Counterintuitive problem: Everyone in a room keeps giving dollars to random others. You’ll never guess what happens next.

June 19, 2017
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SURPRISING POLICY EFFECTS

When we were giving a talk at the Department of Electrical Engineering and Computer Science at Northwestern we met Uri Wilensky, who shared with us a simulation he likes to assign.

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?

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.

How does the distribution look? Play the movie above to see. Here’s how it works.

The movie shows 5,000 clock ticks in less than a minute.

The Y axis shows the number of dollars each person has. It starts at 45 dollars each.

On the x-axis we have 45 people.

The red bars show the wealth of each person at each tick of the clock.

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.

Don’t believe it? Play with R and tidyverse and gganimate code yourself.

Inequality can arise from seemingly innocuous of policies — you need to keep an eye on it.

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