= 27d567bc2d48d9f40e9ccc20ea370b15)
TimFreeman comments on A summary of Savage's foundations for probability and utility. - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (88)
If there are only a finite number of options, utility can only be unbounded if at least one of the options has the possibility of utilities with arbitrarily large absolute value. It is hard to deal with an infinite number of options, but it might be possible depending on how that works with the other axioms, but this is irrelevant because P6 was not connected to the proof of bounded utility.
That is why I was initially concerned about P6.
I don't think real numbers are the best field to use for utility because of Pascal's mugging, some of the stuff described here, and this paper.
Are we agreed that bounded real-valued (or rational-valued) utility gets rid of Pascal's mugging?
Yes. Bounded utility solves tons of problems, it just doesn't, AFAICT, describe my preferences.
The bound would also have to be substantially less than 3^^^^3.
As you know, if there is a bound, without loss of generality we can say all utilities go from 0 to 1.
Repairing your claim to take that into account, if you're being mugged for $5, and the plausibility of the mugger's claim is 1/X where X is large, and the utility the mugger promises you is about 1, then you get mugged if your utility for $5 is less than 1/X, roughly. So I agree that there are utility functions that would result in the mugging, but they don't appear especially simple or especially consistent with observed human behavior, so the mugging doesn't seem likely.
Now, if the programming language used to compute the prior on the utility functions has a special instruction that loads 3^^^^3 into an accumulator with one byte, maybe the mugging will look likely. I don't see any way around that.