Comments
These results are super interesting! Thanks for writing and sharing! (I happened to have already read a bunch of the original papers you're summarizing, and some of your work, too.)
By the way, I think you can capture common intuitions against fanaticism and dependence on unaffected things with a multi-step procedure:
- Ignore anything unaffected between your options,[1] and keep only the remaining differences between options.
- Use some method that's not fanatical with respect to the remaining differences between options, e.g. the expected value of a bounded function of the differences.
However, this means violating stochastic dominance with respect to outcomes, and the approach might seem ad hoc. While these do count against the approach in my mind, I don't think they rule it out decisively, because the approach seems to match other intuitions of mine so well otherwise. So, I give a decent amount of weight to something like this approach under normative uncertainty. I also give some weight to fanatical views, of course, too.
I discuss these ideas a bit in this post, but kind of scattered across the subsections of this section.
- ^
Either just pairwise, dealing with pairwise comparisons first, or across all of them together at the same time.
I don't have a big issue with much of this philosophically, I'm just extremely skeptical about the validity of most small percentages.
My intuition is that small percentages are often greatly overestimated, therefore giving far higher expected values then is really the case. My inclinations is that where uncertainty is greater, numbers are often exaggerated. Examples where I have this intuition is in animal welfare and existential risk. This seems like it should be testable in some cases. Although it might seem like a strange thing to say, I think conservative small percentages are often not conservative enough.
Often I think that pascall's mugging is a mugging as much because the "low" probability stated is actually far higher than reality, than just because the probability is low persay.
I don't have any data to back this up, obviously we overweight many low probabilities psychologically, things like probability of aeroplane crashes and I feel like its the same in calculations. This has almost certainly. been written about before on the forum or in published papers, but I couldn't find it on a quick look.
I am also skeptical of small percentages but more so because I think that the kinds of probability estimates that are close to 0 or 1 tend to be a lot more uncertain (perhaps because they’re based on rare or unprecedented events that have only been observed a few times).
I’m no statistician, but I’m not sure that we can say that small percentages tend to be exaggerated though… For one, I recall reading in Superforecasters that there’s evidence that people tend to underestimate the likelihood of rare events and overestimate the likelihood of common ones in forecasting exercises, so that’s an piece of evidence pointing towards small probabilities generally being too low rather than too high. Secondly, a low probability can equally be framed as a high probability of that event not happening. So in short - I agree that probability estimates that are close to 0 or 1 tend to be less certain, but not that probability estimates close to 0 tend to be overestimates any more than underestimates