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Taleb makes the claim in this paper (and others) that there exists some sort of bound on the variance of a binary forecast such that if a forecaster's binary predictions exceed the bounds on variance there exists a method to arbitrage him. Would someone familiar with the dispute (and perhaps various other papers) be able to explain exactly and technically what he means?

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    $\begingroup$ Can you provide a link? I think I know what the discussion is about, but without a link, I may be making assumptions regarding the discussion. $\endgroup$ – Dave Harris Aug 9 '19 at 22:34
  • $\begingroup$ Is it about this issue? $\endgroup$ – Raskolnikov Aug 10 '19 at 22:09
  • $\begingroup$ Yes. I think his main point revolves around the volatility of Silver's forecasts being too high. He claims that this would expose Silver to arbitrage if he were to trade on his forecasts. I do not understand how he can know this. Is there a rigorous proof or is it just Taleb's "feeling" that the vol of Silver's forecast is too high. $\endgroup$ – roz Aug 11 '19 at 2:29
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Taleb argues that under uncertainty, election forecasts should be seen as a Binary option. A similar thought is presented by De Finetti's principle that probability should be treated like a two-way "choice" price. Therefore, under high levels of volatility, forecast should not have extreme variation across time (equivalently, the price of the binary option should not change significantly even if polls reveal a large change in the dynamics among candidates). Under high levels of uncertainty, the price of the binary option converges to 0.5. Therefore, the probability of winning the elections in a two-candidate environment should converge to 0.50. A quick look on Silver's forecasts, shows high volatility across time. For instance, Trump's probability of winning the elections ranges roughly from 0.15 to 0.45

enter image description here Source: https://towardsdatascience.com/why-you-should-care-about-the-nate-silver-vs-nassim-taleb-twitter-war-a581dce1f5fc

For more details on Taleb's no-arbitrage argument, one should check his recent publication and a response to this publication:

  1. Taleb, Nassim Nicholas. "Election predictions as martingales: an arbitrage approach." Quantitative Finance 18.1 (2018): 1-5.

  2. https://www.tandfonline.com/doi/citedby/10.1080/14697688.2019.1639802?scroll=top&needAccess=true

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  • $\begingroup$ I understand that as volatility increases the price of the binary approaches 0.5. I also understand the mapping between binary bets, choice prices, and probabilities. What I do not understand is what exactly the arbitrage process is. Taleb makes a claim that Silver can be arbitraged via a Dutch book sort of procedure. But I do not see how. I have read the papers you linked and either they do not explain it or I am just not understanding it. Do you know how? $\endgroup$ – roz Aug 12 '19 at 13:34
  • $\begingroup$ Buying the binary when its price is very low and selling it when its price is very high based on the assumption that vol is very high is not an arbitrage; you are just trading vol. So if this is the process that Taleb is referring to when he says arbitrage, I think he is not correct. $\endgroup$ – roz Aug 12 '19 at 13:38

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