From the annals of Rhys' strange hobbies...
I finally got around to tidying up the plots from my talent-luck simulator :
https://repl.it/@RhysTaylor1/TalentVersusLuck
This is an attempt to reproduce the recent Pluchino claim that sheer luck can explain the wealth distribution in society and that talent plays only a minor role. More details and a link to my critique of the model can be found in the above link.
Now that the model is working and the graphs are comparable to the original Pluchino plots*, I've decided the first thing to do is to see how robust this result is to its own parameters. You can see a bunch of different alterations in the graphs below. The basic model is a simple world populated with "people" at fixed positions who encounter "events" moving around randomly. If they encounter a lucky event, they have a chance to double their wealth, which depends on their talent. If they have an unlucky event, then they always halve their wealth, regardless of their talent.
* The axes labels are wrong on the money histogram, which also doesn't display properly when the wealth range is very large, but meh. Also note that the slope on the wealth distribution plot has a fixed gradient for comparison to Pluchino, it's not a fit to the data.
In addition to their plots, Pluchino quote the total wealth fraction of the 20% wealthiest people in the simulation, noting that they have 80% of the total wealth. Therefore I've also plotted the fraction of the total wealth of the 20% richest as a function of time.
The results are as follows. In each case I've only changed a single parameter, to make comparisons with the original easier.
- The fiducial run uses identical parameters to the Pluchino original, and gets a very similar result. Hurrah !
Allowing this to continue for longer doesn't change things much except to make the fraction of wealth held by the richest 20% rather higher. This time variation isn't mentioned by Pluchino.
- Doubling the number of events to 1,000 alters the slope of the money distribution and the 80:20 rule is reached very quickly, and by the end of the simulation the 20% richest own nearly all of the wealth.
- Doubling the number of agents to 2,000 doesn't really change anything.
- Allowing both the events and agents to move around doesn't really change anything.
- Having the events change their luck status doesn't really change anything.
- Allowing talent to prevent bad luck doesn't really change anything, except for maybe at the extremes (the wealthiest and poorest individuals now have a greater talent difference).
- What does affect things rather strongly is how much the events move in each timestep. Changing this by a factor 2 has a dramatic difference in the slope of the wealth distribution. If they move less, then the wealth difference becomes more extreme more quickly, and if they move more slowly, the reverse happens. This choice of event movement is completely arbitrary.
The other key thing to note about this is that talent has no direct affect on wealth. This means that any trends due to talent are necessarily very weak. Also, wealth can only vary as a fraction of an individual's wealth : no-one can ever lose more than they have.
There are more many comments at musings on future improvements at the bottom of the code. There's still a whole bunch of things to play with here.
If a person states that talent matters more than luck, then I usually assume (s)he has had more of the latter than the former ;-).
ReplyDeleteI wonder if this couldn't be proven outright...
ReplyDeleteWith a large population, if we define an instance of luck as making the right choice when there is no significant reason to do so (a limited aspect of luck), it seems to me that this would translate directly into a normal distribution, simply because it is fairly unlikely that a person will be lucky in all cases, or unlucky in all cases.
Meanwhile, talent, at best is being better at finding reasons for the right decision, somewhat reducing the amount of decisions luck has to work with ... but everyone has some talent, and extreme talent will be extremely rare ... so differences in talent will mainly serve to... flatten the curve a bit? I am not sure about that bit.
If we also take into consideration that luck (circumstance) affects other things than just decisions (unlike talent), it seems like these two phenomena are of vastly different magnitudes, with talent being underpowered to begin with.
Andreas Geisler Well what you have here is a Gaussian for talent (Pluchino claims this is known observationally, but without justification) but a power law for wealth (which seems on more secure footing).
ReplyDeleteI would like to demonstrate that such a distribution can arise based largely from talent as well as luck. Not because I believe that's really the case in society, but just to show how different approaches can give similar results.
There are a number of ways to do this. My idea for the next stage is to have events have no intrinsic luck status, but have this dependent on the talent of the person they encounter. More talented people seem anecdotally to not only be better able to exploit lucky events, but have more good ideas to begin with (at least this is certainly no worse an assumption than the original model). This would then be in keeping with the style of the original whilst possibly allowing talent to have a much stronger correlation with wealth. It would also be a trivial modification to make.
Further down the line, different philosophical interpretations of what talent actually is can be explored and differentiated, e.g. the ability to make better decisions, creativity to generate new ideas in the first place (having more event particles being generated by the most talented people but then being exploitable by anyone would be interesting), differences between ideas and events, then there's ambition and generosity... all kinds of possibilities.
Realised there was a glaring problem in the code... when I tried to make talent control if an unlucky event was successful, I forgot to get rid of the old code where unlucky events happen no matter what. Actually, this makes quite a difference. Although the wealthiest 20% still have ~80% of the total wealth, a clear (but weak) trend is visible in the scatter plot of talent against money. I'm also going to try plotting what fraction of wealth is controlled by the 20% most talented, rather than the 20% richest. That would be an interesting comparison, I think.
ReplyDelete