Chaotic Foundations: Chaos in Markets

This article discusses why markets are stable, but notes that there is still significant and important chaos in markets.

A chaotic system is, formally, a dynamical system which is highly sensitive to its initial conditions.

A dynamical system is a stupid term which means what the term dynamic system means etymologically, but scientists wanted to confuse us so they call it a dynamical system instead.

A dynamical system is, formally, a system in which a fixed rule (also called a function, in the mathematical sense) describes the time dependence of a point in a geometrical space.

Be sure to read the stupid definition page for the stupid term.

In real life, a dynamical system is a dynamic system and is usually called that. In turn, a dynamic system is a system which changes over time. In real life, it is not that the geographic space output depends on time, it is that any output depends on time.

Hilariously, chaotic systems are usually thought of in the literature as fully deterministic system. In common language, of course, this is the opposite of what a chaotic system means. Nonetheless, the term chaotic is employed due to their extreme sensitivity to initial conditions. These systems are so wildly divergent that their determinism does not allow for predictable behavior. So there is common ground in the academic language and the common language due to the lack of predictable behavior regarding the system.

Markets are also complex systems and adaptive systems. They are complex adaptive systems. They are adaptive in that the individual and collective behavior mutate and self-organize corresponding to the change-initiating micro-event or collection of events.

The Kicker

The kicker is that economies are aggregated entities which are stable, but they are built on chaotic foundations. The individual decision of the individual actor is a chaotic output. I will describe why now:

  • An individual reaches a decision based on their predicate knowledge. That is, their collection of suppositions regarding the matter at hand.
  • A single changed belief alters the entire predicate knowledge structure.
  • While the economic idea of Free Information, along with the philosophical counterpart idea of omniscience, can both reconcile the Chaotic Knowledge Problem, they cannot deal with the One Bad Idea Problem.
  • The One Bad Idea Problem (OBIP) is a form of the Chaotic Knowledge Problem (CKP) which current economics is not prepared to deal with. It implies that a society of little information can be better off than a society with near omnipotence. It flies in the face of the idea of Free Information leading to ideal optimization.

The Free Market

The immature understanding of free market economics is that proponents want to create a free market and, once achieved, everything will fall into place. All we need to do is strive to achieve a set of basic structural characteristics, such as the conditions for perfect competition, or these other conditions, and we will be good to go.

The free market antagonist or skeptic will then easily retort that such basic structural characteristics are literally impossible to achieve in practice. Usually they are right. Free information, for example, is certain to never exist by virtue of the human condition.

Unfortunately for the free market antagonist, there is not a sophisticated free market thinker around who thinks in such a way. The sophisticated student of free market economics realizes that an economy is a self-correcting process which already acts according to free market principals. It is not the case that we need to do anything to create a free market, such as setting those initial conditions, or that we even should. The moral argument for free markets is entirely separate, and the conditions are self-emergent.

The free market student holds two essential facts as true:

  1. The efficiency of a market increases as the market approaches congruence with a free market.
  2. Markets automatically self-seek maximum efficiency in the long run.

These facts occur not by preference, but by necessary economic law, which is a kind of natural law, like gravity. Supposedly, these two facts demonstrate that a market adapts to become a free market of its own volition, for efficiency reasons.

Separately, many economists advocate that we should also prefer to maximize efficiency, because maximum efficiency results in maximum utility, but this moral argument is entirely separate from the descriptive endeavor of economics.

The One Bad Idea Problem

Picture three actors. One can grow and sell apples, while two others can buy and eat apples. The eaters have enough money to eat as much as they want. The seller is trying to sell to them. Should they bite?

The first eater knows that these apples are poisonous, but doesn’t know anything else about apples. The second eater knows that apples are red, tasty, grow in regions with clay soil and average rainfall, cost about 50 cents each and provide about 150 calories each.

Clearly, the second eater is much better informed. Yet the first eater chooses not to eat and the second eater chooses to eat, then dies. There was ultimately only one idea which made the difference.

Belief systems, and the decision-making systems which they help determine, are therefore chaotic. It is first true that a single missing or altered belief can lead to radically different decisions or preferences, and in the next place it is also true that a significantly uninformed actor can achieve superior efficiency when compared to a near omniscient actor if they have the right kind of information.

Consider this on a market level. If the eaters were markets instead of individuals, the second eater market would usually be said to have more free information. It becomes apparent that the common conception of information in markets is false. The idea that omniscience allows perfect choice is true, but even slight deviation from omniscience can send us to a worse off position than if we only had one correct and appropriate belief.

This is a problem for the sophisticate free market economic thinker, because the sophisticate realizes that economics is a process, not a series of policies designed to create some desirable end, because the free market is actually unattainable.

The sophisticate would not say that we must have perfectly free information to achieve a perfect allocation, but would instead claim that a market with more free information produces a more perfect allocation. Unfortunately, the One Bad Idea Problem introduces an “information trap,” in which we can obtain more information, but it can reduce efficiency because it is the wrong kind of information.

This is essentially a “Strong Problem of Information Asymmetry.” Information asymmetry is well known as a cause of adverse selection, but in a classic asymmetric information problem it is the party with more information who is presumed better off, which is consistent with the usual idea that more information can cure the problem. In this case, an infinite amount of information will not cure the problem if it is the wrong kind of information. In this strong case, an actor who is 1 belief less than omniscient can be worse off than an actor who is 1 belief better than perfectly ignorant. This strong case is interesting because it points out that

Reinforcing this problem, there is empirical evidence that social structures and markets do have structurally selective systems of belief. These may in part be reflected in a society’s culture, institutional beliefs and leadership. In a structurally selective system of belief, signaling and screening games equilibrium fail to constitute points of efficient information because actors can sincerely and honestly communicate regarding and come to agreement on a common piece of information – which is nonetheless completely objectively wrong. In other words, they will efficiently communicate and agree to something which is objectively wrong, rendering the whole market in trouble. Efficient communication is not the same as efficient information.

The Solution

I think there are two solutions.

First, we should admit that more information is not always better. Individual actors, and the economies they constitute, are not better off by having more information. They are not even better off by having more true information, although that’s a step in the right direction. Individuals and economies are better off by having more true and appropriate information. There is such a thing a genuinely bad information, which is not limited to information which is untrue. Digging into the deep parts of what appropriate information means is something not only deserving of its own post, but perhaps its own book. In short,

Secondly, we can make a probabilistic or associative argument. Instead of saying that marginally more free information causes a marginally better economy, we can say that marginally more free information sometimes causes a marginally better economy, but never causes a worsened economy. Therefore, free information is sometimes causal of a better economy; that is, when the free information is also appropriate. By virtue of being sometimes causal, it is always partly explanatory, always probabilistically causal and/or always associated with a marginally better economy. While we may not know the level of this probability yet, it could be estimated, and the direction is certainly positive, even if small.

The only concern might be if the size was infinitesimal, but the very same empirical data which attests to the improvement to economies by technology may be used to indicate that there is some contribution by free information which is greater than infinitesimal.

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