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.
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.
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.
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.
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.