Virtual governors and Arrow's impossibility theorem

Arrow’s impossibility theorem is a foundational result in the field of social choice theory that says that a social choice can be rational or it can be democratic, but not both. If you want a rational social choice, it has to be dictatorial.

Obviously, Arrow’s impossibility theorem is a surprising and downright counterintuitive result. While democracies do struggle to make rational decisions, dictatorships often seem much more irrational—launching wars, starving the populace, etc. It’s also hard to understand why democratic decision-making can’t be rational. Surely there’s a chance of rational decision-making.

The literature on Arrow’s impossibility theorem is voluminous and discusses, attacks, extends, generalizes, and modifies the theorem from every possible angle. A general conclusion is that group utility functions do not exist: If we know what I want, and we know what you want, we do not know what we want.

But this finding is in apparent tension with the idea that the price system creates a shared model among the members of the economy. In equilibrium, people agree on everything, and make choices as a collective by only choosing plans that are consistent with the plans chosen by everyone else. The result is rational collective decision-making. How is this consistent with Arrow’s impossibility theorem?

A possible solution is to relax the implicit assumption that the dictator is a human being. Traditionally, dictators are people—tyrants like Hitler and Pol Pot. But in social choice theory, a dictator is just whatever entity determines the group decision. That could be a human, or it could be some other kind of unconventional intelligence.

All intelligences are collective intelligences. They’re put together out of parts, assembled or constructed by some process, such as morphogenesis. This means that a dictator could actually be constructed by the people whom the dictator “rules”: the members of the collective can create the governing entity that makes rational decisions for the group. And rather than ruling by fear and force, the dictator could rule by self-interest, controlling the group by managing the energy landscapes of the members of the collective so that they naturally do what the dictator wants—in which case the dictator only commands the group to the extent that it successfully renders their plans mutually compatible, such that all the individual plans of the members of the group can be seen as parts of one greater plan.

Norbert Wiener, the originator of cybernetics, called such governing systems virtual governors because they control the group without really having a material form in the ordinary sense. They’re entirely real, of course, albeit as a pattern in a system of signals, but we only notice them by their coordinating effects on the members of the group. The members of the group may not even perceive the existence of the virtual governor apart from the signals they personally interact with.

Probably the best known example of a virtual governor is the price system. The price system exists as a set of signals, one that is constructed entirely by the activities of the members of the economy, i.e,. people. In this sense, the price system has no existence separate from the people who create it, and it exists as a kind of conversation between their preferences and information to find a mutually agreeable solution for all. At the same time, the price system functions as the economy’s dictator, with the actions of all of the members of the economy serving as elements of the price system’s singular overarching plan.

Of course, this dictator that is the price system rules not through fear and force but by manipulating the signals that the members of the economcan access, i.e., the prices, so that when each economic agent acts to fulfill their own plans, they also inadvertently act to fulfill the plan of the price system.

In our paper on cognitive glues as price systems, Mike Levin and I point out that the price system itself can be seen as a rational agent, as a dictator must be. The goal of the price system is to be an accurate and rational model of the relative scarcities of the goods and services for sale in the economy, and it pursues these goals intelligently by incentivizing agents to improve its accuracy and rationality when they place trades to exploit arbitrage opportunities that correct flaws in the price system. Not only does this show that virtual governors really are rational agents in their own right and therefore viable dictators, but it also shows that the dictator only functions well by inviting corrections from the members of the collective who are “ruled” by the dictator. When the dictator’s plan is a bad one, the members of the collective do not have to go along with it, and they will not go along with it; instead, they will correct and improve the plan by placing trades that exploit arbitrage opportunities.