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Stuart_Armstrong comments on Extreme risks: when not to use expected utility - Less Wrong
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Comments (36)
To be technical, A and B are random variables, though you can usefully think of them as generalised lotteries. A+B represents you being entered in both lotteries.
Hum, if this is causing confusion, there is no surprise that my overal post is obscure. I'll try taking it apart to rewrite it more clearly.
That has nothing to do with the independence axiom, which is about Wei Dai's first suggestion of a 50% chance of A and a 50% chance of B (and about unequal mixtures). I think your entire post is based on this confusion.
I did wonder what Stuart meant when he started talking about adding probability distributions together. In the usual treatment, a single probability distribution represents all possible worlds, yes?
Yes, the axioms are about preferences over probability distributions over all possible worlds and are enough to produce a utility function whose expectation produces those preferences.
That's how it looks to me as well.
No, it isn't. I'll write another post that makes my position clearer, as it seems I've spectacularly failed with this one :-)