Thanks!

]]>> We argue that all these sources of information are necessary, and if any are not included, the forecaster is implicitly making assumptions about the missing pieces

Necessary in which sense, to make good predictions? Isn’t this just a case of P(Y|X) being on average further from the truth than P(Y|X,Z) when Z has predictive value conditional on X? I don’t think we really need to assume something about information we don’t use when we condition on some other information. For instance, I think it would be interesting in its own right to study P(Y|X) where X is fundamentals but no polls and see what you get for that. The literature discussed in the paper seems to indicate this already does substantially better than a 50% prediction would. It’s just that you could do far better still when adding polls to the analysis.

> Given all our uncertainties, it would seem pretty ridiculous to claim we could forecast to that precision anyway, right?

If I understand this right, the win probability in this example is conditional on a mu and sigma for Biden’s vote share and it is pointed out that it changes a lot if mu=0.535 instead of mu=0.54. But why can’t you include uncertainty about mu into the win probability by averaging over its posterior distribution? Doesn’t the resulting unconditional win probability adequately reflect if the conditional-on-mu win probability is very sensitive to mu and we can’t pin mu down very precisely?

>that is, the prediction at time t is based on the fundamentals at time t, not on the forecasts of the values these predictors will be at election day and thus we would not expect these predictions to satisfy the martingale property

Is this necessary to satisfy the martingale property? You could simply model P(Biden wins| fundamentals_t) which could be allowed to change with t. I thought this is what 538 and the Economist already do with polls: If there was no polling error at all, P(Biden wins | vote_share_t) depends on how close t is to the election. I think if this model was correct, its stream of win probabilities would be a martingale.

“With the proliferation of polls have come aggregators such as Real Clear Politics and the

Huffington Post…”

I think Huffington Post is pretty much out of this business. It’s been nearly two years since they update Pollster: https://elections.huffingtonpost.com/pollster/polls

]]>Is the model uncalibrated and underreports uncertainty? Or do you account for that flaw somehow or expect the effect to be offset by other flaws in the model or have estimated the effect to be negligible?

> How many decimal places does it make sense to report the win probability?

Maybe you accidentally a word?

]]>Anon:

Thanks. I went through, fixed a bunch of typos, and, and reposted the correct version.

]]>> we see forecasting as an essentially collaborative exercise.

Before 2007/8, when talking about meta-analysis I found it very strange that almost no one seemed to be doing meta-analysis of reported polls.

At some point (early in 2008), I contacted Sam Wang at Princeton who seemed to be an exception and asked him why he thought most were avoiding it. If I recall correctly, he said it mostly due to a competitive stance with most arguing other polls would just ruin their much better one. Here, Wang suggests combining became only popular in 2008 https://web.math.princeton.edu/~sswang/wang15_IJF_origins-of-poll-aggregation.pdf

Now, to me meta-analysis never meant taking weighted averages or even obtaining combined estimates, but rather trying to make the most sense one could of multiple endeavors and the inputs they generated.

> Combining forecasts more formally is an intriguing idea

So if I am getting right, this would be trying to make the most sense one could of multiple modelling endeavors and the outputs they generated.

“If we bump Biden’s predicted 2-party vote down to 53.5%, we get a probability Obama wins of Φ((0.545 − 0.517)/0.02) = 0.816, now just an 80% chance.”

I think you mean “…probability *Biden* wins…”. Also, it should be “0.535 − 0.517”.

Great paper, but there are at least a few other typos throughout.

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