Talent versus luck : the story continues...
I added a couple of new sections, hope the links work, let's see..
https://docs.google.com/document/d/1TD1PCW1IG2BlBQ27GPe5Nqi5phjg4qXwhpgEfJAgbBw/edit#heading=h.oa3a1zrn8fhn
https://docs.google.com/document/d/1TD1PCW1IG2BlBQ27GPe5Nqi5phjg4qXwhpgEfJAgbBw/edit#heading=h.1rdxtmtmxpl4
(They do, but give it a second to load properly)
So far I've tried adjusting the effects of talent, the movement of the events, and the initial distribution of talent. All of these turn out to be rather important, and unlike the original claims, it can be shown that a Gaussian distribution of talent can transform into a power law distribution of wealth. I wondered just how strong this could be, if it could overcome initial disadvantages from an unfair wealth distribution. Thus far the wealth has always been initially uniform, so here I tried using an initial power law.
Admittedly I did this in a lazy and somewhat contrived way. I let the simulation run once, then reset the counter, move the agents to new random positions and run it again. As found at great length, the positions do matter : the random walk of the events meant that repeat encounters with the same events can be very significant. So moving the agents puts them in entirely new locations far from the places where fortunes were won and lost. However, any subtle trends between talent and wealth (which are present, albeit weakly) are likely to continue to be enhanced.
What happens is the agents who finish the first run as very wealthy continue to amass even more wealth. The most talented agents show a lot more fluctuation. But this doesn't seem to be due to resetting their position : the same thing happens if the standard conditions are used but allowed to run for longer. I think this is because the chance of multiple repeat encounters (which can have dramatic effects) is just low enough that they're unlikely to happen during the standard 80 timesteps but fairly probable over 160. Individuals who have much higher wealth than the rest become more probable the longer the simulation goes on, and they can dominate the end results.
More interesting might be to start with a wealth distribution that's completely "wrong", that is, give most of the money to the stupid people and start with the geniuses in poverty. It would be fun to see if altering the effects of talent can be sufficient to overcome initial disadvantages.
In the second new section, I tried allowing talent to control the reward/loss level of events, rather than the levels being fixed at doubling or halving wealth as before. Now agents can only double their wealth if their talent is maximum (1.0) and only halve it if it's zero. This gives the most talented people a much greater share of the wealth, despite, quite interestingly, there still being no obvious trend in the talent-money plot (which now has a weird fan-shaped structure which for some reason I found absurd).
Next up I think will be to allow talent to vary, i.e. agents to gain the benefit of experience.
What is the gist of this?
ReplyDeleteThere was a paper earlier this year which models how the highly unequal (power law) distribution of wealth in society could arise due to luck. They claim observational evidence for this in the form of wealth having a power law distribution whereas abilities have a Gaussian. They tested this using a numerical model that consists of virtual agents and events, which move around randomly. Agents have a talent parameter which is fixed (with a Gaussian distribution), and an initial starting wealth. When agents and events intersect, lucky events have a chance to double the agent's wealth, in proportion to their talent. Unlucky events halve their wealth regardless of their talent. They show that this can recreate the power law of wealth from a Gaussian of talent, with no correlation between talent and wealth.
ReplyDeleteI recreated their code in Python. I show that with only minor modifications, a power law distribution of wealth can arise from a Gaussian distribution of talent, whilst showing a clear correlation between talent and wealth. Thus the observed difference in distributions (which is itself open to dispute) cannot be taken as evidence that luck plays a dominant role : the same unequal distribution could be due to abilities.
The reason for the differences is that the original model several limits the role of talent while the doubling/halving of wealth essentially inevitably leads to a power law distribution. Their model actually does show trends between talent and wealth, but they're disguised by a strong scatter and small numbers.
Thus far I've been concentrating on the richest and most talented agents. I'm now starting to look at the effects on the poorest and least talented, how different conditions change their relative successes, and also how some of the results are dominated by small number statistics (i.e. a very few agents who happen to amass far more wealth than the others).
Rhys Taylor - I tend to agree that there is a strong correlation between talent and wealth, but it certainly doesn't seem to be an absolute. There are other variables. I think the starting point, wealth wise, could very likely be a variable. I think there are other environmental factors too.
ReplyDeleteOh, I completely agree. I'm looking at this entirely from the perspective of the models. Even in the most talent-dominated case there's a very strong scatter. The model is far too simple to allow direct real-world comparisons.
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