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nyan_sandwich comments on Why you must maximize expected utility - Less Wrong
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Yes. If you think this conclusion is repugnant, you have not comprehended the meaning of 1000000001 times as much utility. The only thing that utility value even means is that you'd accept such a deal.
You don't "give" people utilons though. That implies scarcity, which implies some real resource to be distributed, which we correctly recognize as having diminishing returns on one person, and less diminishing returns on lots of people. The better way to think of it is that you extract utility from people.
Would you rather get 1e9 utils from one person, or 1 util from each of 1e9 people? Who cares 1e9 utils is 1e9 utils.
Again, by construction, we take this deal.
VNM should not have called it "utility"; it drags in too many connotations. VNM utility is a very personal thing that describes what decisions you would make.
It is permissible to prefer the outcome that has a constant probability distribution to the outcome that has the higher definite integral across the probability distribution.
What do you mean? Specifically, what is a "constant probability distribution"?
If you mean I can prefer $1M to a 1/1000 chance of $2B, then sure. Money is not utility.
On the other hand, I can't prefer 1M utils to 1/1000 chance of 2B utils.
A constant probability distribution is a flat distribution; i.e. a flat line.
And the outcomes can be ordered however one chooses. It is not necessary to provide additive numeric values.
Are you saying that utils are defined such that if one outcome is preferred over another, it has more expected utils?
Yes. That's exactly what I mean.
And I'm afraid I still don't know what you are getting at with this constant probability distribution thing.
I mean an outcome where there is 1-epsilon chance of A.
It is permissible to assign utils arbitrarily, such that flipping a coin to decide between A and B has more utils than selecting A and more utils than selecting B. In that case, the outcome is "Flip a coin and allow the coin to decide", which has different utility from the sum of half of A and half of B.
Perhaps if you count "I flipped a coin and got A" > A.
You can always define some utility function such that it is rational to shoot yourself in the foot, but at that point, you are just doing a bunch of work to describe stupid behavior that you could just do anyways. You don't have to follow the VNM axioms either.
The point of VNM and such is to constrain your behavior. And if you input sensible things, it does. You don't have to let it constrain your behavior, but if you don't, it is doing no work for you.
Right. If you think "I flipped a coin to decide" is more valuable than half of the difference between results of the coin flip (perhaps because those results are very close to equal, but you fear that systemic bias is a large negative, or perhaps because you demand that you are provably fair), then you flip a coin to decide.
The utility function, however, is not something to be defined. It is something to be determined and discovered- I already want things, and while what I want is time-variant, it isn't arbitrarily alterable.
Unless your utility assigns a positive utility to your utility function being altered, in which case you'd have to seek to optimize your meta-utility. Desire to change one's desires reflects an inconsistency, however, so one who desires to be consistent should desire not to desire to change one's desires. (my apologies if this sounds confusing)
One level deeper: One who is not consistent but desires to be consistent desires to change their desires to desires that they will not then desire to change.
If you don't like not liking where you are, and you don't like where you are, move to somewhere where you will like where you are.