Asher Meir points us to this article, “The geometry of decision-making in individuals and collectives,” by Vivek Sridhar, Liang Li, Dan Gorbonos, Máté Nagy, Bianca Schell, Timothy Sorochkin, Nir Gov, and Iain Couzin, which begins:
Choosing among spatially distributed options is a central challenge for animals, from deciding among alternative potential food sources or refuges to choosing with whom to associate. Using an integrated theoretical and experimental approach (employing immersive virtual reality), we consider the interplay between movement and vectorial integration during decision-making regarding two, or more, options in space. In computational models of this process, we reveal the occurrence of spontaneous and abrupt “critical” transitions (associated with specific geometrical relationships) whereby organisms spontaneously switch from averaging vectorial information among, to suddenly excluding one among, the remaining options. This bifurcation process repeats until only one option—the one ultimately selected—remains. Thus, we predict that the brain repeatedly breaks multichoice decisions into a series of binary decisions in space–time. Experiments with fruit flies, desert locusts, and larval zebrafish reveal that they exhibit these same bifurcations, demonstrating that across taxa and ecological contexts, there exist fundamental geometric principles that are essential to explain how, and why, animals move the way they do.
I’m kinda skeptical of this whole “critical transitions” thing, but the idea of modeling how animals move, that’s cool. So I think we should be able to take the basic model of the paper while not believing all this geometry and physics-analogy stuff.
In any case, Meir makes an interesting connection to social science:
Human beings were also animals. So there is good reason to believe that these findings have relevance for the study of human decision making. The paradigm is a lot different than “continuously act to globally maximize the discounted expected value of some stable single-valued intertemporal function of all world outcomes” and not very easy to reconcile with it. You know where my money is.
This seems related two of our posts:
From 2012: Thinking like a statistician (continuously) rather than like a civilian (discretely)
From 2022: The psychology of thinking discretely
The story here is that I think continuously, and lots of real-world data show continuous variation, but lots of people, including many scientists, think discretely. It does seem to me that discrete thinking is the norm, even in settings where no discrete decision making is required.
I guess this is consistent with the above-linked paper, in that if animals (including humans) use discrete decision rules about how to move, so then it makes sense for us to think discretely, and then we think that way even when it’s counterproductive.
I don’t see the difficulty.
First, these are decisions between equally attractive targets.
Imagine you start out equally distant from two posts with some bills of unknown denomination stapled to them. The best thing to do is walk towards the center until you can see if one post is a $100 bill but the other is a $1 bill, then obviously turn towards the one you percieve to be higher.
But if after a certain point you become confident that the two bills are equal, you would just arbitrarily turn towards one or the other.
Then lets say there are 4 equally distant posts, you’d walk towards the center of all to see if you could tell whether any pair was going to be higher value, and if they seem equal turn towards one pair. Then as you approach that pair there will be a point you decide those options are both equal, so arbitrarily head towards one target.
And if you figured out all options are always equally attractive, then the optimal trajectory is to simply pick one and head right towards it. That is the shortest path.
Now what if you have non-symmetric targets? Eg, use different denomination bills and decorate the posts to appear more or less attractive or camouflaging of the bills.
Also add a “predator” that observes your current/previous trajectories and guesses a time/place to intercept you. Now there is incentive to move more unpredictably rather than only minimizing the path length and reward.
I’d also like to see it applied to retrieving rewards from targets and bringing them back to a “home base”. Now, while retrieving one target you might get a better look at the quantity/quality of other targets in that area. So rather than returning home then heading out towards the next closest target (to home), the optimal decision may sometimes be return to where you got that last reward and grab the sure thing nearby.
This makes me wonder whether decision trees are a better algorithm for approximating the way the human brain works than are neural nets.
I don’t understand what you mean. Empirically, neural networks can be trained to function as decision trees (or as anything which has a detectable pattern); decision trees cannot be trained to function as neural networks.
A neural net doesn’t look like a decision tree to me though perhaps it can be trained to function the same way (perhaps I am wrong to make a distinction there). But a decision tree clearly breaks a problem into a series of binary decisions which seems to match the way the quoted statement describes animal decisions. Also, to the extent that is a way of making complex decisions, it has the potential problem that simple decision trees have – the order can easily be suboptimal (presumably evolution prevents this in animal behavior, but I’m not too sure about human decisions such as what stock to invest in, whether a new medical treatment is more effective than an alternative, etc.).
