[yellowstuff]

I don't understand your (or Taleb's) point. If you insist on "no probability without ergodicity" then you can't put a probability on stock price movement, or any election or sporting event. But people put probabilities on those all the time. If that breaks the assumptions of frequentist models then it's the frequentists who are wrong about what people mean when they use probabilities.

I agree with the idea that Nate Silver is an entertainer, and if he were a bookie he'd need to be more precise about the odds he places on things and his range of uncertainty. But to me that doesn't suggest that Silver shouldn't speak in terms of probability at all. For a journalist (a big caveat) he's remarkable for being rigorous, open about his level of certainty, and willing to admit to mistakes.

[patrick5415]

I disagree that statisticians should adjust their definitions to fit common usage.

I can put any probably on anything I want. That doesn’t imply those numbers mean anything usefu or that what I’m doing is backed by any established theory.

[kgwgk]

There are established theories of probability that have nothing to do with ergodicity. See for example:

Laplace - Théorie analytique des probabilités - 1812

Keynes - A Treatise on Probability - 1921

Jeffreys - Theory of Probability - 1939

Savage - The Foundations of Statistics - 1954

de Finetti - Teoria delle Probabilità - 1970