Comment on Infinite Certainty

Sat, 29 Jun 2013 15:11:03 GMT

Your calculations aren't quite right. You're treating EU(action) as though it were a probability value (like P(action)). EU(action) would be more logically written E(utility | action), which itself is an integral over utility * P(utility | action) for utility∈(-∞,∞), which, due to linearity of * and integrals, does have all the normal identities, like

E(utility | action) = E(utility | action, e) * P(e | action) + E(utility | action, ¬e) * P(¬e | action).

In this case, if you do expand that out, using p<<1 for the probability of an error, which is independent of your action, and assuming E(utility|action1,error) = E(utility|action2,error), you get E(utility | action) = E(utility | error) * p + E(utility | action, ¬error) * (1 - p). Or for the difference between two actions, EU1 - EU2 = (EU1' - EU2') * (1 - p) where EU1', EU2' are the expected utilities assuming no errors.

Anyway, this seems like a good model for "there's a superintelligent demon messing with my head" kind of error scenarios, but not so much for the everyday kind of math errors. For example, if I work out in my head that 51 is a prime number, I would accept an even odds bet on "51 is prime". But, if I knew I had made an error in the proof somewhere, it would be a better idea not to take the bet, since less than half of numbers near 50 are prime.

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