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New from me - Effective Aspersions: How the Nonlinear Investigation Went Wrong, a deep dive into the sequence of events I summarized here last week. It's much longer than my typical article and difficult to properly condense. Normally I would summarize things, but since I summarized events last time, I'll simply excerpt the beginning:
I'm getting incredibly sick of the "rationalist" affectation/verbal tic of "statistically" "quantifying" your predictions in contexts where this is completely meaningless.
"But I think it would still have over a 40% chance of irreparably harming your relationship with Drew"
"Nonlinear's threatening to sue Lightcone for Ben's post is completely unacceptable, decreases my sympathy for them by about 98%"
What it does mean to have a 40% chance of irreparably harming her relationship with Drew? Does that mean that there's a 60%, 70% etc. chance of it harming her relationship with Drew, but in a way that could be fixed, given enough time and effort? What information could she be presented with that would cause her to update her 40% prediction up or down?
The numbers are made up and the expressions of confidence don't matter. It's just cargo cult bullshit, applying a thin veneer of "logic" and "precision" to a completely intuitive gut feeling of the kind everyone has all the time.
I disagree. Even if the numbers are somewhat made up, having a ballpark figure that tells you the relative probability of certain events that would result from a decision you’re planning to make.
Going to the Drew example, if I think that doing something (say going to school in another city and trying to have a LDR is going to result in a 40% chance that I’ll lose the relationship entirely, and a 60% chance that I’ll damage it in away that would be difficult but not impossible to fix, then I can use that to decide if that would be more important to me than the job opportunities, the scholarships, or whatever else I gain from going to school away from him. Might doesn’t give you enough information for a true reality check imo, because it treats low probability events equally to large probability events. Even using verbal categories like low, medium and high probability, especially when making a group decision aren’t precise enough to communicate what I’m actually thinking. Low is how low? For you it might be 5%, for me it’s 20%. We can’t communicate that well if we don’t know what the terms are.
I think part of the point is the numerical values convey an unwarranted degree of precision based on the process that generated them. Say your estimate is 20% probability for X. Why not 21%? 19%? 25%? 15%? What's the size of the error term on your estimate? Is your forecasting of this outcome so good as to warrant a <1% margin? Of course, estimation of that error term itself has the same problems as generating the initial estimate.
I don't think this is a good objection. Numbers are often approximate. 20% means 'somewhere between 10% and 30%' as much as 'around a hundred pounds' might mean '75-125 pounds'. On the other hand, I usually think it's better to actually say what ideas and conditionals inform your judgement rather than just saying a number, and I'm not sure what the number adds to the former.
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
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