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One of the difficulties that I see comes in that it's hard to overestimate such a huge skew. If we're guessing jellybeans, your guess of 100 is countered by my guess of 900, in a jar of 500 beans. But with wealth distribution at the 85% mark, it's hard to 'overestimate' that number: it's unlikely anyone will say the top 1% controls 99% of the wealth.


Although he seems to be over-hyped (especially by himself), Nassim Taleb makes a pertinent point about this problem in The Black Swan.

Certain things in like can accurately be described by a normal distribution curve (the Gaussian or Bell Curve). What we see from the examples of crowd sourcing is a real-life version of a central limit theorem: if you have enough observations in a sample, the sample mean will approach the population mean, if the distribution of the population is normal. Many natural phenomena are normally distributed, making the bell curve a fantastically useful statistical tool.

However, Taleb goes on to note that while the normal distribution is very good with natural phenomena, it often does very poorly with social phenomena. Many social phenomena are best approximated with power law distributions rather than bell curve distributions. As such, attempting to model social phenomena with a normal distribution will end up underestimating extreme occurrences or fat tails. This is Taleb's critique of using standard inferential statistics, based on the normal distribution, to examine social phenomena such as income distributions or financial markets.

In the article, we see that the central limit theorem does not hold when the distribution that is being modeled/approximated is too skewed. (One of the statistical tests for normality measures skewness.) Things like income and wealth distributions, as social phenomena, have been shown time and again to follow a power law distribution rather than a normal distribution. Thus it shouldn't be a surprise that averages estimates of the distribution fail to capture the 'fat tail' of the top quintile.


While I agree in spirit, I disagree with your implied definition of the central limit theorem:

"If you have enough observations in a sample, the sample mean will approach the population mean, if the distribution of the population is normal."

That's not even close to the central limit theorem.


Yeah, that seems likely. I wonder if some confusion with income distribution is also a factor. People might assume that income distribution and wealth distribution are similar, so might be influenced by figures that they've heard for income--- the top quintile earning 55% is almost correct for income.




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