When (Not) To Use Probabilities
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I'll also disagree with the argument Eliezer gives here. See Robin's post. In addition to coming up with a probability with which we think an event will occur, we should also quantify how sure we are that that is the best possible estimate of the probability.
e.g. I can calculate the odds I'll win a lottery and if someone thinks their estimate of the odds is much better then (if we lack time or capital constraints) we can arrange bets about whose predictions will prove more accurate over many lotteries.