Thursday, October 21, 2010

And Now for Something Completely Different: The Fractal Nature of Human Cognition

Below is repost of a half-baked theory of human-managed systems that I developed in July of 2009.

The basic theory is that human beings are really "expectation machines" that compare what they experience to what they expect and adjust their state accordingly.  The function of the expectation machine includes hysteresis (positive feedback) to maintain the current state unless what is experienced deviates from expectations by too far a margin.  In cognitive science and behavioral economics, this hysteresis is known as cognitive bias, of which confirmation bias is but one example. (A good example of how hysteresis is used in electronic systems is the Schmitt Trigger.)  The amount of hysteresis applied to a given decision depends on the level of abstraction/uncertainty involved in the decision.  There's very little hysteresis applied in the decision of whether or not to eat something because that decision is usually based on feeling a physical need to eat something.  There's a LOT of hysteresis applied in speculative endeavors such as "investing" in the secondary bond and equity markets, which can give the impression of manic-depressive market behavior.

The two primary reasons why all mathematical models of economies will fail is: (1) they assume everybody is loaded with the same "expectation function" (e.g., that of utility theory or that of prospect theory) and (2) they model risk without properly considering the hysteresis (a form of memory) induced by uncertainty. 

The fact is, though, that the founders of the neoliberal schools of economics (Chicago and Austrian) knew that their mathematical models were bogus.  Otherwise, they would not have set up think tanks and similar institutions to bombard the public with neoliberal propaganda that shapes people's understanding of reality and, thus, shapes people's expectations.  They knew that economic decisions are not based solely on purely selfish interest but are influenced deeply by societal institutions.  At the end of the day, Mises, Friedman and Hayek were really institutionalist economists who hid behind false mathematical models to mask their neofeudal ideology as the new liberalism.

FYI -- Back in March, attempter (aka Russ) coined the phrase "fractal Walmartization" in a comment over at Naked Capitalism.  I thought it to be an apt description of what he observed, and it is consistent with my half-baked theory.

The Fractal Nature of Human Decision-Making
I spent some of this past weekend diving into George Soros’ The Alchemy of Finance, and I have developed some initial conclusions that I think are interesting.

Before getting into the details of my exploration, I should explain why I’m bothering with Soros at all.

I initially embarked on my present journey by studying the works of philosophers such as Popper, Arendt, and Marx, which led me quickly to other philosophers (e.g., Plato, Hegel, Kant, Smith, Hume, etc.) and economists, which I now call “applied philosophers” (I can’t call them scientists). One of the things that struck me about philosophers is that many of them start out to understand the world only later to shift towards changing the world. They start out by describing the world as they see it (something I viewed as the “descriptive function”) and then turn to prescribing the world as they believe it ought to be (something I viewed as the “prescriptive function”). Marx, a philosopher and applied philosopher rolled into one man, was a perfect example of this tendency. Ayn Rand was another. By comparing what many of these luminaries had to say about the way the world works to empirical evidence to the contrary, I noticed major discrepancies and came to realize that all human beings tend to interpret life rather than experience it, subconsciously applying their “Useful Fictions” and confirmation bias in real time to filter events to shape their understanding of the world.

As the study of philosophy led me to study economics, I ran across Soros’ latest book, which discusses the causes of the current economic upheaval. In that book, he talks about his model of human behavior (he studied under Popper), which was remarkably similar to mine. What I call “Useful Fictions” he calls “Frutiful Fallacies.” What I call the “descriptive function” appeared to be the same as what he calls the “cognitive function.” What I call the “prescriptive function” appeared to be the same as what he calls the “manipulative function.” What he introduced that was different was reflexivity. While reflexivity is similar to confirmation bias, it is actually quite different, at least definitionally. Reflexivity is based on the observation that participants in a market affect the operation of the market and can do so in a manner that makes the market somewhat different than what the participant understood. That is, the cognitive function and the manipulative function act against each other: by successfully manipulating the world, you act to change it into something other than you understand it to be, transforming what was a known known into an unknown known. Markets can be brought to their knees when participants finally recognize that their assumptions were wrong.

