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Comment by lmkg | Hacker News Reader

I doubt the PRNG will have an effect, unless it's a bad one. For any individual, the flow out is fixed at 1 dollar per round, but the flow in is unbounded. This favors wealth accumulation. If five people happen to select the same donor target, that person will take five rounds to get rid of that money, during which time they are likely to receive more.

Meanwhile if someone only has one dollar, they lose their entire wealth if no one targets them immediately. Only large amounts have staying power.

There is a second-order effect that as money becomes more concentrated there are less donations per round. If one person has five dollars, four dollars are not being donated. This makes being targeted for multiple donations less likely as time goes on.

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If you run this for very long time frames everyone should end up both broke and wealthy. It's basically just several bounded random walks which will diverge in both directions and then flip around.

And really this is just another case where random does not seem random to us.

I want to believe that this is true because there are no absorbing states, but it could be false. Let's not forget Pólya's theorem: random walks on integer lattices are recurrent at dimension 1 and 2 (always come back to the origin) and transient in any higher dimension (eventually never come back).

But the number of states for the wealth distribution problem isn't infinite, hm, because the total amount of money never changes. Yeah, I think I just convinced myself that you may be right, no state is absorbent so they must all be positive recurrent.

Maybe that's how we can restore our intuition on this problem. Everyone should be wealthy and poor, but it may take very long time to see the wealth flip around. While we wait for that to happen, we'll see gross wealth inequality.

The finite states argument feels kind of wrong. You're usually interested in the general behavior for n people, and the number of states is exponential in n, which means that you need time exponential in n to repeat yourself. What you're seeing here is the early behavior of the system. Your arguments is a bit like saying every computer is actually a finite state machine, because of the finite memory it's going to repeat itself eventually. The argument is fundamentally flawed because you inflated one part of the question (time of running the question) while keeping the more significant part (number of particiants) fixed.

It favors wealth accumulation, but the winner isn't locked in because eventually any person will lose all they have if they don't get any income for a long stretch.

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