If the probabilities that Wang’s model computes for each state were right, you could have used the resulting probability distribution of the outcomes in the electoral college to straightforwardly derive the probability that Clinton was going to win, which is just the probability that she gets at least 270 votes in the electoral college.
No. Even if Wang had reasonable probabilities of Clinton individually winning in each state, the aggregation procedure described in the post (I haven’t checked if this is what Wang actually did) for using these probabilities to get a probability that Clinton will win the election assumes that winning each state is independent, which is a completely ridiculous assumption. Most sources of uncertainty about elections are correlated between states; for example, widely publicized news stories that make Clinton or Trump look bad a certain number of days before the election. The independence assumption horrendously exaggerates the probability of Clinton winning given that she has a slight edge.
Also, to be clear, in order to compute his prediction, Wang did assume that non-sampling errors were somewhat correlated, just not nearly enough. As I say in the post, he is a very smart guy, so it’s not as if he didn’t know the things I explain.
I agree with you that the probabilities of Clinton winning individual states are correlated, but I’m not sure this makes what I wrote false, although you’re probably right that it’s a bit misleading. The fact that the probabilities of Clinton winning individual states are correlated is only relevant to calculate the probabilities for each possible outcome in the electoral college. It means that, as I explain later in my post, you have to take into account the fact that non-sampling polling errors in different states are correlated in order to calculate the probabilities for each possible outcome in the electoral college. One of the sources of non-sampling error that I describe in my post is measurement error, which if you read my post carefully I define in such a way that if someone doesn’t vote for the candidate they claimed they would vote for when they participated to a survey for whatever reason (e. g. because they heard a news story that made Clinton or Trump look bad), it counts as measurement error. I agree that it’s probably an unusual definition of this concept, which is typically construed more narrowly. But I defined measurement error in that unusually broad way precisely because I didn’t want to introduce the complication that, even if someone who tells a pollster n days before the election that he’s going to vote for X and would really vote for X if the election took place on the day he participated to that survey, he might not vote for X on election day. (Wang takes that, among other things, into account in order to calculate his prediction, but I was only describing the way in which he calculates a snapshot of where the race stands at any given time, since I think it’s where the most interesting mistakes were made. I may be wrong about that, but judging by what he said after the election, I think Wang would agree with me on that.) Now, if the probabilities you calculated for each possible outcome in the electoral college are correct, then you can just use the aggregation method I describe above the passage you quoted in my post. What is misleading in my post is that I say the assumption for that method to be reliable is that the probabilities of Clinton winning individual states are correct (instead of the probabilities for each possible outcome in the electoral college), because it suggests that we can assume they are probabilistically independent (although I never said that and the rest of my post makes clear that I wasn’t making that assumption), which of course they are not. Do you agree with that or do you think that there is a more serious problem here?
I was just reading my post again, and I guess this passage is also misleading, for exactly the same reason: “if you had calculated a probability that Clinton was going to win in each state using the method I explained above (which you then use to compute a probability that Clinton is going to win the electoral college)”.
No. Even if Wang had reasonable probabilities of Clinton individually winning in each state, the aggregation procedure described in the post (I haven’t checked if this is what Wang actually did) for using these probabilities to get a probability that Clinton will win the election assumes that winning each state is independent, which is a completely ridiculous assumption. Most sources of uncertainty about elections are correlated between states; for example, widely publicized news stories that make Clinton or Trump look bad a certain number of days before the election. The independence assumption horrendously exaggerates the probability of Clinton winning given that she has a slight edge.
Also, to be clear, in order to compute his prediction, Wang did assume that non-sampling errors were somewhat correlated, just not nearly enough. As I say in the post, he is a very smart guy, so it’s not as if he didn’t know the things I explain.
I agree with you that the probabilities of Clinton winning individual states are correlated, but I’m not sure this makes what I wrote false, although you’re probably right that it’s a bit misleading. The fact that the probabilities of Clinton winning individual states are correlated is only relevant to calculate the probabilities for each possible outcome in the electoral college. It means that, as I explain later in my post, you have to take into account the fact that non-sampling polling errors in different states are correlated in order to calculate the probabilities for each possible outcome in the electoral college. One of the sources of non-sampling error that I describe in my post is measurement error, which if you read my post carefully I define in such a way that if someone doesn’t vote for the candidate they claimed they would vote for when they participated to a survey for whatever reason (e. g. because they heard a news story that made Clinton or Trump look bad), it counts as measurement error. I agree that it’s probably an unusual definition of this concept, which is typically construed more narrowly. But I defined measurement error in that unusually broad way precisely because I didn’t want to introduce the complication that, even if someone who tells a pollster n days before the election that he’s going to vote for X and would really vote for X if the election took place on the day he participated to that survey, he might not vote for X on election day. (Wang takes that, among other things, into account in order to calculate his prediction, but I was only describing the way in which he calculates a snapshot of where the race stands at any given time, since I think it’s where the most interesting mistakes were made. I may be wrong about that, but judging by what he said after the election, I think Wang would agree with me on that.) Now, if the probabilities you calculated for each possible outcome in the electoral college are correct, then you can just use the aggregation method I describe above the passage you quoted in my post. What is misleading in my post is that I say the assumption for that method to be reliable is that the probabilities of Clinton winning individual states are correct (instead of the probabilities for each possible outcome in the electoral college), because it suggests that we can assume they are probabilistically independent (although I never said that and the rest of my post makes clear that I wasn’t making that assumption), which of course they are not. Do you agree with that or do you think that there is a more serious problem here?
I was just reading my post again, and I guess this passage is also misleading, for exactly the same reason: “if you had calculated a probability that Clinton was going to win in each state using the method I explained above (which you then use to compute a probability that Clinton is going to win the electoral college)”.