I was far more intrigued by the similarity in Soros’ conclusions about human behavior than I was about the causes of the financial crisis. Knowing that somebody who studied under Popper and who has been immensely successful applying his model of human behavior in trading commodities and equities had developed a model of human behavior that was similar to mine encouraged me to continue developing my own model.

So, I delved deeper and deeper into the issue of confirmation bias. Jonah Lehrer’s How We Decide was particularly illuminating of the role that brain chemistry, and especially the dopamine system, plays in decision-making. My interpretation is that the dopamine system does at the physical level what confirmation bias does at the cognitive level. While I think it most likely that most cognitive scientists view the dopamine system as the cause of cognitive bias, I view them as two distinct things despite their striking similarity. The dopamine system essentially engages in real-time pattern-matching that compares actual outcomes to expected outcomes. If everything meets expectations, positive signals are sent. If something is amiss, negative signals are sent. The reason why I believe that cognitive bias arises at a higher level of abstraction is because the possibility of cognitive bias only arises if the dopamine system has alerted the person that something does not quite meet expectations. A strong negative signal would bash through any cognitive bias because, well, SOMETHING IS WRONG!!! The chemical reactions are really strong.

Upon recognizing that confirmation bias is similar to how the dopamine system works but occurs at a different level of abstraction, I struck upon the idea that reflexivity as described by Soros is similar to confirmation bias but occurs at an even higher level of abstraction. Hmmmmm. Isn’t there an example of something that appears similar at every level of detail (i.e., abstraction) and is recursive in nature? Yep, and it is called a fractal.

Once I observed that the dopamine system, confirmation bias and Soros’ reflexivity concept seemed fractal in nature, I started to refresh my understanding of calculus and fractals. Let’s be clear: I don’t believe that any mathematical function can accurately describe human behavior, whether at the micro or micro levels. I do know, however, that “quants” apply fractal algorithms to market data to make buy/sell decisions in the stock market with some success. Could it be that the fractal nature of markets, first observed by Mandelbrot himself, can be explained by the fact that human decision-making itself is fractal in nature? And human decision-making is fractal in nature, could a mathematical model of that fractal at least help identify and agree upon trends that will harm the economy if left unchecked?

While waiting for books to help me bone up my math (I’m still waiting, actually), I decided to dive into Soros’ The Alchemy of Finance in hopes of finding a mathematical expression of the reflexivity function as he saw it. I hoped in vain. In spite of the fact that that the book was first published over twenty years ago, the math explaining it has never been developed. In fact, I believe that the math can never be developed because it is fundamentally flawed.

It turns out that Soros himself offers no mathematical function to support reflexivity, but he does provide examples of how he has detected reflexivity at work in markets and used that fact to make money (lots of money). Others have actually tried to take his narrative description of reflexivity and create a mathematical function, and I think their literal translation of the description into a function was accurate. Unfortunately, the function is wrong because it assumes a constant feedback loop: it assumes that human beings are always consciously comparing reality to expectations. That simply is not the case.

Soros’ examples are based on comparing the price of a commodity to his view of the fundamental value of that commodity over time. By so doing, he can identify a “prevailing bias” and an “underlying trend.” If these two things appear to be “self-reinforcing,” that indicates a boom that can be bought into and sold out of before the inevitable bust. If these two things appear to be “self-correcting,” that indicates a bust that can be shorted.

The problem with Soros’ theory of reflexivity as described is that humans do not constantly consciously compare reality to expectations. The dopamine system does not allow that. The only time that humans check their assumptions is when the dopamine system tells them that something is wrong, and much of the time, the confirmation bias reassures them that everything is alright. The only time that reflexivity comes into play is when social imperatives (i.e., the fact that everybody else seems okay with what is happening) overcome personal concerns that are not tamped down by the cognitive bias. Reflexivity is not a continuous function and cannot be explained by things like stock price. Stock price is, in fact, a derivative of collective decision-making and not a direct indicator of it.

Thus, a better way of expressing of Soros’s reflexivity is as a bias error function that leads to discontinuities (i.e., step functions) in the derivative function that is stock price. And the best way that I can think of to express that function is as a fractal. I don’t expect to succeed in doing that, but I do think that I can make the case that somebody who is actually competent should try to do so. I will explain why later.