Eliezer: So when I say that two punches to two faces are twice as bad as one punch, I mean that if I would be willing to trade off the distance from the status quo to one punch in the face against a billionth (probability) of the distance between the status quo and one person being tortured for one week, then I would be willing to trade off the distance from the status quo to two people being punched in the face against a two-billionths probability of one person being tortured for one week.
So alternatives that have twice the probability of some good thing X happening have twice the utility? A sure gain of a dollar has twice the utility of a gaining a dollar on a coin flip? Insurance companies and casinos certainly think so, but their customers certainly don’t.
I think you are conflating utility and expected utility. I’m not convinced they are the same thing, although I think you believe they are.
Eliezer: So when I say that two punches to two faces are twice as bad as one punch, I mean that if I would be willing to trade off the distance from the status quo to one punch in the face against a billionth (probability) of the distance between the status quo and one person being tortured for one week, then I would be willing to trade off the distance from the status quo to two people being punched in the face against a two-billionths probability of one person being tortured for one week.
So alternatives that have twice the probability of some good thing X happening have twice the utility? A sure gain of a dollar has twice the utility of a gaining a dollar on a coin flip? Insurance companies and casinos certainly think so, but their customers certainly don’t.
I think you are conflating utility and expected utility. I’m not convinced they are the same thing, although I think you believe they are.