More fun with the talent-luck simulations...
https://repl.it/@RhysTaylor1/TalentVersusLuck-1
I was wondering what would happen if talent was allowed to vary. Most people are capable of learning and it's often said that mistakes are more valuable than successes. So I tried implementing a variety of ways in which talent can change, including the two examples shown here. The basic approach is to allow talent to vary whenever an event occurs. In these examples, talent increases either when an agent is unlucky (top) or lucky (bottom). The effects of talent are limited in both cases to allowing agents to exploit lucky opportunities, the standard behaviour proposed in the original model - the only thing which varies is the distribution of talent.
The top plot shows that if talent increases when agent's "learn" from their mistakes, then there's a an anti correlation between talent and wealth. The least talented (faint red line in the left hand plot) possess a roughly constant share of the total wealth whereas the most talented generally lose out. The slope of the wealth distribution is the same as in the non-varying talent case while the distribution of talent can be seen to be non-Gaussian at the end (I capped the maximum at 1.0, hence the spike). If anything, this mock-society is anti-meritocratic, rewarding the stupid people more than the brightest.
In constant, if good events are rewarded, the effects are totally different. The wealth of the most talented evolves in almost exact parallel with that of the richest (solid red line in the leftmost plot) whereas the least talented always lose out.
When I saw this, I thought, "hmmm, that's funny", and then I had to go out. It was a very counter-intuitive finding. Since talent plays only a very limited role in this situation at any timestep, I didn't expect to be much of a shift. I certainly didn't think that increasing talent based on good results could result in a strongly meritocratic but highly unequal result whereas learning from experience should make the most intelligent people fail miserably.
A few hours later while walking home in the rain and rather tipsy, I realised what was going on, and I think this is a nice example - if more were needed ! - of correlation not equalling causation. I know that talent has only a very little role in this setup, and that doesn't change throughout the simulation. Consider the top set of plots. Here, every time a bad event happens, the agent loses money. But their talent is also increased. The more money they lose, the more talent they gain. The role of talent is so limited that this doesn't actually help them very much at all : sure, they're now better exploiting good opportunities when they do come along, but if those don't happen then they just keep getting poorer and smarter. The overall trend is far more reflective of the distribution of talent than it is of the effects of talent. If talent is allowed to affect the results of negative events and the status of the events themselves, then a positive correlation re-emerges.
I hope by now it's clear that how this applies to the real world is anyone's guess. I'm using these labels of talent and wealth more for convenience than anything else - they should not be taken literally, the model is nowhere near that sophisticated.
I didn't realize that the write up last time was over 20 pages. Very engaging. At least for me.
ReplyDeleteWee edits: s/constant/contrast/, s/talent's/talent/
ReplyDeleteAny thoughts on the glitch at the end of the most-talented line at upper left? Both the rise and the decay seem surprisingly fast, but particularly the former.
Dante Johnson Thanks !
ReplyDeleteGreg Roelofs I think that's "just one of those things". When I tried running the standard conditions for longer, I found that usually things get a bit chaotic. I think there's a low but non-negligible chance that one (or a few) agents happen to encounter a series of events in rapid succession, which can cause them to become very much wealthier than everyone else - so much so that they can even dominate the overall total. I've reduced this by putting in an upper limit : not enough to affect the overall trends, but enough to prevent extreme outliers. Still it's possible for a few to get very lucky/unlucky, especially since the distribution of agents is random in space but not in time.