| There are two probabilites is you want to make it so in your model. In the coin example it may make sense, you model the coin as a binomial probability and you can estimate it. You can repeat the events, it makes sense to talk about frequencies and you can improve your estimate of the parameter. In the election model it's not clear to me what's to gain by saying that there are two probabilities (or more) instead of one. There is one single event. >Hillary had a 95% chance to win the election. But on top of the fact that 1 in 20 times she'd lose that election if that really was the probability, Which is the only thing that matters if we say that the probability was 95%. > the 95% number was uncertain because the measurements were difficult to pin down - maybe she'd have lost 1 in 40 times, or maybe she'd have lost 1 in 5 times. You have lost me here. Did she have a 95% chance to win or not? If this 95% is uncertain, because it could have been 97.5% or 80%, then the probability would be the weighted average of those numbers and not 95%. And if it was so uncertain that nothing was known at all it would be 50%. Consider the following cases: a) You are going to flip a coin that I know is completely fair. I would say that the probability of heads if 50%. b) You have flipped a coin that I know is completely fair. Nobody knows what has been the result. I would say that the probability of heads is 50%. c) You have flipped a coin that I know is completely fair. You know the result but I don't. I would say that the probability of heads is 50%. In some cases you would say that I'm 100% right on my assesment of the probability being 50% while in others the actual probability is either 100% (with probability 50%) or 0% (with probability 50%). This seems irrelevant as far as my statement about the probability being 50% is concerned. |