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Qiaochu_Yuan comments on Naturalism versus unbounded (or unmaximisable) utility options - Less Wrong Discussion

34 Post author: Stuart_Armstrong 01 February 2013 05:45PM

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Tags: utility infinity paradox resolution determinism ethics choice

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Comment author: Qiaochu_Yuan 01 February 2013 05:57:44PM *  9 points [-]

Suppose that you die, and God offers you a deal. You can spend 1 day in Hell, and he will give you 2 days in Heaven, and then you will spend the rest of eternity in Purgatory (which is positioned exactly midway in utility between heaven and hell). You decide that it's a good deal, and accept. At the end of your first day in Hell, God offers you the same deal: 1 extra day in Hell, and you will get 2 more days in Heaven. Again you accept. The same deal is offered at the end of the second day.

This isn't a paradox about unbounded utility functions but a paradox about how to do decision theory if you expect to have to make infinitely many decisions. Because of the possible failure of the ability to exchange limits and integrals, the expected utility of a sequence of infinitely many decisions can't in general be computed by summing up the expected utility of each decision separately.

Comment author: Stuart_Armstrong 01 February 2013 06:38:18PM 7 points [-]

This isn't a paradox about unbounded utility functions but a paradox about how to do decision theory if you expect to have to make infinitely many decisions.

Yes, that's my point.

Comment author: Andreas_Giger 02 February 2013 12:05:19AM 2 points [-]

This isn't a paradox about unbounded utility functions but a paradox about how to do decision theory if you expect to have to make infinitely many decisions.

I believe it's actually a problem about how to do utility-maximising when there's no maximum utility, like the other problems. It's easy to find examples for problems in which there are infinitely many decisions as well as a maximum utility, and none of those I came up with are in any way paradoxical or even difficult.

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