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orthonormal comments on What's the Value of Information? - Less Wrong
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The reason it works like that is that in this artificial setup, there's no difference in your action if your odds are 100:1 or 1.1:1. If you could (say) make hedge bets with other customers at the bar, then the first number on the page has positive utility for you again.
It doesn't seem enormously artificial to me. I could just do this, had I £1000 to spare, and there are plenty of people round here who'd be sophisticated enough to enjoy playing.
Imagine you're in a real bar, and a real (trustworthy) person comes in and says this. What will you pay for the first number? If that's a 2, what will you pay for the second? If that's a 12, what will you pay for the third?
orthonormal's making the more subtle point that decisions are binary, and so certainty is crudely partitioned into two regions. With hedging and other financial instruments, then relative degrees of certainty matter- if I'm 90% sure that it's 1d12 and you're 80% sure that it's 1d12, then we can bet against each other, each thinking that we're picking up free money. (Suppose you pay me $3 if it's 1d12, and I pay you $17 if it's 2d6. Both of us have an expected value of $1 from this bet.) The more accurate my estimate is, the better odds I can make.
With the decision problem, we both decide the same way, and will both win or lose together.
What Vaniver said. I'm claiming that it's artificial as a decision theory problem, not in the sense of being unrealistic, but in the sense of having constrained options that don't allow you to make full use of information.