Imagine a room full of 100 people with 100 dollars each. With every tick of the clock, every person with money gives a dollar to one randomly chosen other person. After some time progresses, how will the money be distributed?<\/p><\/blockquote>\n
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.<\/p>\n
How does the distribution look? Play the movie above to see. Here’s how it works.<\/p>\n
The movie shows 5,000 clock ticks in less than a minute.<\/p>\n
The Y axis shows the number of dollars each person has. It starts at 45 dollars each.<\/p>\n
On the x-axis we have 45 people.<\/p>\n
The red bars show the wealth of each person at each tick of the clock.<\/p>\n
The blue bars are the same as red bars, but sorted to show how wealth is distributed. The rightmost blue bar is the height of the highest red bar, and so on down.<\/p>\n
Don’t believe it? Play with R<\/a> and tidyverse<\/a> and gganimate<\/a> code yourself.<\/p>\nInequality can arise from seemingly innocuous policies — you need to keep an eye on it.<\/p>\n
ADDENDUM<\/p>\n
There’s some confusion in the comments below and on other sites that we thought we’d address. The point is not that some people become rich and never lose their top position. This runs infinitely and will contain every possible sequence of good and bad luck for every person. The richest will become the poorest, everyone will experience every rank, and so on. The interesting thing is that this simple simulation arrives at a stationary distribution with a skewed, exponential shape<\/em>. This is due to the boundary at zero wealth which, we imagine, people don’t consider when they think about the problem quickly.<\/p>\nSee this paper<\/a> and see mathematician Jordan Ellenberg’s post on this post<\/a> <\/p>\n