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.
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.