mattnewport comments on Is Rationality Maximization of Expected Value? - Less Wrong
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A coin flip is not fundamentally a less singular non-repeating event than the weather at a specific location and specific time. There are no true repeating events on a macro scale if you specify location and time. The relevant difference is how confident you can be that past events are good predictors of the probability of future events. Pretty confident for a coin toss, less so for weather. Note however that if your probability estimates are sufficiently accurate / well-calibrated you can make money by betting on lots of dissimilar events. See for example how insurance companies, hedge funds, professional sports bettors, bookies and banks make much of their income.
'Small enough' here would have to be very much smaller than 1 in 100 for this argument to begin to apply. It would have to be 'so small that it won't happen before the heat death of the universe' scale. I'm still not sure the argument works even in that case.
I believe there is a sense in which small probabilities can be said to also have an associated uncertainty not directly captured by the simple real number representing your best guess probability. I was involved in a discussion on this point here recently.
How small should x be? And if the argument does hold, are you going to have two different criteria for rational behavior - one with events where probability of positive outcome is 1-x and one that isn't.
And also, from Nick Bostrom's piece (formatting will be messed up):
Of course, by your reasoning, you would hand your wallet. Bravo.