Real-world uncertainty is often not resolved by individual expected-value optimization but by population-level hedging that forms an equilibrium — as shown by ducks foraging in ratios matching resource distribution rather than all choosing the single best option.
Jordan uses a duck-foraging example to argue that good decision-making under uncertainty isn't a purely individual Bayesian calculation — real ducks hedge their foraging in proportions matching resource ratios, which is a Nash equilibrium at the population level. ✦ AI generated
Michael Jordan · Machine Learning Street Talk · 2026-05-20 · original ↗
starts at this moment · 71:55
“Why does the language model not really have any idea about its confidence?”
The actual ducks don't do that. They go to probably 2/3 to that side of the lake and one third to the other side. They're hedging... but they're actually getting the right ratio. And the explanation is that you weren't thinking about the context of this uncertainty — if they all have that same uncertainty, then they can sample with probability 2/3, and that's actually a Nash equilibrium of the bigger system.
verbatim transcript · starts at 71:55
71:55this a statistician duck. So it's kind of calculated that over the last year there tends to be you know twice as much grain on that side of the lake than on this side. 2:1 ratio. All right. So now the next day I I need to decide and the duck uh which side of the lake I go to and the the basian duck um who has those probabilities would then do the maximal
72:15expected value and they go to the left side of the lake with probability one because they're all right but the actual ducks don't do that. They go to probably 2/3 to that side of the lake and one third to the other side. They're hedging. Um but but it's not just a hedging thing. Hedging would just do occasionally going to the the other side of the lake. they're actually getting
72:31the right ratio. And and and so the explanation is that you weren't thinking about the context, right, of this uncertainty. Okay? It's not just you, the individual duck. Probably you evolved in a world where there are many ducks. And if all the ducks went to the same side of the lake, obviously you've missed out on a resource. And so is there an algorithm that allows many ducks to cooperate here? Um well, if
72:51they all have that same uncertainty, then they can sample with probability 2/3 and go to this side versus 1/3. And that's actually a Nash equilibrium of the bigger system. All right? Right. So the the right way to think about uncertainty there is that in the context of the population what should be how should I use my uncertainty. Another kind of uncertainty that's kind of the economic side. Another uncertainty in
73:10economics is the one I've alluded to information asymmetry. You know things I don't know and you have expertise I don't know about but we're going to work together and I'll maybe give you a contract a menu of options. Um but even if I interact with you for a while I still might not know. You'll there's things you're going to know that you're not going to give away to me and maybe
73:27you'll hedge you know you'll lie a little bit. So I I don't know about that. That'll never that's not just sampling. That's a different kind of uncertainty. Okay. And then finally there's what I like to call providence. You know that's more like a database kind of uncertainty. Um if you um if I want to do a medical operation and um you're a doctor and you look at the data
73:47for people like me uh here's the you know if you do the operation this way the probability of survival versus this and I look at that I say great but now you tell me oh that data was gathered 10 years ago. And I'm going to say, okay, my confidence interval should go up. All right. Well, classical statistics, you know, could talk about that. In fact, it' be I'd be more of a basian to