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This reminds me of the problem Mitzenmacher’s “power of two choices” load balancing scheme solves [1]. The problem is that basically, if you throw n balls into n bins completely at random, some bins will have no balls while some bins will have more than one. Ultimately, the difference between the bin with the least amount of balls and the bin with the most goes up with log(n)/log(log(n)). This can actually become a pretty significant effect with large n.

So, yeah, if you simply distribute money randomly, the difference between the people with the most money and the people with the least money won’t be very well load balanced. What’s more, in the case of this thought experiment, there’s an additional effect which is that some rounds, some players are out of money and can’t redistribute, which reduces the overall flow of money that round.

Mitzenmacher’s power of two choices load balancing scheme is to randomly choose two bins, then place the next ball into the bin with the lesser amount of existing balls. With this strategy, the maximum skew is more like log(log(n))/log(2), which is way better distributed.

I have no idea on how that load balancing observation could be used to create better wealth inequality policy.

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I have no idea on how that load balancing observation could be used to create better wealth inequality policy.

Well, it would seem that a random distribution creates clumps and hidden money (all money past 1\$ is “hidden”).

So, a system where everyone gets the money would be a better way. Like UBI. The payment of goods and services may still be skewed, but UBI would not lock people out of it. The other half would be a progressive tax to lower overall effectiveness of higher end and rebalance the monetary system.

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tl;dr: in the long run, everyone has their moments of wealth and poverty, but at any given time, the distribution of wealth is exponential.

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Within that experiment, sure. Unfortunately in the real world, having more money allows you to acquire more money much easier (e.g., not having to pay the bank interest for loans, actually having money you can invest, etc.), so there’s a bit of a runaway problem where fairness won’t necessarily come in the end without intervention.

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Practical forms of “intervention” include exponential dilution via children, marriages, etc.

You can get around this with e.g. primogeniture but this is evolutionarily sub-optimal so most people don’t. Even the oldest banking families around today aren’t really all that old on a historical scale.

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I can see this could prevent long-lasting dynasties but when few hold money it’s still bad for the economy even if it was just for a single generation. The poor spend a much larger portion of their income than wealthy even in contrived environments. I do think the property rights (yes unlike the founding fathers I do view property as a right) of the few do not outweigh the rights of life liberty and the pursuit of happiness. If the income inequality is so extreme that those basic rights are infringed I think it is a responsibility of the government to normalize that effect.

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Obviously, the random selection algorithm is secretly enabling a meritocracy- the people with all the money obviously deserve it more, because they have more of it.

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Seems pretty stupid to imply the real world is totally random and not a mixture of both chance and skill.

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I don’t think remy_porter ever implied that. Obviously it is a criticism of the idea that people who have more money necessarily earned it, but not at all a statement that the world is “totally random”.

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Fair enough, I took the absurdity in the other direction.

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If on quick reflection you thought “more or less equally”, you are not alone. I asked 5 super-smart PhDs this question and they all had the same initial intuition.

I wonder if any of these had their degrees in Physics or Physical Chemistry. The problem sounds conceptually similar to a thermodynamics problem, where you don’t get uniform distributions. For example, the Maxwell-Boltzmann distribution arises from ideal gas molecules exchanging energy and momentum in random collisions, and it’s far from uniform.

This also demonstrates why I prefer simulations when thinking about these kinds of things. With the thermodynamics analogy, one might be able to work out some analog of the partition function and calculate the theoretical distribution. But running a simulation directly works out to be much easier.

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It makes sense, if you have 2\$ and you give a dollar that’s 50% of your total, if you have 1,000\$ and you give a dollar that’s .1% of your total. The more you have the less impact giving has on your total.