When selecting a model to demonstrate some dynamic behaviour:
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.
* 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.
Having built models like this by programming before [1]. I think you can only "prove" things about the system you construct. Meaning, in reality it has (or could have) little to no basis. That being said, I think building models that reflect something we know can be valuable in providing insights - just ahouldnt be used as proof.
Also 0.62 is not near average depending on simulation count / size. That's a pretty significant margin (>20%) above average.
> I think you can only "prove" things about the system you construct. Meaning, in reality it has (or could have) little to no basis.
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.
I think you can only "prove" things about the system you construct.
While this is true in a literal sense, often the question is not whether a model is definitively correct, it is whether a simpler model is sufficient to explain real-world phenomena where more complex models have been previously hypothesized. In those cases, we should generally prefer the simpler explanation, even if neither is yet proven in a formal sense.
Why does it need to be a simulation at all? The model is essentially a geometric random walk with number of trials N and probability of success in each trial P, with P varying.
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?
> I recently came across the paper titled Talent vs Luck: the role of randomness in success and failure, by A. Pluchino. A. E. Biondo, A. Rapisarda, on Hacker News on Hackernews.
> 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).
A key purpose of the original paper is to inform policy to improve public funding of research [1]. Thus, to a first-order approximation, it should reflect realities. However, ...
The number of lucky and unlucky events in the paper (figure 5, page 8) are each around 5-7 events per agent on average, where 'lucky' is defined as doubling the capital (or success) accumulated so far and 'unlucky' as halving it. In the real world, how many regular people/scientists have that many career-defining events? Most are quite risk-averse, especially later in their careers. Some entrepreneurs could be exceptions but they are a small minority (single-digit percentage or fewer) [2].
This parameter (no. of big lucky/unlucky events) diminishes the role of talent in the simulation. In real life, most talented people can avoid having 5-7 big 'unlucky' events in their career. This renders the simulations questionable.
--> It's like saying talent doesn't matter much for blackjack players who regularly bet half of all their chips. Yes, if one gambles that much, then talent would probably matter relatively little. Do most people do something like that with their career? [3]
Research has shown that Log-Normal Distribution could fit data on real-world success as well as Power Law and sometimes better. [4] This suggests that multiple independent factors could play multiplicative roles in success. Talent, luck, grit, location of birth/childhood, educational opportunity, parental guidance, ambition, etc are some candidates. [5]
If several factors interacting multiplicatively influence success, the number of individuals who achieve success at a very high level would be quite small, as they need to 'score' high on several of them. This can be modeled quite well with Log-Normal Distribution.
[2] As an entrepreneur myself, I would avoid betting half my capital unless the potential gain is far, far higher than doubling my capital. I believe most other entrepreneurs think similarly.
[3] Note that capital/success appears to be quite broadly defined in the paper, and can be interpreted to include expertise, reputation, and other resources as well as tangible capital.
[4] https://arxiv.org/pdf/1304.0212.pdf "Moreover, even if the data do not rule out the power-law model usually the evidence in its favour is not conclusive – some rivals, most notably the log-normal and stretched exponential distributions, are also plausible fits to wealth data."
[5] Note that luck as defined in the paper does not reflect factors like location of birth, educational opportunity, or parental guidance.
> each around 5-7 events per agent on average [...] In the real world, how many regular people/scientists have that many career-defining events?
A significant event every half decade or so does not seem unrealistically high to me.
> that Log-Normal Distribution could fit data on real-world success as well
Power laws (eg Pareto distribution) and log-normal are extremely different though in the tails. The log of a log-normally distributed RV is normally distributed, and thus effectively restricted to a fairly small support area (+/- 5 std devs), as the tail falls off extremely fast (exponentially). The log of a Pareto distributed RV is exponentially distributed, and can get pretty high (the tail of the pdf decays only with some power, ie polynomially).
So, I'd expect the properties and conclusion to be quite different (more extreme wealth under power law/Pareto than under lognormal).
> Research has shown that Log-Normal Distribution could fit data on real-world success as well as Power Law and sometimes better. [4]
This surprised me, and I don't think the paper [4] supports your claim. It examines only the super rich (Forbes Billionaires), not the entire population. Log-normal might model a few hundred rich people reasonably well, but if you fit to the entire population, I'd think log-normal is basically ruled out by the rich (while I'd expect Pareto still to sort of work).
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.