If tail probability PK does not hedge tail expectation GK, then skill at predicting PK provides no information on GK.

This is a mathematical claim from Taleb's 2023 work (on binary forecasting versus payoffs). The proposition: if the tail probability P_K does not hedge (is not tightly linked to) the tail expectation G_K, then skill at predicting P_K conveys no information about G_K. True: the paper's derivation, or standard probability theory, supports that under fat tails or where P_K and G_K are not hedged, forecasting skill on P_K does not translate into information about G_K, and the paper states this as a result. Mostly true: the result holds but needs a qualification (e.g. 'little' rather than 'no' information, or under fat tails only). Mixed: it holds only in special cases that the claim treats as general. Mostly false: the paper or standard analysis shows substantial information transfers in general, with the claim true only at extremes. False: the statement is mathematically wrong.

Set before the research began.

1. E1 On the Statistical Differences between Binary Forecasts and Real World Payoffs arXiv (Taleb) · 6 February 2018 Own record

   “Given that the former are bets paying a fixed amount and the latter have full payoff, one cannot be properly replicated (or hedged) using another, especially under fat tails and parametric uncertainty –meaning performance in one does not translate to performance into the other.”

2. E2 On the Difference between Binary Prediction and True Exposure With Implications For Forecasting Tournaments and Decision Making Research Taleb and Tetlock (hosted on stat.berkeley.edu course page) · 2013 Own record

   “Hedging variable exposures with binary bets can be disastrous”

3. E3 Election predictions are arbitrage-free: response to Taleb arXiv (ar5iv rendering) · 1 January 2016

   “We show that under mild assumptions all such political forecasts are arbitrage-free and that the heuristic that Taleb’s argument was based on is false.”

4. E4 Separating the Verbalistic from the Mathematical in Risk and Decisions NYU School of Engineering Extreme Risk Initiative working paper (Taleb) · 10 February 2026 Own record

   “In short, the vanilla has another dimension, the payoff, in addition to the probability, while the binary is limited to the probability.”

5. E5 On the Statistical Differences between Binary Forecasts and Real World Payoffs arXiv (author: Nassim N. Taleb) Own record

   “Given that the former are bets paying a fixed amount and the latter have full payoff, one cannot be properly replicated (or hedged) using another, especially under fat tails and parametric uncertainty –meaning performance in one does not translate to performance into the other.”

6. E6 On the Statistical Differences between Binary Forecasts and Real World Payoffs arXiv (author: Nassim N. Taleb) Own record

   “The reverse is also true, and the effect is exacerbated under nonlinearities. A binary forecasting record is likely to be a reverse indicator under some classes of distributions or deeper uncertainty.”

7. E7 On the Difference between Binary Prediction and True Exposure With Implications For Forecasting Tournaments and Decision Making Research Taleb & Tetlock (working paper, hosted at UC Berkeley) Own record

   “Hedging variable exposures with binary bets can be disastrous–and because of the human tendency to engage in attribute substitution when”

8. E8 Election predictions are arbitrage-free: response to Taleb arXiv (independent academic authors responding to Taleb)

   “We show that under mild assumptions all such political forecasts are arbitrage-free and that the heuristic that Taleb’s argument was based on is false.”

9. E9 Election predictions are arbitrage-free: response to Taleb ar5iv (arXiv paper 1907.01576) · 1 January 2016

   “We show that under mild assumptions all such political forecasts are arbitrage-free and that the heuristic that Taleb’s argument was based on is false.”

Taleb's paper states the result directly: binary bets and full-payoff exposures cannot replicate or hedge each other, especially under fat tails and parametric uncertainty, so performance in one does not carry over to the other (E1, E5). The Taleb and Tetlock working paper says, in qualitative terms, that hedging variable exposures with binary bets can be disastrous (E2, E7). However, the paper also says a binary forecasting record can be a reverse indicator under some distributions (E6). That is a qualification of "no information", and the paper says the effect is strongest under fat tails and parametric uncertainty (E1, E5). The independent sources (E3, E8, E9) address a separate argument about arbitrage in election forecasts and do not dispute this proposition.