Nassim Talebs case against Nate Silver is bad math
So... I wrote this. Maybe I can clarify a little what I meant by the statement &quot;Since Silver’s forecasts begin with probability models, it’s safe to assume they obey all the rules, including Bayes’, and would be arbitrage-free.&quot;, since this seems to be confusing some people:<p>What I&#x27;m addressing here is Taleb&#x27;s claim that Silver&#x27;s probabilities would allow for arbitrage (i.e., riskless profit, not just profit on average) if turned into betting prices. This is in the sense of arbitrage-through-time, buying low and then selling high. As I discussed in the piece, an old argument due to de Finetti says that if prices are arbitrage-free they must satisfy the equations of probability, meaning you can in some sense think of the price as giving a probability of the outcome. For time-dynamic arbitrage the relevant equation is Bayes&#x27; Theorem. All I meant by my statement above is that the converse to de Finetti&#x27;s argument is also true, trivially. If prices obey the equations of probability they are automatically arbitrage-free. And since Silver&#x27;s probabilities begin life as probabilities, they satisfy all the relevant equations (one would expect).<p>Technically, the way we&#x27;d express this in modern finance is through the Fundamental Theorem of Asset Pricing, which says a (complete) market is arbitrage-free if and only if there exists an equivalent measure under which asset prices are martingales. Silver&#x27;s probabilities are necessarily martingales, just because of the way conditional probability math works, so unless Taleb can claim that his and Silver&#x27;s probabilities aren&#x27;t equivalent, meaning they disagree on what events have probability zero, then there is no chance of arbitrage. That&#x27;s just the mathy way of saying the same thing I said in the post.<p>There are many other possible errors Silver could be making, and many other possible criticisms Taleb could have made but did not. In this case he wrote a paper claiming a mathematical result that just isn&#x27;t true.<p>Hope that&#x27;s helpful!