afaik, Taleb has repeatedly & explicitly stated “no probability without ergodicity”, which is pretty much a frequentist mantra. The problem with non-statisticians like Nate Silvers (who holds a BS in Econ, as opposed to Taleb who earned his PhD in Statistics), is that they traffic in electoral polls involving human subjects which are anything but ergodicity. Yet, they brazenly attribute probability models to their conclusions. That has severe definitional issues, which is what Taleb objects to.
As to the gatekeeping issues, my mom buys eggs for $3 and groceries for $7. 3+7=10, so she hands over a $10 bill. Wait a minute, does that mean my mom is a mathematician, because she has engaged in arithmetic, which is math ? That’s the issue here. Silvers can simply post how many people want to vote which way & leave it at that. It’s just an opinion poll. Instead he engages in an elaborate charade where he takes polls of polls, ensemble averages, then says this is what is most likely, then on election day when most likely becomes least likely, he washes his hands off. Thats just clearcut fraud. All Taleb is saying is that you simply don’t have ergodicity here so you don’t have a probability. You just have a [0..1] fraction that doesn’t mean much because it doesn’t converge to a limit as information approaches infinity. So if you had skin in the game and purchased an option based on the projected outcome you would lose big time.
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.
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.
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
https://projects.fivethirtyeight.com/checking-our-work/
Probability theory, whether frequentist or otherwise, is "just" math. Identifying that mathematical structure with real-world events is always going to involve a judgment call. So if your framework requires assumptions that don't hold in the real world, then maybe it's not the appropriate framework to use. Because clearly people are making decisions based on numbers between 0 and 1, and they're not generally losing big time.
Would you lose at any odds? Then the probability is zero.
Would you (expect to) lose at some odds and win if the odds offered were different? Then the probability is somewhere in between.
Wrong.
https://helyettegeman.com/phd-students/
Not so different from economics.
"Perfect ergodicity means that each one of us, should he live forever, would spend a proportion of the time in the economic conditions of the entire cross-section[of the U.S. population]: out of, say, a century, an average of sixty years in the lower middle class, twenty years in the blue-collar class, and perhaps one single year in the one percent"
In fact article makes a mistake by requiring stationary nature from ergodic process. You can have an ergodic process of the first kind where ML expectation is equal to the value of the process function, which nonetheless is not stationary in absolute sense. (Because definite integral does not match indefinite.) Just perfectly predictable and having the indefinite integral identical to integral over space state. Which implies strictly bounded but not exactly stationary in any defined term.
Likewise you can prove an equivalence class of the process to be identical to another known ergodic process without actually calculating such difficult to obtain complete integrals.
And ergodicity is not required for representative sampling either, just definite error bounds on predictive (statistical) power or likelihood estimates. Which can be estimated or directly calculated for many kinds of processes accurately. It is only required for certainty.
No, ergodicity is more about visiting the each part of the phase space with some positive frequency i.e. on a long trajectory you see everything that can happen, and not too infrequently.
Dictionaries don't actually tell you what a word means, they give examples of what it may mean from common usage.
1. of or relating to a process in which every sequence or sizable sample is equally representative of the whole (as in regard to a statistical parameter)
2. involving or relating to the probability that any state will recur especially : having zero probability that any state will never recur
Nassim Taleb mostly uses ergodicity in the second meaning, while the article concentrates on the first. I find it utterly confusing.