Thanks!
Kevin Dorst
Karma: 440
Thanks for the thoughtful reply! Cross-posting the reply I wrote on Substack as well:
I like the objection, and am generally very sympathetic to the “rationality ≈ doing the best you can, given your values/beliefs/constraints” idea, so I see where you’re coming from. I think there are two places I’d push back on in this particular case.
1) To my knowledge, most of these studies don’t use incentive-compatible mechanisms for eliciting intervals. This is something authors of the studies sometimes worry about—Don Moore et al talk about it as a concern in the summary piece I linked to. I think this MAY link to general theoretical difficulties with getting incentive-compatible scoring rules for interval-valued estimates (this is a known problem for imprecise probabilities, eg https://www.cmu.edu/dietrich/philosophy/docs/seidenfeld/Forecasting%20with%20Imprecise%20Probabilities.pdf . I’m not totally sure, but I think it might also apply in this case). The challenge they run into for eliciting particular intervals is that if they reward accuracy, that’ll just incentivize people to widen their intervals. If they reward narrower intervals, great—but how much to incentivize? (Too much, and they’ll narrow their intervals more than they would otherwise.) We could try to reward people for being calibrated OVERALL—so that they get rewarded the closer they are to having 90% of their intervals contain the true value. But the best strategy in response to that is (if you’re giving 10 total intervals) to give 9 trivial intervals (“between 0 and ∞”) that’ll definitely contain the true value, and 1 ridiculous one (“the population of the UK is between 1–2 million”) that definitely won’t.
Maybe there’s another way to incentivize interval-estimation correctly (in which case we should definitely run studies with that method!), but as far as I know this hasn’t been done. So at least in most of the studies that are finding “overprecision”, it’s really not clear that it’s in the participants’ interest to give properly calibrated intervals.
2) Suppose we fix that, and still find that people are overprecise. While I agree that that would be evidence that people are locally being irrational (they’re not best-responding to their situation), there’s still a sense in which the explanation could be *rationalizing*, in the sense of making-sense of why they make this mistake. This is sort of a generic point that it’s hard (and often suboptimal to try!) to fine-tune your behavior to every specific circumstance. If you have a pre-loaded (and largely unconscious) strategy for giving intervals that trades off accuracy and informativity, then it may not be worth the cognitive cost to try to change that to this circumstance because of the (small!) incentives the experimenters are giving you.
An analogy I sometimes use is the Stroop task: you’re told to name the color of the word, not read it, as fast as possible. Of course, when “red” appears in black letters, there’s clearly a mistake made when you say ‘red’, but at the same time we can’t infer from this any broader story about irrationality, since it’s overall good for you to be disposed to automatically and quickly read words when you see them.
Of course, then we get into hard questions about whether it’s suboptimal that in everyday life people automatically do this accuracy/informativity thing, rather than consciously separate out the task of (1) forming a confidence interval/probability, and then (2) forming a guess on that basis. And I agree it’s a challenge for any account on these lines to explain how it could make sense for a cognitive system to smoosh these things together, rather than keeping them consciously separable. We’re actually working on a project along these lines for when cognitive limited agents might be more advantaged by guessing in this way, but I agree it’s a good challenge!
What do you think?
Crossposting from Substack:
Super interesting!
I like the strategy, though (from my experience) I do think it might be a big ask for at least online experimental subjects to track what’s going on. But there are also ways in which that’s a virtue—if you just tell them that there are no (good) ways to game the system, they’ll probably mostly trust you and not bother to try to figure it out. So something like that might indeed work! I don’t know exactly what calibration folks have tried in this domain, so will have to dig into it more. But it definitely seems like there should be SOME sensible way (along these lines, or otherwise) of incentivizing giving their true 90% intervals—and a theory like the one we sketched would predict that that should make a difference (or: if it doesn’t, it’s definitely a failure of at least local rationality).
On the second point, I think we’re agreed! I’d definitely like to work out more of a theory for when we should expect rational people to switch from guessing to other forms of estimates. We definitely don’t have that yet, so it’s a good challenge. I’ll take that as motivation for developing that more!