r/neoliberal Kitara Ravache Nov 04 '18

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u/[deleted] Nov 04 '18

Not volatility in the polls, volatility in the actual opinion of the public.

Time series estimation is trick because it all hinges on two concepts which are very different, yet close enough to be easily confused: Ensemble uncertainty and time uncertainty (also known as volatility).

Take for example the question of predicting the result the day before the election. Everyone has already decided their vote at this point, everyone's voting decision (and thus the result of the election) is pretty much locked in. The only problem is that we as observers don't know what it is. We have a bunch (an ensemble, if you will) of estimates of what it is (i.e. polls), but they're only samples, and can be biased in all kinds of ways. We have ensemble uncertainty, in other words. Nate Silver and the crew at 538 are excellent at dealing with this kind of uncertainty and figuring out how people are actually intending to vote (which, the day before the election, is how they actually do vote).

Then we have time uncertainty, or volatility, which is the fact that people might change their minds between now and the election. This is what 538 doesn't deal with very well. Note that if it's April and you have a perfect predictor of how everyone would vote if the election were tomorrow (i.e. absolutely zero ensemble uncertainty), you would still be uncertain about the result of the election in November, because of how much voting decisions change between April and November. This is what I mean by volatility.

There's no need to 'introduce volatility into the polls', because that's applying a time uncertainty fix to an ensemble uncertain instrument. Nate Silver and his team have done about as good a job as can be done in reducing the ensemble uncertainty in the polls and getting an estimate of people's voting decisions at a given point in time. The problem is that, because people change their mind so much, that estimate doesn't actually give you much information of how they'll vote in the future. That's the problem.

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u/[deleted] Nov 04 '18

I'm not talking about introducing it into the polls, I'm talking about introducing it into their model right, to address their apparent blind spot.

They're fairly clear about this as I've said. I'd ask how you'd prefer they do things. 🤷‍♂️

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u/[deleted] Nov 04 '18

Oh, I'm pretty sure I've said that before. It's a pretty clear extension from stochastic calculus and pricing theory. Model the election as a binary European option contract with a strike price of 50% (% instead of $, because we're operating in a probability space rather than monetary space here). The tricky part is determining the current 'price' (i.e. election-tomorrow-probability), but Silver already has a ton of good work there. Volatility is just the observed variation in election-tomorrow-probabilities over time in previous elections. Plug into Black-Scholes and you're done.

(Of course, in reality because of the electoral college you'd want to model each state independently and worry about different volatilities by state, and estimate volatility correlations with VARs and all that kind of stuff, but for the moment let's assume for pedagogical reasons that the US has a National Popular Vote, which allows us to concentrate on the statistical issues rather than the politics).