That's pretty interesting, but I always find myself wondering how to interpret this. Is the wealth distribution unfair, or are people just clueless about wealth distribution? Probably both. I feel pretty clueless about it myself.
To be honest, the very way the data is presented seems unintuitive to me. I mean, I'm a physicist, so what I consider "intuitive" is all out of whack. But seriously, the wealth owned by the top 20%? I have very little sense of what to expect from such a number. It has to be somewhere between 20% and 100%. 84% seems like too much, but what do I know?
If I were to pick a wealth distribution, I would start with a model, and from there calculate the percentage owned by the wealthiest 20%. So here's my model: wealth has a normal distribution on a log scale.* People who are one standard deviation above the mean own N times more than the median. People who are one standard deviation below own N times less than the median. N is a number that we can choose. For graphing purposes, I am choosing N=2.718 (Euler's number).
In the above graph, the median wealth is 1, meaning that half of people earn more than that and half earn less. But the mean wealth is actually more than that, since the distribution is skewed. And the most common amount of wealth (called the "mode") is about 40% of the median.
The next step is to translate this to the amount of wealth owned by the top 20%. So that's what I did for a few values of N:
(Note that though my plot has similar colors to the one at top, they aren't exactly the same since I split the top 20% into three groups.)
I showed N=6.5 because that's the number that seems to correspond to reality, according to Norton & Ariely. I showed N=2.718, because that's the number I would have guessed if I had never seen the real data. I showed N=1.5, because that's what strikes me as a "fair" distribution. In other words, I would think it was fair if people who are one standard deviation above the median own 50% more wealth. But in reality, they earn more than six times as much wealth.
I was surprised how similar my bar graph is to the one in Norton & Ariely. I'm quite sure that most people answering this poll have no understanding of normal distributions or log scales, and I was all set to conclude that people are clueless. I'm surprised to find that I agree with the popular opinion, because I think N=1.5 seems ideal.
Of course, the "ideal" value of N is completely arbitrary. What do you think is an ideal value of N? If you like, I can calculate the resulting wealth distribution.
*Some technical details: A normal distribution means that the probability density is exp[-y2/(2*log(N)2)]. But here, y is not the amount of wealth, but the log of the wealth. When I transform from a log scale to a linear scale, the probability density becomes exp[-log(x)2/(2*log(N)2)]*1/x, where x is the ratio of the wealth to the median wealth. This is the function I have plotted in the graph. This is, by the way, just about the simplest model imaginable.
