army1987 comments on Checklist of Rationality Habits - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (186)
Comparing these numbers tells you pretty much nothing. First of all, taking log($50k) is not a valid operation; you should only ever take logs of a dimensionless quantity. The standard solution is to pick an arbitrary dollar value $X, and compare log($50k/$X), log($120k/$X), and log($10^9/$X). This is equivalent to comparing 10.8 + C, 11.69 + C, and 20.7 + C, where C is an arbitrary constant.
This shouldn't be a surprise, because under the standard definition, utility functions are translation-invariant. They are only compared in cases such as "is U1 better than U2?" or "is U1 better than a 50/50 chance of U2 and U3?" The answer to this question doesn't change if we add a constant to U1, U2, and U3.
In particular, it's invalid to say "U1 is twice as good as U2". For that matter, even if you don't like utility functions, this is suspicious in general: what does it mean to say "I would be twice as happy if I had a million dollars"?
It would make sense to say, if your utility for money is logarithmic and you currently have $50k, that you're indifferent between a 100% chance of an extra $70k and a 8.8% chance of an extra $10^9 -- that being the probability for which the expected utilities are the same. If you think logarithmic utilities are bad, this is the claim you should be refuting.
This is what I immediately thought when I first read about the Repugnant Conclusion on Wikipedia, years ago before having ever heard of the VNM axioms or anything like that.