Nice point! I think I’d say where the critique bites is in the assumption that you’re trying to maximize the expectation of q_i. We could care about the variance as well, but once we start listing the things we care about—chance of publishing many papers, chance of going into academia, etc—then it looks like we can rephrase it as a more-complicated expectation-maximizing problem. Let U be the utility function capturing the balance of these other desired traits; it seems like the selectors might just try to maximize E(U_i).
Of course, that’s abstract enough that it’s a bit hard to say what it’ll look like. But whenever is an expectation-maximizing game the same dynamics will apply: those with more uncertain signals will stay closer to your prior estimates. So I think the same dynamics might emerge. But I’m not totally sure (and it’ll no doubt depend on how exactly we incorporate the other parameters), so your point is well-taken! Will think about this. Thanks!
Nice point! I think I’d say where the critique bites is in the assumption that you’re trying to maximize the expectation of q_i. We could care about the variance as well, but once we start listing the things we care about—chance of publishing many papers, chance of going into academia, etc—then it looks like we can rephrase it as a more-complicated expectation-maximizing problem. Let U be the utility function capturing the balance of these other desired traits; it seems like the selectors might just try to maximize E(U_i).
Of course, that’s abstract enough that it’s a bit hard to say what it’ll look like. But whenever is an expectation-maximizing game the same dynamics will apply: those with more uncertain signals will stay closer to your prior estimates. So I think the same dynamics might emerge. But I’m not totally sure (and it’ll no doubt depend on how exactly we incorporate the other parameters), so your point is well-taken! Will think about this. Thanks!