Wealth distribution and feedback loops
Property rights don’t exist in nature. You can only hoard what you can defend. A tiger gets self-reinforcing benefits from expanding its territory. More territory means more access to prey means more energy and growth, which means the ability to expand its territory–a positive feedback loop. Yet more territory also means more time and energy spent patrolling and defending, which means less energy, which means less territory protected, which means access to prey–a negative feedback loop.
When a process like this is balanced, the resulting distribution is a gaussian distribution, or a normal curve, and it remains that way over time. Yes there will be a tiger with the most territory, and it may be much larger in comparison, but you won’t have 1 tiger with 90% of the territory, and thousands of tigers with less than .01% of it. When one of these opposing forces is removed, this shifts. Rather than the resulting distribution being normal, it turns into an exponential distribution.
In our society, our material possessions are protected by property rights. This is a good thing in my opinion. Those property rights are enforced by an entity or a handful of entities which have been assigned a monopoly on violence, which seems better than chaotically distributed violence in the absence of a clear alternative. Even though “monopoly on violence” is a phrase that sounds bad, I think most reasonable people can say that they prefer some publicly provided enforcement agency defend their property from potential attackers. However this does something important to the dynamic equilibrium of wealth distribution. It gives a (relatively) flat cost to the cost of hoarding. So while the benefits of hoarding continue to have their positive feedback loop, it removes the primary source of negative feedback from the equation, or turns it into something that grows slowly in comparison to the positive feedback.
If we were designing a society and attempting to optimize it for survival, we might initially think we want distribute wealth to people according to certain properties. Perhaps their efforts or their talents. These things tend to be normally distributed. However if we look at our wealth distribution it definitely doesn’t follow a normal distribution, what exactly it does follow I’ll discuss below.
If wealth were apportioned to people according to some combination of these factors, we should expect a normal distribution. That would make sense. We might also find a skew normal distribution if these factors were not evenly distributed within the population. The distinction between a power law distribution and exponential is also worth noting.
In a power law distribution, the difference between the highest and lowest values is not as extreme. We expect to observe this sort of distribution when there is some uniformly distributed value which is then compounded by some process which exaggerates the result, such as galaxy formation due to the force of gravity. As more mass clusters into a galaxy, it pulls in more mass, however the amount of mass it pulls it in is limited by the existing mass around it. As it pulls in more mass, it is pulling on particles around it harder, but they are also further away on average because it has already consumed the closer particles. So while it has a significant positive feedback loop, it does have some negative feedback as well which stops it from being as extreme as the exponential distribution
This is commonly associated with network effects. For instance words which are used more frequently then become more likely to be used by other people. See Zipf’s law. In terms of economics, we might expect investment funding to follow this pattern, if those who have already received investment are perceived to be better investments, and so each of many investment firms apportions a set amount of investment to each company that they flag with a yes or no. This would fall into distinction with an exponential distribution where companies provide funding in an amount directly proportional to the existing funding provided.
So how *is* wealth distributed? According to this paper, it appears to be an exponential distribution for most of us at least. But according to this one at the top this tapers off to a power-law distribution. One reason I suspect is that the effect of the negative feedback loop never truly goes to zero. What this means practically for this topic is that the number of very rich people is slightly higher than it would otherwise be. However, as time continues to move on, if nothing is done to add a negative feedback loop back, I believe that difference will continue to shrink and shrink, because according to this model, as time moves forward from the removal of said negative feedback loop, the transition from normal curve to exponential distribution becomes more complete. It could also be that different rules and dynamics start to apply to wealth aggregation at that level and dominate the exponential effects.
Either way, what this means for most of us is that we’re in an inherently unstable positive feedback loop. The income gap is only going to keep increasing until something snaps or a replacement negative feedback mechanism is introduced. In the US’s heyday, the top marginal tax rate was 90%. That was still not enough to stop the eventual exponential runaway and regulatory capture that comes from unfettered wealth aggregation due to this lack of negative feedback mechanism. It’s also not something that we will probably ever see voted into government again, despite the fact that it was responsible for funding the most important inventions of the century.
