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Culture War Roundup for the week of December 18, 2023

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There is some deep epistemological stuff operating here.

If the complaint is that numbers are too "precise", and the solution is to add ranges (whether implicit or explicit), the obvious next question is what these ranges mean.

In formal Bayesian epistemology, there are no "error bars" around probability estimates. The probability estimate is simply the probability you believe X will occur, which can be computed using Bayes formula and a prior probability in simple cases (more complicated cases yield more complicated formulas).

In less Bayesian epistemology, you can recapture much of this using something like proper scoring rules, but, again, a scoring rule only asks for a number - not a range, so it's still unclear what it even means to say "somewhere between 10% and 30%".

In human language, you might want to say something like "I'm saying 20%, but that's because I've consulted the important evidence, but I know there is smaller evidence I'm not considering that might tweak that ±10pp." In this case, you are using error bars to indicate logical uncertainty.

Alternatively, there is a decent analogue in finance: market makers often have both buy and sell limit orders. The spread between them is an indicator of confidence. Note: in finance, the spread is useful only because finance is a fundamentally social endeavor. If you choose to offer a very small spread, what you're really doing is saying that you don't think anyone else can do better than you. [note: this is less true for non-market-makers, who, for binary instruments mostly just care about point estimates].

The financial framing has an obvious betting analogy here: when you say "between 10% and 30%" under this interpretation, you're actually saying is that you would accept a bet that X is true if the odds given were higher than 9:1 and that X is false if the odds were better than 7:3. If we wanted to formalize error bars on probability, this is the model I would advocate for.

[To be a tad pedantic, finance also cares about risk. If I'm market making, I might actually have multiple buy and sell limit orders with different volumes. Likewise, me saying "between 10% and 30%" might mean I'm willing to bet 1¢ at those odds, but it doesn't necessarily imply I'm willing to bet half my 401k.]

@Gillitrut