OK, Eliezer, let me try to turn your example around. (I think) I understand—and agree with—everything in this post (esp. the boldface). Nonetheless:
Assume your utility of money was linear. Imagine two financial investments (bets), 3A and 3B:
3A: 100% chance of $24,000
3B: 50% chance of $26,000, 50% chance of $24,000.
Presumably, (given a linear utility of money), you would say that you were indifferent between the two bets. Yet in actual financial investing, in the real world, you receive an (expected) return premium for accepting additional risk. Roughly speaking, expected return of an investment goes up, as the volatility of that return increases.
It seems that I could construct a money pump for YOU, out of real-world investments! You appear to be making the claim that all that matters for rational decision-making is expected value, and that volatility is not a factor at all. I think you’re incorrect about that, and the actual behavior of real-world investments appears to support my position.
I’m not sure what the correct accounting for uncertainty should be in your original 1A/1B/2A/2B example. But it sure seems like you’re suggesting that the ONLY thing that matters is expected value (and then some utility on the money outcomes) -- but nowhere in your calculations do I see a risk premium, some kind of straightforward penalty for volatility of outcome.
Again, if you think that rational decision-making shouldn’t use such information, then I’m certain that I can find real-world investments, where you ought to accept lower returns for a volatile investment than is offered by the actual investment, and I can pocket the difference. A real-world money pump—on you.
OK, Eliezer, let me try to turn your example around. (I think) I understand—and agree with—everything in this post (esp. the boldface). Nonetheless:
Assume your utility of money was linear. Imagine two financial investments (bets), 3A and 3B: 3A: 100% chance of $24,000 3B: 50% chance of $26,000, 50% chance of $24,000.
Presumably, (given a linear utility of money), you would say that you were indifferent between the two bets. Yet in actual financial investing, in the real world, you receive an (expected) return premium for accepting additional risk. Roughly speaking, expected return of an investment goes up, as the volatility of that return increases.
It seems that I could construct a money pump for YOU, out of real-world investments! You appear to be making the claim that all that matters for rational decision-making is expected value, and that volatility is not a factor at all. I think you’re incorrect about that, and the actual behavior of real-world investments appears to support my position.
I’m not sure what the correct accounting for uncertainty should be in your original 1A/1B/2A/2B example. But it sure seems like you’re suggesting that the ONLY thing that matters is expected value (and then some utility on the money outcomes) -- but nowhere in your calculations do I see a risk premium, some kind of straightforward penalty for volatility of outcome.
Again, if you think that rational decision-making shouldn’t use such information, then I’m certain that I can find real-world investments, where you ought to accept lower returns for a volatile investment than is offered by the actual investment, and I can pocket the difference. A real-world money pump—on you.
Or have I completely missed the point somehow?