I'm calling this one done. There's plenty more that could be done, but this is a good place to stop. The next step is to turn this into a paper and become a computational sociologist. Because no-one in history has ever claimed the title of Nazi space farming computational sociologist astronomer before... but I digress.
Anyway, I've gone through and redone a bunch of the earlier simulations so that the figures are now (mostly) consistent. I also wondered if the wealth fraction plots were misleading, since they select the agents of a specified wealth fraction independently at each timestep rather than following the fortunes of a fixed group of agents. Tests reveal that actually this makes very little difference.
For those who have no idea what this is, here's an abstract...
Last year there was a paper claiming that the role of luck may be underestimated. The authors claim that abilities are known to follow a Gaussian distribution whereas wealth is a power law. They demonstrated through a numerical, agent-based model that one way to get the financial power law from the Gaussian talent distribution is through luck, with no correlation between ability and money. Agents, with varying ability levels, wander around a world intersecting events which cause them to alter their wealth levels depending somewhat on their talent.
What I did was to recreate their code in Python (link's in the document). We all know that correlation doesn't equal causation. Well, it turns out their model actually provides an example of lack of correlation not equalling a lack of causation... In their model, talent only allows agents to exploit lucky events. This is a pretty weak effect but it should show up. The reason it doesn't is because their sample size was too small (so it doesn't contain enough agents with extreme high/low talents) and doesn't compare agents who experience the same levels of events. Basically, in their model, the mediocre people are more likely to get lucky compared to the genius simply because their are far more of them. If you compare populations of similar ability levels who experience similar numbers of events, the most talented always win.
I also found two ways to alter this model which produce a genuine model while still being in keeping with the spirit of the original. The first is to allow talent to have stronger effects on the outcome of events. The second is to allow talent to encourage agents to move towards areas where there are more good events and less bad ones. And a third, weird option is to allow talent to vary... but this turns out to be perverse : a talent-wealth correlation emerges, but it's only because wealth drives talent rather than the other way around.
I also discuss the ethics of meritocracies and why they're not necessarily very nice.
Enjoy...
https://docs.google.com/document/d/1TD1PCW1IG2BlBQ27GPe5Nqi5phjg4qXwhpgEfJAgbBw/edit?usp=sharing
It is well known that exceptional success has large elements of luck as well as initially favorable conditions, especially plentiful resources. If you have your nets in many good waters you are far more likely to get lucky multiple times over and get bigger catch. A talented fisherman with a rod, line, and hook is never going to beat an average joe who owns a fleet of trawlers.
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