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Tomorrow, on the First of May, many countries celebrate the so called International Workers’ Day (or Labour Day): time to talk about the unequal distribution of wealth again!

A few months ago I posted a piece with the title “If wealth had anything to do with intelligence…” where I argued that ability, e.g. intelligence, as an input has nothing to do with wealth as an output. It drew a lot of criticism (as expected), most of it unfounded in my opinion but one piece merits some discussion: the fact that the intelligence quotient (IQ) is normally distributed by construction. The argument goes that intelligence per se may be a distribution with fat tails too but by the way the IQ is constructed the metric is being transformed into a well formed gaussian distribution. To a degree this is certainly true, yet I would still argue that the distribution of intelligence and all other human abilities are far more well behaved than the extremely unequal distribution of wealth. I wrote in a comment:

There are many aspects in your comment that are certainly true. Obviously there are huge problems in measuring “true” mental abilities, which is the exact reason why people came up with a somewhat artificial “intelligence quotient” with all its shortcomings.

What would be interesting to see is (and I don’t know if you perhaps have a source about this) what the outcome of an intelligence test would look like without the “quotient” part, i.e. without subsequently normalizing the results.

I guess the relationship wouldn’t be strictly linear but it wouldn’t be as extreme as the wealth distribution either.

What I think is true in any case, independent of the distributions, is when you rank all people by intelligence and by wealth respectively you wouldn’t really see any stable connection – and that spirit was the intention of my post in the first place and I still stand by it, although some of the technicalities are obviously debatable.

So, if you have a source, Dear Reader, you are more than welcome to share it in the comments – I am always eager to learn!

I ended my post with:

But if it is not ability/intelligence that determines the distribution of wealth what else could account for the extreme inequality we perceive in the world?

In this post I will argue that luck is a good candidate, so read on…

In 2014 there was a special issue of the renowned magazine Science titled “The science of inequality”. In one of the articles (Cho, A.: “Physicists say it’s simple”) the following thought experiment is being proposed:

Suppose you randomly divide 500 million in income among 10,000 people. There’s only one way to give everyone an equal, 50,000 share. So if you’re doling out earnings randomly, equality is extremely unlikely. But there are countless ways to give a few people a lot of cash and many people a little or nothing. In fact, given all the ways you could divvy out income, most of them produce an exponential distribution of income.

So, the basic idea is to randomly throw 9,999 darts at a scale ranging from zero to 500 million and study the resulting distribution of intervals:

library(MASS)

w <- 5e8 # wealth
p <- 1e4 # no. of people

set.seed(123)
d <- diff(c(0, sort(runif(p-1, max = w)), w)) # wealth distribution
h <- hist(d, col = "red", main = "Exponential decline", freq = FALSE, breaks = 45, xlim = c(0, quantile(d, 0.99)))

fit <- fitdistr(d, "exponential")
curve(dexp(x, rate = fit\$estimate), col = "black", type = "p", pch = 16, add = TRUE)


The resulting distribution fits an exponential distribution very well. You can read some interesting discussions concerning this result on CrossValidated StackExchange: How can I analytically prove that randomly dividing an amount results in an exponential distribution (of e.g. income and wealth)?

Just to give you an idea of how unfair this distribution is: the richest six persons have more wealth than the poorest ten percent together:

sum(sort(d)[9994:10000]) - sum(sort(d)[0:1000])
## [1] 183670.8


If you think that this is ridiculous just look at the real global wealth distribution: here it is not six but three persons who own more than the poorest ten percent!

Now, what does that mean? Well, equality seems to be the exception and (extreme) inequality the rule. The intervals were found randomly, no interval had any special skills, just luck – and the result is (extreme) inequality – as in the real world!

If you can reproduce the wealth distribution of a society stochastically this could have the implication that it weren’t so much the extraordinary skills of the rich which made them rich but they just got lucky.

Some rich people are decent enough to admit this. In his impressive essay “Why Poverty Is Like a Disease” Christian H. Cooper, a hillbilly turned investment banker writes:

So how did I get out? By chance.

It’s easy to attach a post-facto narrative of talent and hard work to my story, because that’s what we’re fed by everything from Hollywood to political stump speeches. But it’s the wrong story. My escape was made up of a series of incredibly unlikely events, none of which I had real control over.

[…]

I am the exception that proves the rule—but that rule is that escape from poverty is a matter of chance, and not a matter of merit.

A consequence would be that you cannot really learn much from the rich. So throw away all of your self help books on how to become successful. I will end with a cartoon, which brings home this message, on a closely related concept, the so called survivorship bias (which is also important to keep in mind when backtesting trading strategies in quantitative finance, the topic of an upcoming post… so stay tuned!):