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)
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)