>If over time, your forecasts predictably change, then they are not the best forecasts you could make with the information on hand.

And this is precisely the complaint Taleb is making.

An arbitrage is just a strategy that's guaranteed to make money. If you know for sure that something will go up and down at different points you could make money risk free. Simply buy at any point below the current price and sell at any point above.

> An arbitrage is just a strategy that's guaranteed to make money. If you know for sure that something will go up and down at different points you could make money risk free. Simply buy at any point below the current price and sell at any point above.

This is not arbitrage. Also this is precisely the kind of strategy Taleb would have argued against in his book about black swan events.

Time arbitrage is arbitrage.

If someone was flipping a coin and raising their price when it landed heads and lowering it when tails, arbitraging using reversion to the means would be a perfectly legitimate arb strategy.

Taleb's argument is that Silver's estimates are based on random noise, and are thus vulnerable to this form of arbitrage.

It think it’s… sort of the reverse? Flipping a coin results in Brownian motion, which is an example of a “martingale”, a function whose expected future value is equal to its current value; and the evolution of a share price being a martingale (at least under a modified probability measure) is exactly the condition for the market to not have arbitrage:

https://en.m.wikipedia.org/wiki/Risk-neutral_measure

I’m not sure exactly how the arbitrage works, though.

But the argument in the paper seems to be not that there’s noise but that there’s too much of it. In fact, it assumes that the expected vote share over time is subject to Brownian motion with specific parameters (which is a rather flawed assumption), but then concludes that 538’s probability distribution is more swingy what he’d calculate from those parameters.

The point is that Silver's predictions are the result of coin flips, but that the underlying probability isn't. If he's updating further than he should then you can make money by updating the correct amount and betting against him.

A price set by coin-flips does not revert to any mean. It's a random walk and it diverges. The idea that heads and tails must eventually even out is a common fallacy.

You don't need the price to revert, you just need to have a better estimate of the underlying probability.

Oh so the coin-flipper is not setting the price, but trying to predict it? I think at least I understand what you're explaining. I don't see how that is a useful model for what is going on though.

Predicting the result of a vote for a day when it's not going to be held is a form of entertainment that can't be verified. Is Silver claiming any more than that?

Yes, Silver is absolutely trying to forecast elections months in advance. Taleb's argument is that the polls at that point are largely noise, and so Silver is updating too much on them when he should basically ignore most of them until shortly before the election.