If you can’t multiply B by a probability factor, then it’s meaningless in the context of xB + (1-x)C, also. 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”. nyan_sandwich even agrees that 0 and 1 aren’t magic numbers, they’re just rescaled utility values.
I’m 99% confident that that’s not what nyan_sandwich means by radiation poisoning in the original post, considering the fact that comparing utilities to 0 and 1 is exactly what he does in the hell example. If you’re not allowed to compare utilities by magnitude, then you can’t obtain an expected utility by multiplying by a probability distribution. Show the math if you think you can prove otherwise.
It’s getting hard to reference back to the original post because it keeps changing with no annotations to highlight the edits, but I think the only useful argument in the radiation poisoning section is: “don’t use units of sandwiches, whales, or orgasms because you’ll get confused by trying to experience them”. However, I don’t see any good argument for not even using Utils as a unit for a single person’s preferences. In fact, using units of Awesomes seems to me even worse than Utils, because it’s easier to accidentally experience an Awesome than a Util. Converting from Utils to unitless measurement may avoid some infinitesimal amount of radiation poisoning, but it’s no magic bullet for anything.
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.
[edited out emotional commentary/snark]
If you can’t multiply B by a probability factor, then it’s meaningless in the context of xB + (1-x)C, also. 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”. nyan_sandwich even agrees that 0 and 1 aren’t magic numbers, they’re just rescaled utility values.
I’m 99% confident that that’s not what nyan_sandwich means by radiation poisoning in the original post, considering the fact that comparing utilities to 0 and 1 is exactly what he does in the hell example. If you’re not allowed to compare utilities by magnitude, then you can’t obtain an expected utility by multiplying by a probability distribution. Show the math if you think you can prove otherwise.
It’s getting hard to reference back to the original post because it keeps changing with no annotations to highlight the edits, but I think the only useful argument in the radiation poisoning section is: “don’t use units of sandwiches, whales, or orgasms because you’ll get confused by trying to experience them”. However, I don’t see any good argument for not even using Utils as a unit for a single person’s preferences. In fact, using units of Awesomes seems to me even worse than Utils, because it’s easier to accidentally experience an Awesome than a Util. Converting from Utils to unitless measurement may avoid some infinitesimal amount of radiation poisoning, but it’s no magic bullet for anything.
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.