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Computationally bounded probability theory Probability theory is about how to manage incomplete information. One way to interpret a statement like “the probability of event \(X\) is \(p\)” is in terms of betting odds - you think the probability of \(X\) is \(p\) if you value a lottery ticket that pays out $1 if \(X\) happens at \(p\) dollars. From this interpretation, all the laws of…
Computationally bounded probability theory Probability theory is about how to manage incomplete information. One way to interpret a statement like “the probability of event \(X\) is \(p\)” is in terms of betting odds - you think the probability of \(X\) is \(p\) if you value a lottery ticket that pays out $1 if \(X\) happens at \(p\) dollars. From this interpretation, all the laws of probability theory (except arguably those involving infinite conjunctions of events) follow, if we add the requirement that your valuation is “inexploitable” - in other words, if we require that no smart bookie can get you to make a series of bets that always loses money.Read on /complexity-theory-probability/ ↗
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