The Pluchino model is one in which wealth is generated through sheer luck. The only influence talent has is in determining if an agent is able to exploit a potentially lucky event. Unlucky events are always unlucky in their model, and there's no correlation between talent and wealth at all. They reproduce Pareto's Rule, where the 20% richest have 80% of the wealth, and show that wealth follows a power law. Although they don't show it, their model (which I have reproduced and can show gives excellent agreement with their other results) produces little or no change in the wealth fraction held by the 20% most talented people. So the rich always get richer, but the most talented are still at the mercy of chance.
I should stress that I'm not trying to examine the real-world here, just comparisons between models for the time being. Also, it's not clear (though I could easily test this) if it's actually the same individuals who get richer, or if the individuals in the richest 20% vary as a function of time while the wealth of that demographic increases.
Anyway, I made two small changes. First I set it so that unlucky events work in the same way as lucky events in the Pluchino model : the chance that they will actually cause an effect is proportional to the agent's talent. This made a small change, with a weak trend visible in the talent-money plot that wasn't visible before. Then, taking clues from the Discworldian notions of "inspiration particles", I set it so that the luck status of an event is also set to be good with a probability in proportion to each agent's talent. Events no longer have intrinsic good or bad properties but are entirely dependent on the agents they encounter. It's more like how some people seem to have lots of good ideas, rather than being entirely the victims of a capricious reality.
And that second change - I've only looked at this in combination with the first - makes a big difference. Now there's a clear trend in talent-wealth, albeit with strong scatter. Whereas the fraction of wealth held by the most talented 20% was previously flat, now it shows a very clear rise to 50% by the end of the run. The slope of the power law of wealth distribution appears to be entirely consistent with the original version.
So here we see a situation in which a Gaussian distribution of talent produces a power law of wealth distribution, while the most talented get justly rewarded. Things are getting more interesting.
I'm going to steal this line : The only influence talent has is in determining if an agent is able to exploit a potentially lucky event.
ReplyDeleteIn accordance with Weegee's Law, he of all those ghoulish crime scene photos, it's "f/8 and be there" . The "be there" part should be obvious, but the f/8 part says to get the great shot, we must have our cameras set, not optimally, but in the middle of the road for the greatest chance of success.
/sub
ReplyDeleteOh, that's cool. If I'm to boil it all down after a skim, it's that the original model shows it's possible everything is luck and talent means nothing. Your addition is that it isn't necessarily only luck, and that inspiration and luck could still factor in along with a lot of luck.f
ReplyDeleteI'll spend more time with this when my brain's less full.
That's essentially it, yes
ReplyDeleteIn both models wealth is driven entirely by events which occur at random.
In the first, talent plays a very minor role. Hence it appears that the different wealth/talent distributions are different because talent genuinely doesn't matter in that scenario.
In the second, talent plays a much greater role in the effect the events have. This gives the same distribution as the first scenario, but now talent and wealth are correlated and the most talented people get much richer than the rest. Hence the different distributions don't imply that everything's down to luck, it could also be due to what effects talent actually has.