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PaperclipPerfector  1mo ago (text post)   28212 thread views

Culture War Roundup for the week of October 14, 2024

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Is probability even well-defined for a one-off event? It's not like we can random sample the multiverse on how the election actually went. At the same time, nothing is absolutely certain (supervolcano as October surprise!).

Maybe it makes sense from a Bayesian perspective: given the current knowledge of the system state (polls, voter registrations, demographics, maybe even volcanology reports) we can estimate the probability of a specific outcome. But a frequentist view seems nonsensical, even if a lot of predictions seem to present themselves that way.

One-off events are intractable. Kelly does not work on them.

I completely agree, the frequentist view is nonsensical. This is why forecasters need to be nailed down to a specific outcome (or ‘I don’t know / it’s too close to call’ but this has to be acknowledged as opting-out).

That's my main problem with Nate Silver's modelling.

There should be large error bars around the prediction that slowly close in as the predicted event approaches.

It shouldn't be "X% Trump, Y% Kamala," it should be "X% Trump, Y% Kamala, Z% irreducible uncertainty."

The logic is "if the election were held today then here's the probability." But... the elections won't be held today. That's the whole point of the prediction for a future event, and I think it behooves them to acknowledge that uncertainty is inherent to the modelling process.

If they'd included that back when it was Trump vs. Biden, the conserved probability would have accounted for Biden suddenly dropping out and wouldn't have broken the model instantly. Also helps reflect the chance that one of the candidates dies... which also almost happened.

And if Nate trusts his model, there's a ton of money to be made in the prediction markets.

It shouldn't be "X% Trump, Y% Kamala," it should be "X% Trump, Y% Kamala, Z% irreducible uncertainty."

What would this irreducible uncertainty mean for an event with a binary outcome? I think Silver already accounts for increasing uncertainty as he propagates his current prediction into the future (what he calls forecast vs. nowcast).

Error bars would make sense around the expected vote percentage. Of course the probability distribution over vote percentages becomes broader as you look into the future, and perhaps he does show that to paying customers. But in the end you still have to integrate over that when the layman asks for the probabilities of who wins the election. And that still amounts to two numbers that sum to 100%.

Evaluating a predictor's performance seems straightforward to me via the usual log-likelihood score. Record the final outcome and take the log of the predictor's probability for that outcome. That score can then be summed over multiple different elections, if you like. (Not sure though if I'd call that scoring rule particularly frequentist.)

But the outcome ISN'T really binary, is it?

Biden dropped out, Trump could have been killed by that bullet, and then we'd have a whole new ball game. The "Trump vs. Biden" model almost certainly didn't include a variable for "the Candidate abruptly drops out" and I doubt assassination risk was plugged in either.

And the fact that it tries to 'call' an election months out but has to adjust radically to new info is why I call it 'gimmicky.'

Taleb had his own discussion of this a while back, and this is the best summary of it I've found.

https://towardsdatascience.com/why-you-should-care-about-the-nate-silver-vs-nassim-taleb-twitter-war-a581dce1f5fc

But the outcome ISN'T really binary, is it?

Sure, in this trivial sense it is not.

I've heard this same argument from other Taleb-readers and got the impression that "irreducible uncertainty" means something entirely different than just a "none of the above" outcome.

If it is just that, then the same arguments apply: When you make the final probabilistic prediction, you integrate over the uncertainty, resulting in three numbers that add up to 100%. After recording the actual outcome, take the log of your predicted probability for this outcome, and that's your performance score.

Of course, if Silver rounds down the probability of "none of the above" to 0% for convenience and it still occurs, he'd technically incur a score of -Inf, which should tank his credibility forever. But I find that a boring technicality.

From your linked article:

Because FiveThirtyEight only predicts probabilities, they do not ever take an absolute stand on an outcome: No ‘skin in the game’ as Taleb would say.

Taleb is wrong here. Under this standard, no reasonable predictor could survive any real world application, as it would have to be trashed after the first mistake. And those that do survive would be hopelessly overfitted to past data.

For standard models, like logistic regression, the default decision boundary is assumed to be 50% (or 0.5 on a 0 to 1 scale) or the alternative with the highest value. [...] If FiveThirtyEight has no stated decision boundary, it can be difficult to know how good their model actually is.

The article got it precisely the wrong way round. Classical models such as logistic regression are trained and evaluated using their full probabilistic predictions.

It is only thresholded to a deterministic choice when used as input to a human decision, where the prediction is appropriately weighted for costs of false positives vs false negatives etc. (which you cannot do if it were a deterministic prediction in the first place).

And the fact that it tries to 'call' an election months out but has to adjust radically to new info is why I call it 'gimmicky.'

How's that bad? I'd call that perfectly rational behaviour.

How's that bad? I'd call that perfectly rational behaviour.

Perfectly rational behavior would probably be saying "I don't think I can accurately predict outcomes this far in advance."

So they add in the caveat "if the election were held today here is what the model says about the odds."

But the election isn't being held today. They know that, the audience also knows that but will still read the model.

Without a gimmick they have nothing to sell.

There's not a ton of money to be made if you believe the odds are 50/50. Prediction markets give Trump 60/40 odds, while Nate's model gives 50/50 odds. If your bankroll is $1M, then it's only rational to bet 167k, for an expected value of 40k. Not nothing, but not a ton of money either.

That also ignores other costs, like counterparty risk. Nate also has to deal with reputational risk: people might value his published models less if they thought he was making bets on markets that were influenced by his models. Since that's his main source of actual income, a bet would be substantially negative EV for him.

There's reputational risk for having his model diverge too far from the prediction market's call, if the markets end up looking more accurate.

And I've seen him offer various bets before.

I like Nate generally, but I end up with the feeling that the Presidential Election model is a bit too gimmicky for my tastes. As stated, he should display some factor that accounts for the inherent uncertainty of a long-term prediction, rather than making confident-seeming prognostications which get aggressively revised as new information comes in.

He's not calling his shot well in advance, he's just adjusting to the same information everyone else gets as it comes in. Credit for the model being reasonable, but what new information is it giving us?

There is no new information. We have no reason to think his model is even particularly good. The only thing that it really brings to the table is that he both has a consistent reasonable process that doesn't give much room for human bias to creep in, and that he doesn't abandon it the second it makes partisans mad. This is, apparently, a really hard thing to do.

Or, a bit more optimistically: it actually does provide information that can be new to people. E.g., post-debate the model showed that Biden was going to get walloped because voters just weren't willing to re-elect someone senile, while many Democrats were doing their best to convince themselves otherwise. It's somewhat fair to say, "oh, so all the model does is tell you things that are blindingly obvious?" Yes, with a significant caveat: seeing what's in front of your eyes is a very difficult thing in politics.

"All models are wrong. Some are useful."

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