Do you feel lucky, punk ?

This paper examines the role of luck in determining success in society. The claim is that this is under-appreciated, and that luck is more important than we like to give credit for. Genuine merit goes unrewarded, while the really big-shots are actually just ordinary people who get a lucky break. There's a lot of press releases going round about this, mostly decent enough, but I shall cast a more critical eye over it.

First, I need to say that I like this paper and really hope the authors take this further. It's a nice, accessible work with important implications. But as it stands it's got some gross oversimplifications and the conclusions, in my opinion, are too strongly stated. They don't need to be changed, but I think they should be toned down and the limitations of the study emphasised very much more strongly.


1) The Observations

There are some quite intriguing observations indicating that luck is underestimated. In particular, while abilities seem to follow a Gaussian distribution, wealth seems to follow a power law : that is, if everyone was rewarded according to their skills, the wealth distribution would look different to how it actually does. This does not mean it would be more equal, just different. I do wish they'd stop using wealth as a proxy for success though - there's no benefit to this and it creates many ethical and social issues. Just say wealth !

But there's immediately a bigger problem. While they present many citations for wealth following a power law (including that recent dubious Oxfam study saying the distribution is insanely extreme*), they don't give any demonstrating that abilities follow a Gaussian. Well, not strictly true, they do give one, but it's worse than zero : it's not actually a paper, it's a research proposal !
https://ir.uiowa.edu/cgi/viewcontent.cgi?article=1035&context=mzwp
Aarrgggh.

* I'm not saying this result is necessarily wrong, just that from what I've read it was unconvincing.

They then give numerous examples of how luck has been shown to be important (including the one about successful scientific papers occurring at random throughout academic careers with no correlation with age, which makes an interesting mockery of requiring the death of the Old Guard before new ideas are accepted). They also note how individuals can construct a false narrative to downplay the role of luck in their own success. That's all more convincing stuff, but the Gaussian distribution of talent needs much, much more discussion. Which abilities do this ? Are those the same abilities as the skills that allow exploitation of opportunity ? Because I can well imagine mathematical ability being absolutely uncorrelated with opportunism.

2) Simulations

The simulations are, reasonably enough, very simple affairs. A population of individuals go around for 40 years (their working lives), each starting with some money (equal for everyone) and talent (in a Gaussian distribution). Every six months they experience a chance event, which can be either lucky or unlucky. If they're lucky, then there's a chance (proportional to their talent, which never varies) that they can double their money; if they're unlucky, it halves. Or nothing can happen at all. The end result is that gives a power-law distribution of wealth and a Gaussian distribution of talent. Hurrah !

Except... this is just consistency. It isn't evidence that the world really works like this. Showing that one model works in no way precludes the success of others. Moreover, that this model works with its gross oversimplifcations in no way whatsoever implies that a more realistic version would be a mere refinement and guaranteed to do any better. It could very well make things very much worse !

The problem is that the role of talent is almost completely neglected from the model, except in exploiting opportunities. Individuals never receive any rewards except through luck, and I doubt anyone believes the situation is quite that extreme in the real world except for lottery winners and aristocrats. While they say later that the wealthiest individuals have at least the average talent (i.e. enough to exploit opportunities), rather than being mediocre, since talent by itself is never rewarded a huge factor is missing from their model. Moreover, rewards are only bestowed every six months, rather than continuously as in reality. Because people generally have these things called salaries. I think it's fair to describe the model as setup to succeed - there's no possibility this one could fail.

And talent is assumed to be proportional to the chance of exploiting opportunities. That's not so much a simplifying assumption as it is a huge leap in the dark. It could well be that a small increase in ability reaps disproportionately higher rewards, which could easily lead to a purely talent-based model giving a power law of wealth. Furthermore some individuals probably deal with success and failure assymetically; events which halve or double your capital are bizarre things to suggest; and talent probably doesn't remain constant throughout your life. Learning new skills by definition makes those skills easier to exploit.

Again, being good at something doesn't mean you're good at using it to acquire wealth, and this notion (perhaps not intended) of using wealth as a proxy for success is problematic. They take it for granted that the most talented individuals should get the most money - I suppose in a research grant context that's fair, but not necessarily in broader areas. They assume social benefits would result, but they don't say how. Quite a lot of people are probably content with moderate salaries - not everyone is in a rat race to earn as much money as possible. If they were, the world would be unbearable. They may not want to earn more money. Money is only success if that's your goal and you use it properly. Using a fortune to exploit other people isn't success, it's villainy.

While they do produce the wonderfully rhetorical line...
"...if your life is as unlucky and poor of opportunities as that of the other agent, even a great talent becomes useless against the fury of misfortune."
... they also go on to simulate changing the average level and variance of the talent distribution (they use these, without justification, to model the effects of education). These additional simulations show that both of these increase the chance of more talented individuals earning more, but they appear to be pointless : both of these are simply going to increase the number of talented individuals, hence it's guaranteed that there will be more successful talented individuals.


This might sound harsh, and perhaps it is. But I really do like this paper, I think it's quite important to demonstrate that a pure luck-based model can reproduce the observational results. I just wish the thing was turned down a few notches : there's no evidence here that luck has the strong influence the authors seem to think it does. It's an interesting consistency, but without comparable rival models, it doesn't really say very much.
https://arxiv.org/abs/1802.07068