benelliott comments on St. Petersburg Mugging Implies You Have Bounded Utility - Less Wrong

10 Post author: TimFreeman 07 June 2011 03:06PM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (163)

You are viewing a single comment's thread. Show more comments above.

Comment author: benelliott 07 June 2011 11:02:41PM *  2 points [-]

A bigger problem is your ability to hand out arbitrarily large amounts of utility. Suppose the universe can be simulated by an N state Turing machine, this limits the number of possible states it can occupy to a finite (but probably very large) number. This in turn bounds the amount of utility you can offer me, since each state has finite utility and the maximum of a finite set of finite numbers is finite. (The reason why this doesn't automatically imply a bounded utility function is that we are uncertain of N.)

As a result of this:

P(you can offer me k utility) > 0 for any fixed k

but

P(you can offer me x utility for any x) = 0

To be honest thought, I'm not really comfortable with this, and I think Solomonoff needs to be fixed (I don't feel like I believe with certainty that the universe is computable). The real reason why you haven't seen any of my money is that I think the maths is bullshit, as I have mentioned elsewhere.

Comment author: benelliott 07 June 2011 11:13:28PM *  1 point [-]

Thinking about it more, this isn't a serious problem for the dilemma. While P(you can offer me k utility) goes to zero as k goes to infinity but there's no reason to suppose it goes faster then 1/n does.

This means you can still set a similar dilemma, with a probability of you being able to offer me 2^n utility eventually becoming greater than (1/2)^n for sufficiently large n, satisfying the conditions for a St Petersburg Lottery.

Comment author: Document 08 June 2011 09:22:52PM *  0 points [-]

Thinking about it more, this isn't a serious problem for the dilemma. While P(you can offer me k utility) goes to zero as k goes to infinity but there's no reason to suppose it goes faster then 1/n does.

That's just Pascal's mugging, though; the problem that "the utility of a Turing machine can grow much faster than its prior probability shrinks".