I don’t think this formal argument conflicts with the claim that we should expect the forecasting frequency to affect the average daily Brier score. In the example that Flodorner gave where the forecast is essentially resolved before the official resolution date, Alice will have perfect daily Brier scores: Brierd=0, for any d>N′, while in those days Bob will have imperfect Brier scores: Brierd=BrierN′.
Thanks for the explanation!
I don’t think this formal argument conflicts with the claim that we should expect the forecasting frequency to affect the average daily Brier score. In the example that Flodorner gave where the forecast is essentially resolved before the official resolution date, Alice will have perfect daily Brier scores: Brierd=0, for any d>N′, while in those days Bob will have imperfect Brier scores: Brierd=BrierN′.
Thanks for challenging me :) I wrote my takes after this discussion above.