We have the election estimate F a function of a state variable W, a Wiener process WLOG
That doesn’t look like a reasonable starting point to me.
Going back to the OP...
the process by which two candidates interact is highly dynamic and strategic with respect to the election date
Sure, but it’s very difficult to model.
it’s actually remarkable that elections are so incredibly close to 50-50
No, it’s not. In a two-party system each party adjusts until it can capture close to 50% of the votes. There is a feedback loop.
When you read Silver (or your preferred reputable election forecaster, I like Andrew Gelman) post their forecasts prior to the election, do you accept them as equal or better than any estimate you could come up with?
I’m an arrogant git, so I accept them as bit worse :-P To quote an old expression, (historical-) data driven models are like driving while looking into a rearview mirror. Things will change. In this particular case, the Brexit vote showed that under right conditions people who do not normally vote (and so are ignored by historical-data models) will come out of the woodwork.
to know the true answer
Eh, the existence of a “true answer” is doubtful. If you have a random variable, is each instantiation of it a “true answer”? You end up with a lot of true answers...
We have the election estimate F a function of a state variable W, a Wiener process WLOG
That doesn’t look like a reasonable starting point to me.
That’s fine actually, if you assume your forecasts are continuous in time, then they’re continuous martingales and thus equivalent to some time-changed Wiener process. (EDIT: your forecasts need not be continuous, my bad.) The problem is that he doesn’t take into the time transformation when he claims that you need to weight your signal by 1/sqrt(t).
He also has a typo in his statement of Ito’s Lemma which might affect his derivation. I’ll check his math later.
It’s just masturbation with math notation.
That doesn’t look like a reasonable starting point to me.
Going back to the OP...
Sure, but it’s very difficult to model.
No, it’s not. In a two-party system each party adjusts until it can capture close to 50% of the votes. There is a feedback loop.
I’m an arrogant git, so I accept them as bit worse :-P To quote an old expression, (historical-) data driven models are like driving while looking into a rearview mirror. Things will change. In this particular case, the Brexit vote showed that under right conditions people who do not normally vote (and so are ignored by historical-data models) will come out of the woodwork.
Eh, the existence of a “true answer” is doubtful. If you have a random variable, is each instantiation of it a “true answer”? You end up with a lot of true answers...
That’s fine actually, if you assume your forecasts are continuous in time, then they’re continuous martingales and thus equivalent to some time-changed Wiener process. (EDIT: your forecasts need not be continuous, my bad.) The problem is that he doesn’t take into the time transformation when he claims that you need to weight your signal by 1/sqrt(t).
He also has a typo in his statement of Ito’s Lemma which might affect his derivation. I’ll check his math later.