Comment by MontyCarloHall | Hacker News Reader

Comment by MontyCarloHall | Hacker News Reader

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Seems like wealth according to this model follows a roughly Gaussian distribution around $100; it is not a power law or some other grossly imbalanced distribution as others have conjectured.

  import numpy as np

  W = np.ones(1000, dtype = int)*100

  for _ in range(1000000):
      i = np.random.randint(1000)
      j = np.random.randint(1000)
      if W[j] == 0:
          continue
      W[i] += 1
      W[j] -= 1

yields the following distribution of wealth:

  $0         | #####
  $10        | #########
  $20        | ###########
  $30        | ##############
  $40        | ###############
  $50        | #######################
  $60        | #################################
  $70        | ##################################################
  $80        | ####################################
  $90        | ##############################################
  $100       | #########################################
  $110       | ########################################
  $120       | ######################################
  $130       | ############################
  $140       | #########################
  $150       | #####################
  $160       | ################
  $170       | ########
  $180       | ########
  $190       | #####
  $200       | #

The key difference here is that every player is forced to give money each tick, whereas in your implementation players are randomly selected to give money. The following implementation does yield an exponential distribution:

    for _ in range(10000):
        for i in range(N_players):
            if W[i] > 0:
                j = np.random.randint(N_players)
                W[i] -= 1
                W[j] += 1

Fwiw your implementation will also relax towards an exponential distribution (try 10000000 iterations); it just converges at a different rate.

This is the Central Limit Theorem at work. Your random variables are independent and identically distributed so you're always going to approximate a normal distribution.

Wealth in real life is not independent. People with more wealth have more investment opportunities and thus more ability to grow, tending to a power law. You can see the same phenomenon with craters on the moon.

> Seems like wealth follows a roughly Gaussian distribution

You mean your toy simulation of wealth follows a Guassian Distribution.

Most people I know are not randomnly giving dollars to the entire population pool, they are mostly giving them to already wealthy corporations.

So the crux of the difference between your model and the model posted above, is exactly what causes the imbalance seen!

In your model, on every step a random person gives to another random person if he has money left.

In the model from the post, every step everybody gives something, but a random person gets something. This asymmetry between getting and giving is enough to cause (large) inequality!

Everybody goes down with the same speed, but dumb luck at some point can actually bring your wealth up really high very fast, and since the downward speed is limited, you will stay rich for a long time.

At a higher level: the average behaves the same upward and downward, but the flukes behave differently.

Advantage compounds, so W[i] *= advantage * W[i]

In real life, absolutely. In the simulation, there is no compounding.

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