Tuesday, November 6, 2018

Noise and collective behaviour

"You should never do anything random!", Michael Osborne told the room at large for the umpteenth time during my PhD. Mike, now an Associate Professor at Oxford, is still telling anyone who will listen about the evils of using random numbers in machine learning algorithms. He contends that for any algorithm that makes decisions at random, there is a better algorithm that makes those decisions according to some non-random criterion.
Having seen this debate sporadically erupt over a decade or so has burned the issue of random decision making deep into my psyche, where it has lurked until I recently had reason to think a bit more deeply about the use of random decision making in my own research area: modelling animal behaviour.

Many models of animal behaviour make use of random decisions, or 'noise'. For example, an animal may choose a new direction in which to move by averaging the current directions of the other individuals around itself, and then add some random error to that average to give its own new direction. But why should an animal do something random? Surely there is a 'best' action to be taken based on what the animal knows, and it should do this. Indeed, how would an animal do something random? It is remarkably difficult for humans to write down 'random' series of numbers without the aid of a random number generator, such as a coin or a dice. If you were asked to pick one of two options with a probability of 0.65, how would you do it? Why should an animal be any different?

Usually when we ascribe noise to animal or human decisions, what we are really doing is modelling that part of the decision that we either don't understand, or that we choose to ignore. For example, in a recent paper my coauthors and I looked at factors influencing neighbourhood choice in Stockholm. We modelled choices as being influenced by the characteristics of the moving household and the neighbourhoods they were choosing from, but ultimately being probabilistic - i.e. random. As we say in the paper, this is equivalent to assuming that the households are influenced by many other factors that we don't observe, and that they make the best choice given all this extra information. Because we don't see everything that influences the decision, it appears 'noisy' to us.

So far, so good. This is fundamentally no more controversial than treating a coin toss as random, even though we know that the coin is obeying deterministic physical rules. As long as we use a decent model for the stochasticity in these decisions, we can happily treat what are really deterministic decisions as being random, and still make solid inferences about what influenced them. But we can run into trouble when we forget that only we are playing this trick. This becomes a problem in the world of collective behaviour, where we want to understand how animals are influencing and being influenced by each other. Though we might treat individual animals' decisions as being partly random, we cannot guarantee that the animals themselves also do the same thing. Indeed, it is likely that the animals themselves have a better idea about what factors motivate and influence each other than we do. Where we might, in our ignorance, see a random action, another animal might well see a response to some cue that we haven't thought to look for.

To illustrate, lets imagine that you and I are trying to choose a restaurant. For the purposes of simplicity I will assume that we like very much the same things in a restaurant - we have the same tastes in food and ambience. We approach two seemingly similar-looking restaurants, A and B. I can smell that the food in restaurant A smells somewhat more appetising than in B. Nonetheless, I see you starting to walk in the direction of restaurant B. I know we can both smell that the food in A is better, so what should I make of your decision? If I assume your decision is partly random, I might just assume you made a mistake - A really is better, but you randomly picked B instead. I am then free to pick A. But if I assume you made the best choice with the information available, I must conclude that you have some private information that outweighs the information we share - maybe you earlier read an excellent review of restaurant B. Since our tastes are very similar, I should also conclude that if I had access to your private information as well, I would have made the same choice, since the choice is determined exactly by the information. So now I really ought to pick restaurant B as well.
This place looked great on the web...
[Kyle Moore, CC-SA 1.0]
Looking at collective decision making this way shows that how individuals should respond to each other depends on how much they ascribe the choices made by others to random chance, not how much we do. We therefore need to be careful not to assume that 'noise' in the behaviour of animals in groups is an intrinsic property of the decisions, but instead remember that it depends on choices we make in deciding what to measure, and what to care about. The animals themselves may make very different choices. The consequences of adopting this viewpoint are laid out in detail in my recent paper: Collective decision making by rational individuals. In short they are:

1. The order in which previous decisions have been made is crucial in determining what the next individual will do - the most recent decisions are the most important.

2. Because of the above, how animals appear to interact depends strongly on what we choose to measure. Social information isn't something we can measure in a model-free, neutral way.

3. Group behaviour should change predictably when we observe animals (or humans) in their natural habitat versus the laboratory. In general, social behaviour will probably be stronger in the lab.

None of this is to say that animals or humans always (or ever) do behave rationally. Rather, that they make decisions on the basis of reasons, not the roll of a dice. And their reaction to the choices made by others will be shaped by what they perceive those reasons to be in other individuals. Perhaps, to paraphrase Michael Osborne, we should never assume that other people or animals are doing anything random. Or at least we shouldn't assume that other people are assuming that.........

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