Constructing a dictator
The boring mathematical kind of dictator
Arrow’s impossibility theorem says that a social choice can be rational or it can be democratic, but not both. If you want the social choice to be rational, then it has to be dictatorial. This theorem is a foundational result in social choice theory and has spawned a large literature aimed at trying to figure out what’s going on. Why can’t democracy be rational? Why is dictatorship necessary? How come in real life democracies seem a lot more rational than dictatorships?
Arrow’s theorem was originally meant to describe voting systems, but it generalizes to collective decisions in other contexts [1] [2]. This is really weird because the math is airtight, yet what it seems to be telling us contradicts our own experiences. When a group of people are making a social choice about where to go for lunch, they don’t need a dictatorship to make a rational decision. So is the math wrong, or are our observations misleading?
Arrow’s theorem provides what appears to be a genuine contradict between theorem and empiricism. A proof has primacy in math; observation has primacy in science; science and math ought to go together, yet what we observe contradicts what has been proven. So what gives?
The solution lies in realizing that the dictator doesn’t have to be a person. The dictator can be any system that engenders a rational choice as an economic agent, regardless of how it’s physically embodied. And while the dictator by definition gets what they want, they don’t have to achieve their goals by force. Indeed, the most realistic explanation for how groups make rational decisions isn’t that they submit to a dictator but that they construct one via their interactions with each other.
For intuition about this weird-sounding idea, one way of thinking about human behavior is that individual human behavior is caused by the decisions of a kind of dictator called an internal model. If people as individuals just do whatever a model tells them to, then it stands to reason that if people share a model, then they’ll end up obeying the same model as a group. In other words, people with a shared model will make collective decisions. If that model is rational (internally consistent), then their behavior will be consistent with each other, i.e., their plans will be mutually compatible, and therefore the collective decision or social choice is rational.
In order for people to form a shared model, they need some kind of communication system that keeps them constantly communicating true, relevant information to each other such that the connections between them model the relevant variables. (Such a communication system is called a cognitive glue.) Because the resulting model is very accurate, people will find that it’s in their own self-interest to do as the model predicts, which from a certain perspective will look like doing what the model tells them to. But in this case, if someone doesn’t like what the model is telling them to do, they just don’t have to do it!
In fact, being able to disobey the model is crucial for making it work well. When people disagree with the model, that makes the model realize it’s doing something wrong and update to be more accurate. So this model, the dictator, ends up being constructed out of people’s behavior.
The classic example of a constructed shared model that functions as a social choice dictator that is updated by disobedience is the price system. The price system is a dictator in the sense that it makes all social choices as to how scarce resources are allocated. When the price system is sufficiently complete and consistent, all that self-interested people need to do to maximize their own utility is to follow the instructions of the price system as laid out to them by following the prices—i.e., buy low, sell high. The price system doesn’t tell people what to do in the usual sense but instead serves as an accurate shared model so that people find it useful to do what it says. And the price system is constructed by its subjects instead of conquering them, in particular updating its prices whenever people don’t do what it wants until people do do what it wants, i.e., until it’s an accurate shared model so that people find it more preferable to do what it wants rather than doing anything else.
The term “dictator” in social choice theory has caused a good degree of mischief by making people think that it means humans ruling with violence instead of models persuading with good predictions. A better term for labeling the kind of dictator described in this essay is “virtual governor”, taken from Norbert Wiener’s Cybernetics. The price system, for example, governs in the sense of controlling the allocation of scarce resources with prices but is virtual in the sense that it exists as the relationships between people that form a distributed consensus rather than being what we usually recognize as an entity in our environment with a familiar kind of physical body and form.