But how are various animals “experiencing” these decision making moments? Is there a point along the evolutionary path where simply responding to external stimuli according to a genetically programmed pattern gives way to a “contemplative moment”, like when a human touches his finger to his chin and thinks “hmmmm”?
Rats? Dogs maybe?
I find the data in the supplemental materials really interesting. In the main paper, I believe they dropped the individuals that went directly to one target. In the supplemental materials, they show the heterogeneity within and across species. Really neat to see how some individuals consistently make immediate snap judgements, while others do the bifurcation stuff, and still others wander.
This is a top-notch paper imo.
I played with the basic idea a bit without looking carefully at what they did. For only two targets, it was not difficult to reproduce the results without including any threshold (the bifurcation emerges automatically). But three is interesting.
Basically I treated the trajectory as a markov chain where every pixel has some expected reward value sampled from a normal distribution with sd proportional to the distance. Where there is a target (a single pixel) the mean is some relatively large value, where there is none it is zero. Then I also penalized for distance by dividing by distance^2 (this worked much better for some reason). Each step simply moves 1 pixel in the direction of the highest expected value pixel for that step.
Ie, expected reward is proportional to the actual reward at the target and inversely proportional to distance to target. Then uncertainty about reward is also proportional to distance to target. Random zero-value pixels can also appear to be a target for any given step.
After some dark magic with the parameters, I was able to get a small proportion (~5%) of double bifurcations but nothing near ~50% like they see. Most go directly to the center target or split off towards one of the side targets once close enough for the target reward to overcome the “noise”.
I don’t see why you’re automatically skeptical of the geometry. They measure animals’ decision-making by tracking them in space and seeing where they’re swimming, so it’s just geometry in real physical space. And if one is skeptical of the geometry, I don’t see how one can like the paper as a whole, given that so much relies on it.
I haven’t read the paper but quickly looking, this seems great, and certainly fascinating. There is, by the way, an explosion of wonderful work on what some like to call the “physics of behavior” — looking for rules that explain collective phenomena of large groups, or social interactions between small numbers of agents. This has always existed, but now there’s a lot of actual data, giving the field a lot more depth rather than it being a collection of toy models. Whether the connections to physics are meaningful is an interesting question — is it that (i) it involves phenomena analogous to things that arise in traditionally defined physics, (ii) physics *is* the study of emergent patterns and processes from underlying rules and interactions, (iii) physics is defined as what physicists do, and a fair number of people studying this sort of thing are physicists, (iv) some combination of the above, (v) none of the above. My vote is for (ii), but it’s a tough question.
Your correspondent’s “Human beings were also animals” should be “Human beings are also animals”, though!
It seems like an argument for modeling decision making under local knowledge (a specific case of partial knowledge) rather than under infinite knowledge. In my personal experience, people desperately underestimate the importance of stopping rules for data collection.
What I found interesting is that Andrew believes that ‘most people are like this’ and yet he does not. That kind of exceptionalism draws attention, and raises questions. If most people follow the ‘animal model’ and Andrew doesn’t, why and how? We can dissect some options. Maybe people don’t. Maybe he does. Maybe he doesn’t because of some training and practice, or something in his genetics, that most people don’t have. Maybe it works in a very specific academic environment but would be bad for most people. Or maybe it would be good for everybody but they are suffering for lack of … genetics or practice or whatever else.
This also raised my own metacognition. I’m a multi-model thinker through long practice. I come at problems with a specific bent and sometimes it is helpful, but generally its a ton of mental work. I started with a capacity and inclination towards mental work; and other liabilities. Most people seem to assign their effort in other areas and get good payoff for it. So maybe I’m like Andrew in using a mental strategy that isn’t common? I’m certainly open to that possibility, and it explains a certain division of labor in various settings.
It also suggests that the ‘animal spirits’ approach to the mental process isn’t quite hardwired and that the model they have developed around ‘spatial’ reasoning just captures the unconscious application of heuristics under incomplete knowledge with progressive learning.
Reminds me of Hick’s (1952) original account of what came to be known as Hick’s law (or the Hick-Hyman law): That the logarithmic relationship between entropy and response time resulted from a series of binary decisions.
Interesting. But one thing I was unable to find in it was the effect of the field of vision. If I see two desirable objects in the distance, I can head towards a point intermediate between them. But at some point, I cannot look at both of them at the same time. That’s a good time to pick one and head toward it. Such behavior matches some of the figures.
I find it hard to travel (walk, row, bicycle, or drive) without looking where I am going. I suspect that is also true for little animals.
Bob76