necessary in order to say that a 50% chance of infinite utility is better than a 1/3^^^3 chance of infinite utility. Read the Hajek paper for the full details.

It's probably worth looking at anyway, but if you can say specifically how it's relevant and cite a specific page it would help.

"Empirical stabilizing assumptions" (naturalistic), page 34.

Comment author: AlephNeil 08 June 2011 04:23:22PM 0 points [-]

Hyperreals or some other modification to the standard framework (see discussion of "infinity shades" in Bostrom) are necessary in order to say that a 50% chance of infinite utility is better than a 1/3^^^3 chance of infinite utility.

No it isn't, unless like Hayek you think there's something 'not blindingly obvious' about the 'modification to the standard framework' that consists of stipulating that probability p of infinite utility is better than probability q of infinite utility whenever p > q.

This sort of 'move' doesn't need a name. (What does he call it? "Vector valued utilities" or something like that?) It doesn't need to have a paper written about it. It certainly shouldn't be pretended that we're somehow 'improving on' or 'fixing the flaws in' Pascal's original argument by explicitly writing this move down.

Comment author: CarlShulman 08 June 2011 07:34:37PM 0 points [-]

A system which selects actions so as to maximize the probability of receiving infinitely many units of some good, without differences in the valuation of different infinite payouts, approximates to a bounded utility function, e.g. assigning utility 1 to world-histories with an infinite payout of the good, and 0 to all other world-histories.

Comment author: Will_Sawin 08 June 2011 04:27:24PM -1 points [-]

We are making the argument more formal. Doing so is a good idea in a wide variety of situations.

Do you disagree with any of these claims?

Introducing hyperreals makes the argument more formal

Making an argument more formal is often good

Here, making the argument more formal is more likely good than bad.

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