(I feel a bit weird referencing my post since it did much more poorly than I expected, but I’ll just do it anyway since I know you’ve read it.)
The way in which my post contradicts your argument is that it frames the questions
Did 538 make a good prediction?; and
Was the market’s prediction better than 538′s?
as entirely separate. For the first question, we care about how much information 538′s prediction was based on and how well calibrated it was. Well, we know what kind of information it was based on (the same as every election), and evidence shows that calibration is excellent. In fact, this election made 538′s calibration look better than it did before since it was historically conservative. (I think—I’ve heard Nate say this.) In the two pictures I’ve had in my post, both of them had 538 at the same place on the chart. They were only different in how well the market did. In other words, Nate did a good job regardless of what happened with the market. (And in the article you linked, he wasn’t asked about the market.)
The second question is where we compare the hypothesis that the market was being stupid (1) to the hypothesis that it was smarter than 538/had information about the polling error that 538 didn’t (2). This is where I’ll grant you the update you mentioned in your comment. (2) predicts a narrow margin in the real result, whereas (1) has significant probability mass on a Biden landslide. Since we got the narrow margin, that has to be a significant update toward the market being smart, maybe (1:4) or something. (But I made an even greater update toward the market being stupid based on its behavior on election night, so I come out updating toward the market being stupid in total, which was also my prior (that’s why I bet against it in the first place).)
Yes, that looks like a crux. I guess I don’t see the need to reason about calibration instead of directly about expected log score.
(I feel a bit weird referencing my post since it did much more poorly than I expected, but I’ll just do it anyway since I know you’ve read it.)
The way in which my post contradicts your argument is that it frames the questions
Did 538 make a good prediction?; and
Was the market’s prediction better than 538′s?
as entirely separate. For the first question, we care about how much information 538′s prediction was based on and how well calibrated it was. Well, we know what kind of information it was based on (the same as every election), and evidence shows that calibration is excellent. In fact, this election made 538′s calibration look better than it did before since it was historically conservative. (I think—I’ve heard Nate say this.) In the two pictures I’ve had in my post, both of them had 538 at the same place on the chart. They were only different in how well the market did. In other words, Nate did a good job regardless of what happened with the market. (And in the article you linked, he wasn’t asked about the market.)
The second question is where we compare the hypothesis that the market was being stupid (1) to the hypothesis that it was smarter than 538/had information about the polling error that 538 didn’t (2). This is where I’ll grant you the update you mentioned in your comment. (2) predicts a narrow margin in the real result, whereas (1) has significant probability mass on a Biden landslide. Since we got the narrow margin, that has to be a significant update toward the market being smart, maybe (1:4) or something. (But I made an even greater update toward the market being stupid based on its behavior on election night, so I come out updating toward the market being stupid in total, which was also my prior (that’s why I bet against it in the first place).)