Noosphere89 comments on Flipping Out: The Cosmic Coinflip Thought Experiment Is Bad Philosophy

Noosphere89 13 Nov 2024 19:49 UTC
3 points
2
Growing slower than logarithmic does not help. Only being bounded in t he limit give you, well, a bound in the limit.
Thanks for catching that error, I did not realize this.
I think I got it from here:
https://www.lesswrong.com/posts/EhHdZ5yBgEvLLx6Pw/chad-jones-paper-modeling-ai-and-x-risk-vs-growth
“Bounded utility solves none of the problems of unbounded utility.” Thus the title of something I’m working on, on and off.
It’s not ready yet. For a foretaste, some of the points it will make can be found in an earlier unpublished paper “Unbounded Utility and Axiomatic Foundations”, section 3.
The reason that bounded utility does not help is that any problem that arises at infinity will already practically arise at a sufficiently large finite stage. Repeated plays of the finite games discussed in that paper will eventually give you a payoff that has a high probability of being close (in relative terms) to the expected value. But the time it takes for this to happen grows exponentially with the lengths of the individual games. You are unlikely to ever see your theoretically expected value, however long you play. The infinite game is non-ergodic; the game truncated to finitely many steps and finite payoffs is ergodic only on impractical timescales.
Infinitude in problems like these is better understood as an approximation to the finite, rather than the other way round. (There’s a blog post by Terry Tao on this theme, but I’ve lost the reference to it.) The problems at infinity point to problems with the finite.
I definitely agree that the problems of infinite utilities are approximately preserved by the finitary version of the problem, and while there are situations where you can get niceness assuming utilities are bounded (conditional on giving players exponentially large lifespans), it’s not the common or typical case.
Infinity makes things worse in that you no longer get any cases where nice properties like ergodicity or dominance are consistent with other properties, but yeah the finitary version is only a little better.