Thank you, this is good to know. I'll have to think about this some more.
Hm, I was working under the assumption that the "utility" with paperclips was just the number of paperclips. A universe with X - 10n + 3^^^^3 paperclips is better than a universe with just X paperclips by 3^^^^3 - 10n. Is this not a proper utility function?
The casino version evolved from repeated alterations to Pascal's Mugging, so it retained the 3^^^^3 from there. I had written a paragraph where I mentioned that for one-shot problems, even a more realistic probability could qualify as a Pascal's Mugging, though I had used a 1/million chance of a trillion paperclips instead
Very interesting, thank you!
I think "maximising" still makes sense in one-shot problems. 2>1 and 1000>1, but it's also the case that 1000>2, even without expected utility. The way I see it, EU is a method of comparing choices based on their average utility, but the "average" turns out to be a less useful metric when you only have one chance.
So for cases when an outcome is not a constant amount of paperclips we need more rules than what the object of attention is. So a paperclip maximiser is actually underspecified.
If this is true, it would imply that in a one-shot problem, a utility function is not enough on its own to determine
Thank you for your response!
Are you rejecting Pascal’s mugging because of the prospect of relying on uncertain models that you do not expect to confirm?
My intuition is that in a one-shot problem, gambling everything on an extremely low probability event is a bad idea, even when the reward from that low probability event is very high, because you are effectively certain to lose. This is the basis for me not paying up in Pascal's Mugging and in the casino problem in the post.
I'm trying to keep my reasoning simple, so in my examples I always assume that there are no infinities, no unknown unknowns, every outcome of every choice is statistically independent,
I've had some thoughts on Pascal's Mugging which might be worth sharing. I'm assuming some familiarity with Pascal's Mugging in this post.
Before we get really started, let's transform Pascal's Mugging into a problem that is easier to reason about but still gets at the core idea.
First, forget "utility", forget money, we're maximising paperclips. I know it's kind of silly, but using money or utility really tends to muddy up thinking. I was surprised how much easier it was to reason about the problem when I switched to paperclips[0].
Now, here's my version of the problem. Suppose there's a casino, in which there is a googolplex-sided die (10^(10^100) sides). You can pay 10 paperclips
You're absolutely right. I was starting to get at this idea from another of the comments, but you've laid out where I've gone wrong very clearly. Thank you.