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IMO, this reveals more about human intuition regarding randomness than whatever financial point it purports to make. It's still a useful point though. Reminds

IMO, this reveals more about human intuition regarding randomness than whatever financial point it purports to make. It's still a useful point though. Reminds me of the load balancing literature. There, the explicit goal is to evenly divide the burden across your fleet of servers, and having wide distributions is a problem on both ends: you're paying for servers to sit idle, and some are over burdened and giving customers a bad experience (high pageload times). By way of illustration, I took the code and made a simple modification to it, implementing power of 2 random choice (http://www.eecs.harvard.edu/~michaelm/postscripts/tpds2001.pdf http://www.eecs.harvard.edu/~michaelm/postscripts/tpds2001.p...). Here's the video result: https://www.youtube.com/watch?v=94Vc7gf3ONY https://www.youtube.com/watch?v=94Vc7gf3ONY Much tighter distribution, though you need to be able to identify the size of people's bank accounts. In this model, it's very rare for anyone to give the richest anything, unless you magically choose two people randomly tied for richest.

jldugger 9y ago
It converges there pretty quickly. So I put together another video starting out with an imbalanced curve (maybe due to a rolling app deploy) smoothing back out. As you might expect, it gets there rather quickly: https://www.youtube.com/watch?v=wvnwx4r2ERA https://www.youtube.com/watch?v=wvnwx4r2ERA
execoverride 9y ago
What is happening here is fairly simple: Since each state in the system occurs with the same probability, the distribution that arises is the one that maximizes the entropy. Since the total amount of money is conserved, this means that the mean of the distribution is fixed. The maximum entropy distribution in this case has a geometric shape, which is skewed: https://en.wikipedia.org/wiki/Maximum_entropy_probability_distribution#Discrete_distributions_with_specified_mean https://en.wikipedia.org/wiki/Maximum_entropy_probability_di...
- pishpash 9y ago
  Yep, it's just a simple counting argument, you see the distribution that has exponentially more states than any other, subject to constraints. Specifically, you are allowing the range [0,∞). If you had constrained it to a fixed range of money (e.g. there is corrective feedback when you get too much money), then you would have seen a more uniform distribution.

jldugger 9y ago

It converges there pretty quickly. So I put together another video starting out with an imbalanced curve (maybe due to a rolling app deploy) smoothing back out. As you might expect, it gets there rather quickly: https://www.youtube.com/watch?v=wvnwx4r2ERA https://www.youtube.com/watch?v=wvnwx4r2ERA

execoverride 9y ago

What is happening here is fairly simple: Since each state in the system occurs with the same probability, the distribution that arises is the one that maximizes the entropy. Since the total amount of money is conserved, this means that the mean of the distribution is fixed. The maximum entropy distribution in this case has a geometric shape, which is skewed: https://en.wikipedia.org/wiki/Maximum_entropy_probability_distribution#Discrete_distributions_with_specified_mean https://en.wikipedia.org/wiki/Maximum_entropy_probability_di...

pishpash 9y ago
Yep, it's just a simple counting argument, you see the distribution that has exponentially more states than any other, subject to constraints. Specifically, you are allowing the range [0,∞). If you had constrained it to a fixed range of money (e.g. there is corrective feedback when you get too much money), then you would have seen a more uniform distribution.