The math isn’t super important to see why it’s so cool. His model seems to be that we should try to forecast the election outcome, including uncertainty between now and the end date, rather than build a forecast that takes current poll numbers and implicitly assumes nothing changes.

The mechanism of his model focuses on forming an unbiased time-series, formulated using stochastic methods. As far as I’m aware, the mainstream methods as of now focus on multi-level Bayesian methods.

That seems like it makes more sense. While it’s safe to assume a candidate will always want to have the highest chances of winning, the process by which two candidates interact is highly dynamic and strategic with respect to the election date.

When you stop to think about it, it’s actually remarkable that elections are so incredibly close to 50-50, with a 3-5% victory being generally immense. It captures this underlying dynamic of political game theory, which is itself a higher level abstraction of a simultaneous and recursive algorithm that runs through all citizens.

At the more local level this isn’t always true, due to issues such as incumbent advantage, local party domination, strategic funding choices, and various other issues. The point though is that when those frictions are ameliorated due to the importance of the presidency, we find ourselves in a scenario where the equilibrium is essentially 50-50.

So back to the mechanism of the model, Taleb imposes a no-arbitrage condition (borrowed from options pricing) to impose time-varying consistency on the Brier score. Intuitively, you can think of this as the idea that if you’re 1 month out from the election, and your candidate based on the latest polls has a 70% probability to win, however, variance over the past month has been massive, your model would be more efficient to state that your candidate has closer to a 50% chance to win, due to high uncertainty.

To simplify a little more, you can think of this as using a specific mathematical condition to filter out a ‘true’ probability of winning, from a highly uncertain output that is based on the latest polls data, but doesn’t take into consideration the time-series dynamics of that polls data.

For example, if 3 months out the polls give candidate A a near 100% chance of winning, the ‘true’ probability of winning might be a fair bit lower, as a function of the poll variance up until that point. That is to say, you’d want to bet lower since something could go wrong to lower it, but not increase it.

This would also explain why the variance in forecaster models is much higher than prediction market variance (no empirical data here, this is an observation I had).

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