How would one go about devising and adding a negative feedback mechanism in order to stop this runaway dynamic? That will have to be for later posts, but one starting point to make it easier would be a platform for “policy as code”. This could allow rapid iteration and experimentation with groups of much smaller sizes to see how they behave in the same environment under different incentive structures.
In response to this information people like to respond sometimes justify the exponential distribution by saying that people are paid “according to the *value* the contribute to society,” or something similar and that value isn’t necessarily normally distributed. That’s true, that value isn’t *necessarily* normally distributed. However if you hypothesize it to be something which is exponentially distributed, then there’s the natural question of: why is *that* exponentially distributed? What positive feedback loop is *it* running into then. Is it possible that there’s a significant hidden requirement of wealth that has been conflated into that definition?
A common example is that people say you are paid according to “the value they created for society”. However, that has words that don’t have much meaning. When you run into these “wiggly words,” you must peel them back by trying to be more and more specific in your definitions until you reveal measurements you could perform that would determine the categorization. What is “value.” How do you decide who “created” it when a collaborative process was used.
Let’s define “how much value you created” as “how many products you made available to people” just for a very rough definition. That’s more specific, but we still have some wiggly words in there: “products” and “made available.” So, how can I define who specifically “made a toaster available to someone” and in what proportion? Deliver it? That’s measurable, but delivery drivers aren’t getting outsized paychecks, so that definition doesn’t match the exponential distribution we see. “Man the machines that make them?” Same problem there. “Construct the machine that makes them?” Same problem.
The only measurable definition I can come up with that actually matches the exponential distribution and so would survive substitution back into the original statement is “fund the production of.” With that we can go back to our definition and substitute:
people are paid “according to the *value* the contribute to society” transforms to
=> people are paid “according to how many products they funded the production of in society, ”
We can then look at that statement which now has externally measurable definitions for every word and we can see why it would have a power law distribution. Funding the production of something requires money. Therefore we see the recursion: it takes money to get money. We see the exponential process–the positive feedback loop which results in an exponential distribution.
Another common one is: “Investors get paid more because they risk more.” First let’s decide what we mean by “risk more.” Do we mean take wilder risks with the same amount of money? This would be untrue. Investors who take wild risks tend to end up with *less money*. It’s the disciplined and calculated investors who actually make money. So when we say “risk more” we mean “risk more money.” Hopefully by now the circularity in this one should be obvious as well. Since they have more to begin with, they have the capacity to risk more.
And lastly: a recently popular one that Musk came up with: people are paid “according to the difficulty of the problems they solve”. This one is full of wiggle words as well: “difficulty”, “problem” and “solve.”
What is a measurable definition of difficulty? The one which requires the most intellectual training? Many people feel that difficult problems are those solved by physicists. They don’t seem to make any particularly large sum. Difficult in what way? Intellectually? Certainly not physically. Emotionally? Spiritually? Even if we try to say the software engineers at AI companies currently making $300k+ salaries are working the hardest *intellectual* or *value-creation* problems, then there’s still the question of why their bosses and investors are making more than them.
What counts as a “difficult problem”? How about addiction counseling? It requires a deep understanding of a person’s psychology, as well as understanding of their personal context. It also requires and understanding of how to motivate people, as well as an understanding of how the world works to help them find a sustainable path to get more pleasure from life than their habits. These problems are, in my opinion, extremely difficult. How about nursing, which requires a deep understanding of medicine as well as a patient’s individual context as well. We can see that hospitals are understaffed as well, making the problems they solve more difficult. But their pay is lower than a lot of social media influencers, or people who kept up to date on NFT artists at the right time.
This may come across as cynical, but I find this to be an important issue. Many influential people are lamenting that people no longer want to contribute to society and it is falling apart. The *critical* ingredient in motivating people to contribute is *incentives*. If people do not have a clear path to a good life by working hard, they will not do it. It’s a conservation of energy thing. An institution which consumes more energy from its members than it returns to them *will eventually die*. Being honest without ourselves about what our society does and does not incentivize is critical to keeping it from falling apart.