All this business with radiation poisoning is just a roundabout way of saying the only things you’re allowed to do with utilities are “compare two utilities” and “calculate expected utility over some probability distribution” (and rescale the whole utility function with a positive affine transformation, since positive affine transformations happen to be isomorphisms of the above two calculations).
Looking at utility values for any other purpose than comparison or calculating expected utilities is a bad idea, because your brain will think things like “positive number is good” and “negative number is bad” which don’t make any sense in a situation where you can arbitrarily rescale the utility function with any positive affine transformation.
xB by itself isn’t meaningless; it roughly means “the expected utility on a normalized scale between the utility of the outcome I least prefer and the outcome I most prefer”
“xB + (1-x)0” which is formally equivalent to “xB” means “the expected utility of B with probability p and the outcome I least prefer on a normalized scale with probability (1-p)”, yes. The point I’m trying to make here though is that probability distributions have to add up to 1. “Probability p of outcome B” — where p < 1 — is a type error, plain and simple, since you haven’t specified the alternative that happens with probability (1-p). “Probability p of outcome B, and probability (1-p) of the outcome I least prefer” is the closest thing that is meaningful, but if you mean that you need to say it.
Oh, I was going to reply to this, and I forgot.
All this business with radiation poisoning is just a roundabout way of saying the only things you’re allowed to do with utilities are “compare two utilities” and “calculate expected utility over some probability distribution” (and rescale the whole utility function with a positive affine transformation, since positive affine transformations happen to be isomorphisms of the above two calculations).
Looking at utility values for any other purpose than comparison or calculating expected utilities is a bad idea, because your brain will think things like “positive number is good” and “negative number is bad” which don’t make any sense in a situation where you can arbitrarily rescale the utility function with any positive affine transformation.
“xB + (1-x)0” which is formally equivalent to “xB” means “the expected utility of B with probability p and the outcome I least prefer on a normalized scale with probability (1-p)”, yes. The point I’m trying to make here though is that probability distributions have to add up to 1. “Probability p of outcome B” — where p < 1 — is a type error, plain and simple, since you haven’t specified the alternative that happens with probability (1-p). “Probability p of outcome B, and probability (1-p) of the outcome I least prefer” is the closest thing that is meaningful, but if you mean that you need to say it.