- Suppose one forecaster says the probability Trump wins is q and the other says the probability is p>q. If Trump in fact wins, who was “right?”
- Suppose one forecaster says the probability is q and the other says the probability is 100%. If Trump in fact wins, who was right?
- Suppose one forecaster said q in July and then revised to p in October. The other said q’ < q in July but then also revised to p in October. Who was right?
- Suppose one forecaster continually revised their probabilistic forecast then ultimately settled on p<1. The other forecaster steadfastly insisted the probability was 1 from beginning to end. Trump wins. Who was right?
- Suppose one forecaster’s probability estimates follow a martingale (as the laws of probability say that a true probability must do) and settles on a forecast of q. The other forecaster‘s “probability estimates” have a predictable trend and eventually settles on a forecast of q’>q. Trump wins. Who was right?
- Suppose there are infinitely many forecasters so that for every possible sequence of events there is at least one forecaster who predicted it with certainty. Is that forecaster right?

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## 4 comments

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August 4, 2016 at 12:51 am

Enrique Guerra-PujolIn other words, how many pollsters use sound statistical methods (random samples, unbiased questions, etc.) and how many are hucksters?

October 7, 2016 at 2:43 pm

CI don’t think that is the point. The problem is that you have only one realization of a random process. There is no way to make inferences from one realization.

The “true” probability (if that exists) of Trump winning might be 1e-6; unlikely to occur but it could still happen. If it does is someone predicting a Trump win w.p. 1 correct? Knowing the true probability we would say “no”. However, for these unique events we never see/can estimate the true probability.

November 6, 2016 at 12:43 pm

João rodarteJoão rodarteThoughts Left Lying Around About Election Forecasts | Cheap Talk

October 11, 2017 at 3:16 am

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