Nate Silver’s predictions were changing too much over the time. If those probabilities were legit, you’d be able to sell binary options based on them. If Nate would do that, he’d went bankrupt, because he created lot of arbitrage opportunities.
That paper doesn’t actually justify why 538′s probabilities don’t form a martingale. (In fact it’s plausible that they do—to demonstrate they aren’t I’d want to see someone show a strategy which is successfully arbitraging the probabilities). Since 538′s model isn’t open source, it’s pretty difficult to say whether or not it is a true martingale, but that paper definitely doesn’t show it.
If we were to take a similar model which is open source (specifically The Economist’s model) we can see that it is not far from being a martingale. Specifically if they added forecasting for their [fundamentals model](http://www.stat.columbia.edu/~gelman/research/published/jdm200907b.pdf) (not difficult, just painful). I don’t think the difference made by the fundamentals model is that significant so I think it would have been fairly difficult for anyone to arbitrage those odds. (Not that they were correct, just that they were broadly time-consistent)
Nate Silver’s predictions were changing too much over the time. If those probabilities were legit, you’d be able to sell binary options based on them. If Nate would do that, he’d went bankrupt, because he created lot of arbitrage opportunities.
https://arxiv.org/pdf/1703.06351.pdf
That paper doesn’t actually justify why 538′s probabilities don’t form a martingale. (In fact it’s plausible that they do—to demonstrate they aren’t I’d want to see someone show a strategy which is successfully arbitraging the probabilities). Since 538′s model isn’t open source, it’s pretty difficult to say whether or not it is a true martingale, but that paper definitely doesn’t show it.
If we were to take a similar model which is open source (specifically The Economist’s model) we can see that it is not far from being a martingale. Specifically if they added forecasting for their [fundamentals model](http://www.stat.columbia.edu/~gelman/research/published/jdm200907b.pdf) (not difficult, just painful). I don’t think the difference made by the fundamentals model is that significant so I think it would have been fairly difficult for anyone to arbitrage those odds. (Not that they were correct, just that they were broadly time-consistent)