Show HN: Talent vs. Luck – A recreation of the paper's model

1. First select the simplest model that captures some generic and essential.

2. Vary the parameters and introduce additional variables to that model to see how sensitive it is to different parameters values and variations of the model. The general state phase under variation is what builds confidence to the model.

Some other results:

* Peter Norvig: Simple Economics Simulation: https://github.com/norvig/pytudes/blob/master/ipynb/Economic...

* Uri Wilensky even simpler version http://www.decisionsciencenews.com/2017/06/19/counterintuiti...

* Bouchaud JP, Mézard M (2000) Wealth condensation in a simple model of economy. Physica A 282:536–545. https://arxiv.org/abs/cond-mat/0002374

* Colloquium: Statistical mechanics of money, wealth, and income Victor M. Yakovenko and J. Barkley Rosser, Jr. Rev. Mod. Phys. 81, 1703 – Published 2 December 2009 https://link.aps.org/doi/10.1103/RevModPhys.81.1703

The general stable result that emerges from these simulations again and again is the effect of multiplicative randomness. There may be other factors, but it's usually the largest by far and you need to drill deeper if you want to quantify the effect from other factors.

I think the author is aware of that and the point is more that people generally assume that talent is guaranteed to lead to success, and they have no basis to make that assumption either. This model demonstrates that the intuition is fallible.

In an additive random walk, the distribution of positions after N time steps is Pascal's triangle with zeros injected every other column and with each row multiplied by one half [1], which is just a shifted binomial distribution (with zeros injected at odd distances on even time steps, and at even distances on odd time steps), with probability mass function of `arw_pmf(k, N, P) = (N choose k) * P^k * (1-P) ^ k - N/2`. For large N, the distribution approaches the normal distribution.

In a geometric random walk, the power of the scaling factor takes on the shifted binomial distribution. In this case, the scaling factor is 2, so the probability mass function is `grw_pmf(k, N, P) = 2^arw_pmf(k, N, P)`. Note that this is _not_ a power-law distribution, and therefor will _not_ exhibit a robust 80/20 rule. Even if you convolve this distribution with an input normal distribution over P, as they do in the paper, you would not get a power law distribution.

The effect of a change in P, which is used to model talent, is to shift the distribution, but not to greatly affect its shape. The shift is consistent with our expectations that greater "talent" results in higher probability of accumulating more capital, though there is of course an overlap in the distributions of two agents with differing talent.

All that being said, I suppose it's possible that the 2D discrete simulation introduces temporal correlations that could alter the population's final capital distribution into a power law distribution. If that's the case, then the power law distribution is due entirely to these temporal correlations, which suggests to me a different insight, namely that the source of inequality is these temporal correlations. In other words, if people who have recently been successful are more likely to continue to be successful, then you will have inequality. Since this seems to describe our world pretty well, perhaps inequality is inevitable?

[1]: http://mathworld.wolfram.com/RandomWalk1-Dimensional.html

> People start with the same allotment of capital, and are given a number between 0 and 1 to represent their “talent”. Talent is normally distributed.

Maybe the author meant "uniformly distributed"?

EDIT: Looks like talent is normally distributed with mean 0.6 and stddev 0.1, so it's quite likely between 0.3 and 0.9 (and most likely between 0 and 1, indeed).