Thomas Piketty marveled at the way wealth concentrates under normal capitalist conditions, as if by magic. He chalked it up to the maddening persistence of positive interest rates, even under conditions where capital is in vast excess. Once you have a certain amount of wealth, and given even modest interest, money just breeds on its own, certainly without labor, and almost without thinking.
A recent Scientific American article offered a different explanation, cast in a more physics-style framework. It recounts what is called a "yard sale" model of a perfectly free economic exchange, where each transaction is voluntary and transfers net wealth in a random direction. Even under such conditions, wealth concentrates inexorably, till one agent owns everything. Why? The treatment is a bit like statistical mechanics of gasses, that follow random walks of individual particles. But where gasses are subject to constant balancing force of pressure that strongly discourages undue concentrations, the economic system contains the opposite- ratchets by which each agent greedily holds on to what it has. At the same time, poorer agents can only transact from what little they have, but stand to lose more (relatively) when they do. They thus have a stricter limit on how often they can play the game, and are driven to penury long before wealthier players. Even a small wealth advantage insulates that player against random adversity. Put that through a lengthy random walk, and the inevitable result is that all the wealth ends up in one place.
"In the absence of any kind of wealth redistribution, Boghosian et al. proved that all of the wealth in the system is eventually held by a single agent. This is due to a subtle but inexorable bias in favor of the wealthy in the rules of the YSM [yard sale model]: Because a fraction of the poorer agent’s wealth is traded, the wealthy do not stake as large a fraction of their wealth in any given transaction, and therefore can lose more frequently without risking their status. This is ultimately due to the multiplicative nature of the transactions on the agents’ wealth, as pointed out by Moukarzel." - Boghosian, Devitt-Lee, Wang, 2016
"If we begin at the point 1/2, the initial step size is 1/4. Suppose the first move is to the right, reaching the point 3/4. Now the step size is 1/8. If we turn back to the left, we do not return to our starting point but instead stop at 5/8. Where will we wind up after n steps? The probability distribution for this process has an intricate fractal structure, so there is no simple answer, but the likeliest landing places get steadily closer to the end points of the interval as n increases. This skewed probability distribution is the ratchetlike mechanism that drives the yard-sale model to states of extreme imbalance." ... "If some mechanism like that of the yard-sale model is truly at work, then markets might very well be free and fair, and the playing field perfectly level, and yet the outcome would almost surely be that the rich get richer and the poor get poorer." - Hayes, 2002
It is important to emphasize that the yard sale model is a libertarian's dream. It models perfect freedom and voluntary economic activity, if on a very simplistic level. But its implications are profound. It describes why most people in a free economic system own little more than their labor. The authors supplement this model with three more parameters, to align it better with reality. First is a wealth advantage factor. Our free economic system is not free or fair as a matter of fact, and the wealthy have many economic advantages, from lower interest rates (on loans), better returns on investments, to better education and more political power. Obviously, this is hardly conducive to greater equality, but rather to sharper and faster inequality. Second is a redistribution factor, in recognition that taxes and other costs have a redistributing effect, however small. And third is an allowance for negative wealth, which characterizes a fair portion of most societies, given our addiction to debt. Using these extra factors, these researchers can easily model wealth distributions that match reality very closely.
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| Lorenz curves showing income inequality in the US, and its growth in recent decades. Higher income families are on the right bottom, and their cumulative share of income are dramatically higher than those of lower income families. This graph gives rise to the Gini coefficient. Since this graph is binned in quintiles, it hides even more dramatic acceleration of income at the highest 10%, 1% and 0.1% levels. |
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| An example of a model curve. The teal area (C) represents negative wealth, a fact of life for much of the population. The intersection of curve B with the right axis represents a result where one person or family is has 40% of all wealth. We are not quite there in reality, but it is not an unrealistic outcome considering current trends. Gini coefficients are generally defined as the areas A/(A+B). |
The article, and other work from this group, finds that the redistrubution factor is absolutely critical to the fate of society. Sufficiently high, it can perpetually forestall collapse to total inequality, or even oligarchy, which is the common human condition. But if left below that threshold, it may delay, but can not forestall the inevitable.
What is that threshold? Obviously, it depends quite a bit on the nature of the society- on its settings of wealth advantage and redistribution. But rather small amounts of redistribution, on the order of 1 or 2 %, prevent complete concentration in one person's or oligarchy's hands. To make a just society, however, one that mitigates all this accidental unfairness of distribution, would take a great deal more.
There have traditionally been several social solutions to gross inequality, after humanity gained the capacity to account and accumulate wealth. One is public works and the dole, which the Romans were partial to. In their heyday, the rich vied to attain high offices and fund great works which benefitted Roman society. Another is a debt jubilee, where debts were forgiven at some interval or on special occasions. Another, of course, is revolution and forcible reforms of land and other forms of wealth. Karl Marx, along with many others, clearly sensed that something was deeply wrong with the capitalist system when allowed to run unfettered. And despite all the ameliorating regulations and corrective programs since, we are back in a gilded age today, with all time highs of gross unequality. To make matters worse, we have been backsliding on the principle of inheritance taxes, which should prevent the transgenerational and wholly undeserved accumulation of wealth and power.
Redistribution turns out, on this analysis, to be essential to a sustainable and just society. It is not a pipe dream or violation of the natural order, or of "rights". Rather, it is the right of every member of a society to expect that society to function in a fair and sustainable way to provide the foundation for a flourishing life by building each member's talents and building the social and material structures that put them to effective use. Capitalism and free exchange is only one ingredient in this social system, not its purpose or its overriding mechanism. That is why the weath tax that has been proposed by Elizabeth Warren is so significant and has generated such interest and support. It speaks directly and effectively to one of the central problems of our time- how to make a sustainable system out of capitalism.
- Ah, the memories ...
- When a stroke takes away your hearing.
- An extra paper on gene duplicates.
