3 ms·

Could someone perhaps explain to me how the "random_split" results in wealth accumulation? From the description, I would expect it to have the opposite effect.

Could someone perhaps explain to me how the "random_split" results in wealth accumulation? From the description, I would expect it to have the opposite effect. If two actors with initial values X and Y interact, their expected outcome would be (X+Y)/2, with expected change being (Y-X)/2 and (X-Y)/2 for the two actors. If X<Y, then (Y-X)/2>0, and so the person with less wealth expects to gain, and the person with more wealth expects to lose, for an overall smoothing effect.

qiemem 13y ago
First, accumulation would be the wrong way to think about it. Once the two agents are engaged in transaction, it doesn't matter which is which. Let D be the difference in wealth post-transaction divided by the total. The expected value of D is 1/2. That means that we should expect that one agent will walk away with 75% of the pot and the other with 25%. Thus, although the expected outcome for an agent is 50% of the pot, we're still pretty much guaranteed to get very uneven splits. Next, note that a person's wealth affects the payout of the next transaction. In other words, the person who takes 25% is almost guaranteed to be able to make less on the next transaction than the person who walked away with 75%. Suppose all our agents start out with 100, and that the 75%/25% splits are guaranteed. If each agent engages in exactly one transaction, then half our agents will have 50 and half will have 150. A 50's next transaction will either be (50, 50) or (50, 150). A 150's next interaction will either be (150, 50) or (150, 150). The expected outcome for (50, 50) is (25, 75). The expected outcome for (50, 150) is (50, 150). The expected outcome for (150, 150) is (225, 75). None of the expected outcomes even things up. It just gets more and more spread out.
nhaehnle 13y ago
I find that fascinating as well. A thorough probabilistic analysis could be fun, but I'm too tired for that right now. One thing to keep in mind is that even supposedly uniform distributions can have outliers. For example, if you just throw N balls into N bins, there's going to be a bin with log N balls in it with high probability. Something similar is most likely going on here as well. In a way, the really interesting question is whether the outcomes of that experiment are exponentially distributed. Then again, the simulation has basically nothing to do with real world wealth distribution anyway.
ealloc 13y ago
In physics, if you randomly divide a fixed amount of energy among n particles, you will obtain a boltzmann (exponential) distribution of particle energies, such that a small number of particles have very high energy and while many have only a little. Similarly, if you randomly divide a fixed amount of wealth among n individuals, you end up with a boltzmann distribution of wealth, such that a small number if individuals have a lot of the wealth, while many have only a little. The boltzmann distribution is the maximum entropy distribution, for fixed total energy or fixed total wealth.

qiemem 13y ago

First, accumulation would be the wrong way to think about it. Once the two agents are engaged in transaction, it doesn't matter which is which. Let D be the difference in wealth post-transaction divided by the total. The expected value of D is 1/2. That means that we should expect that one agent will walk away with 75% of the pot and the other with 25%. Thus, although the expected outcome for an agent is 50% of the pot, we're still pretty much guaranteed to get very uneven splits. Next, note that a person's wealth affects the payout of the next transaction. In other words, the person who takes 25% is almost guaranteed to be able to make less on the next transaction than the person who walked away with 75%. Suppose all our agents start out with 100, and that the 75%/25% splits are guaranteed. If each agent engages in exactly one transaction, then half our agents will have 50 and half will have 150. A 50's next transaction will either be (50, 50) or (50, 150). A 150's next interaction will either be (150, 50) or (150, 150). The expected outcome for (50, 50) is (25, 75). The expected outcome for (50, 150) is (50, 150). The expected outcome for (150, 150) is (225, 75). None of the expected outcomes even things up. It just gets more and more spread out.

nhaehnle 13y ago

I find that fascinating as well. A thorough probabilistic analysis could be fun, but I'm too tired for that right now. One thing to keep in mind is that even supposedly uniform distributions can have outliers. For example, if you just throw N balls into N bins, there's going to be a bin with log N balls in it with high probability. Something similar is most likely going on here as well. In a way, the really interesting question is whether the outcomes of that experiment are exponentially distributed. Then again, the simulation has basically nothing to do with real world wealth distribution anyway.

ealloc 13y ago

In physics, if you randomly divide a fixed amount of energy among n particles, you will obtain a boltzmann (exponential) distribution of particle energies, such that a small number of particles have very high energy and while many have only a little. Similarly, if you randomly divide a fixed amount of wealth among n individuals, you end up with a boltzmann distribution of wealth, such that a small number if individuals have a lot of the wealth, while many have only a little. The boltzmann distribution is the maximum entropy distribution, for fixed total energy or fixed total wealth.