> It's how you can prove all non-Bayesian models are irrational
Can you expand or link?
> Error bars and spreads are already outside the Bayesian paradigm, which demands a single number
Not following at all. What do you mean?
>Not following at all. What do you mean?
One assumption is that given a bet, you must choose to take a side of it. If you won't bet for something at X%, you must bet against it at 1-X%.
When I think of Bayesian analysis, I always think of Bayesian models which attempt to model uncertainty and always have a posterior distribution (spread) of outcomes.
For example, in the Dutch Book page, instead of having a point-prior (P=0.51 (delta on P=0.51?)), each degree of belief could have some (different) distribution which could yield a posterior with a distribution and change the math here.
To say that the probability of it being true is a range is incoherent.
It's not incoherent to analyze the posterior distribution by reporting a credibility interval instead of a single number (for example the posterior median).
How well that models an actual election is debatable, of course, but I think it does model it to some degree. In reality, there are not two stages but multiple, and none of those stages are necessarily fundamentally stochastic; rather, you just need exponentially more information to predict one stage than to predict the previous one, and without that information you may as well treat it as stochastic. For example, if I’m about to flip a coin, a god with exact knowledge of the state of my body and brain, the air currents in the room, etc. might be able to predict how I’ll throw it and how it will fall, but mere mortals have to treat a coin flip as random. Similarly, a god with exact knowledge about the state of the universe might be able to predict an election result eons in advance… though quantum randomness might trip them up. Getting more down to earth, if you just could poll every American about their political beliefs, you could make much better predictions than you can with real polls, which have to take random samples and thus accept some level of stochastic polling error. On the other hand, polls can also suffer from methodological error, which is fundamentally different in nature; it can be highly pernicious, but does require a smaller quantity of information to correct for. And so on.
Re polls: still more complicated than that, even with 100% polling you'd still have response error and non-voters. Much of the difference between polls is their assumptions about demographics of voters.
And yes, my discussion of polling error was oversimplified, but I was mainly just trying to explain what I meant about having to treat something as random if it’s theoretically predictable given enough information.
EDIT: Hold on; I don’t think 538 does include error bars for their probabilities. They have error bars for measurables like the vote share, but that’s normal. So I don’t understand what this argument is even about :)
But complaining that a model is incorrect because it enables arbitrage is a standard complaint, it's how you can prove all non-Bayesian models are irrational. That doesn't mean all Bayesian ones automatically pass the test though.
Error bars and spreads are already outside the Bayesian paradigm, which demands a single number.