The first time I saw a model like this, I assumed that randomness would eventually balance things out. But that is not what happened. The rules were completely fair, yet the system still ended up producing significant inequality.
That stuck with me. Sometimes, all it takes is time and a bit of randomness for imbalance to emerge on its own. Inequality does not always come from someone doing something wrong. It can simply be the long-term result of randomness playing out. So the real question is, once we understand that, what do we do with it?
I also assumed randomness would balance things out, but "balance things out" means maximum entropy distribution.
With 100 people, there are only 100 configurations where one person has all of the money. But there is also only one single configuration where everyone has the same amount of money. There are a small number of configurations where everyone has almost the same amount of money.
The vast majority of the configuration space consists of configurations that on a macro level fall under the umbrella category "unequal". This is not because they are more likely states, but just because there are so many of the states we would label "unequal".
Ooo. Very cool. You just set off a storm of interesting connections for me. Assuming some ergodic process for distributing wealth then the asymptotic expectation for wealth inequality reduces to looking at random integer partitions.
Blah blah, jargon. Mostly thinking out loud here.
Basically, you're making the astute observation that the majority of configurations fill all wealth brackets... I think? The maxentropy distribution involves maximizing over products of combinations, and I'm just gut feeling at the moment.
How does this jibe with the supposedly empirical observation that wealth tends to follow a Pareto distribution?
Very cool. Thanks for kicking off the this conceptual avalanche!
The Pareto distribution (and indeed other heavy-tailed distributions) come out of self-reinforcing processes, where each additional amount of something increases the probability of even more of that thing. (This is what it means for a distribution tail to be subexponential.)
In our capitalist system, wealth begets more wealth, thus heavy tails.
But I think the catch is that while the model preserves inequality it doesn't guarantee to preserve wealth for any individual player.
Real life has feedback loops too that help preserve and grow the wealth of the rich so it is worse than the sim. It also has feedback loops the other way like tax. This makes tax very important!
That stuck with me. Sometimes, all it takes is time and a bit of randomness for imbalance to emerge on its own. Inequality does not always come from someone doing something wrong. It can simply be the long-term result of randomness playing out. So the real question is, once we understand that, what do we do with it?