Watch wealth concentrate

One hundred people start with exactly the same amount. They trade with each other at random, and every trade is a fair coin toss. Nobody cheats. Nobody is smarter or lazier. Press play and watch what happens.

What you are seeing

Each trade puts at stake a quarter of what the poorer of the two people has, and a fair coin decides who wins it. Even so, the wealth drifts steadily into fewer and fewer hands. The reason is simple: a loss hurts more than an equal win helps. If you lose half of what you have, you need to double what is left just to get back to where you were. Small differences in luck compound, and over thousands of trades a few people end up with most of everything while most end up with almost nothing.

The universe went through something similar. Just after the Big Bang, matter was spread out almost perfectly evenly, varying by about one part in a hundred thousand. Gravity has no ceiling either: wherever there was slightly more matter, it pulled in more. Over billions of years that produced stars, galaxies and black holes, separated by nearly empty space. Physicists and economists use different equations for the two, but they belong to the same family: processes with positive feedback and no upper limit, in which tiny early differences grow until a few dense clusters hold most of everything and most places hold almost nothing.

Now try the floor and the ceiling. Even a very small floor, half a percent a round, stops the slide: instead of one person ending up with nearly everything, the group settles into a stable spread. Each further step flattens it more, but by less each time. A low ceiling does the same job from the other end. Concentration is not the result of anyone being bad. It is what the rules produce when nothing pushes back.

Is there a best setting? This model cannot say, because it leaves out work and production altogether: nobody makes anything, they only trade. What it does show is the direction. The more a society shares, the flatter it stays, and a society that does not allow accumulation at all does not drift into this pattern in the first place.

What this demonstration does not show

It is a deliberately simple model. Real economies also have production, skills, inheritance, interest, taxes, safety nets and political power, and some of those push towards concentration while others push against it. The point is narrower and, for that reason, hard to dismiss: even under perfectly fair rules, an economy with no limit on accumulation drifts towards extreme inequality unless something actively counteracts it.

Why concentration captures government

The second readout is not part of the trading model; it is a separate, deliberately simple illustration of a well-documented dynamic. Money is not only a claim on goods. It is also a claim on political attention, and the two compound. As wealth concentrates, those who hold it can fund campaigns, sustain lobbies, own the channels through which others learn what is happening, and move between private office and public post. The more concentrated the wealth, the more the machinery of government tilts toward the preferences of the few who hold it.

This is measured, not merely asserted. Studying nearly 1,800 US policy questions, Martin Gilens and Benjamin Page found that the preferences of economic elites and organized business groups had substantial influence on what became law, while the independent influence of average citizens was near zero: the chance a proposed policy was adopted barely moved whether a few percent or a large majority of ordinary people favored it, yet rose sharply with elite support (roughly 18% adoption at low elite support to about 45% at high). Larry Bartels found senators far more responsive to the views of affluent constituents than to the poor; and the wealthiest Americans hold systematically different policy preferences from everyone else. The readout above is calibrated to the shape of these findings, not their exact numbers — a pared-down picture of a mechanism, meant to show direction, the same way the trading model does.

The practical point connects the two halves of this page. Floors and ceilings are not only about fairness in who has what. By holding concentration down, they also hold down the political capture that concentration produces — which is why entrenched wealth resists them, and why they are hard to win back once lost.

Sources and further reading

• Martin Gilens and Benjamin I. Page, “Testing Theories of American Politics: Elites, Interest Groups, and Average Citizens”, Perspectives on Politics 12(3), 2014, pp. 564–581 — the near-zero independent influence of average citizens, and the source for the capture readout’s shape.
• Larry M. Bartels, “Economic Inequality and Political Representation”, in Unequal Democracy (Princeton University Press, 2008) — senators respond to the affluent, not the poor.
• Benjamin I. Page, Larry M. Bartels and Jason Seawright, “Democracy and the Policy Preferences of Wealthy Americans”, Perspectives on Politics 11(1), 2013, pp. 51–73 — the wealthy hold distinct preferences.
• Bruce M. Boghosian, “Is Inequality Inevitable?”, Scientific American, November 2019 — the “yard-sale model” this demonstration is based on.
• Anirban Chakraborti, “Distributions of money in model markets of economy”, International Journal of Modern Physics C 13 (2002).
• Boghosian et al., “Oligarchy as a phase transition: The effect of wealth-attained advantage in a Fokker–Planck description of asset exchange”, Physica A 476 (2017) — adds redistribution, and shows how small advantages for the already-wealthy tip the model into oligarchy.
• On this site: The Structural Dynamics of Oligarchic Capture, the full mathematical treatment.