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TheAncientGeek comments on Political ideas meant to provoke thought - Less Wrong
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Apple's and oranges. Virtually nowhere is socialist in the one party state sense.
The point is that Europe is more socialist than the US.
Europe is also more equal than the US. The counterargument put forward to that is that the Iron Curtain countries were not particularly egalitarian. My countercounterargument is that social democracy is not commensurable with single party state socialism.
That is precisely the claim being disputed. In particular, as Taleb points out in the document I quoted in the great-grandparent, when you stop trying to use static measures of inequality and instead base it on the amount of turnover at the top, you see that Europe is much more unequal (almost an oligarchy) than the US.
Europe is more equal on empirical measures such as the Gini Coefficient.
The comment in Talebs aphorisms does not refute that, because it is not evidence based. Instead, Taleb is making some sort of circular, ideology driven argument...that Europe is "socialist" and under "socialism" the state runs everything., therefore no healthy competition, therefore stasis..but no. in Socially Democratic Europe, the government does not intervene in the boardroom.
What's more, the empirical evidence actually contradicts Talebs untested expectation:
"according to the latest Global 500 CEO Departures™ study by global public relations firm Weber Shandwick, departing European chief executives were also more likely to be forced out of office than North American and Asia Pacific CEOs during this 2007 time period."
http://www.reputationrx.com/Default.aspx/CEOTURNOVER/GLOBAL500CEODEPARTURES%E2%84%A2andCEODEPARTURESSTUDY%E2%84%A2
Here is Taleb's paper about the problems with measures like the Gini Coefficient.
If I understand Taleb correctly, his objection is that if X's distribution's upper tail tends to a power law with small enough (negated) exponent α, then sample proportions of X going to the distribution's top end are inconsistent under aggregation, and suffer a bias that decreases with sample size. And since the Gini coefficient is such a measure, it has these problems.
However, Taleb & Douady give me the impression that the quantitative effect of these problems is substantial only when α is appreciably less than 2. (The sole graphical example for which T&D mention a specific α, their figure 1, uses α = 1.1). But I have a hard time seeing how α can really be that small for income & wealth, because that'd imply mean income & mean wealth aren't well-defined in the population, which must be false because no one actually has, or is earning, infinitely many dollars or euros.
[Edit after E_N's response: changed "a bias that rises with sample size" to "a bias that decreases with sample size", I got that the wrong way round.]
Um no. They're not well defined over the distribution, they will certainly be well defined over a finite population.
You seem to be confused about how distributions with infinite means work. Here's a good exercise: get some coins and flip them to obtain data in a St. Petersburg distribution notice that even though the distribution has infinite mean all your data points are still finite (and quite small).
I'm lost. A statistical distribution characterizes a population (whether the population is an abstract construction or a literal concrete population); if the mean isn't well-defined for the population it oughtn't be well-defined for the distribution allegedly characterizing the population.
Taking annual income for concreteness, the support of a power law distribution would include, for example, $69 quadrillion. But no one actually earns so much (global economic activity, denominated in dollars, is simply too small), so the support of the actual annual income distribution must exclude $69 quadrillion. Consequently the actual annual income distribution and the power law distribution cannot actually be the same distribution; they have different support.
In the case of the St. Petersburg distribution one defines an abstract data-generating process which, by construction, implies a particular distribution with infinite mean. In the case of people's incomes or wealth, by contrast, we know that the output of the data-generating process is constrained from above by the size of the economy, so the resulting population (and the distribution representing that population) must have finite mean income and finite mean wealth. (It's as if we were talking about an imperfect real-life instantiation of the St. Petersburg process where we knew the casino had a limited amount of money.)
Every actual population differs from a parameterised mathematical function with few parameters, and for pretty much anything you can measure, if the mathematical distribution has infinite support, there will be some reason that the population cannot. But the question to ask is not, are they different, but, does the difference make a difference?
The way to answer this question is to repeat the analysis in the paper Eugine cited using a truncated power law. The bounds must be placed at the limits of what is possible, not at the accidental maximum and minimum values observed in the current population, as the point here is that the population is not fully exploring the tails.
I have not done this, but I did once do a simulation for the Cauchy distribution (which has no mean), finding empirically the standard deviation of the mean of samples of size N. Each individual set of N values has a mean, but they will be wildly different for different samples. Increasing N does not reduce the effect for any practical value of N (and I did this in Matlab, which is optimised for fast number-crunching on arrays). This is completely different from what happens for sample means drawn from distributions with finite mean and variance, whose means converge with increasing N to the population mean.
For my experiment with the Cauchy distribution, not a single one of my samples had to be rejected due to exceeding the limits of finite precision arithmetic. The absence of infinite tails from the samples made no difference to the experimental results, even though it is the presence of those infinite tails that gives the Cauchy distribution its lack of moments.
This may look like a paradox. You have two distributions, the Cauchy distribution and its truncation at 1e50 or wherever. The former has no moments, and the latter does. Yet the empirical behaviour of samples drawn from the latter agrees with mathematical analysis of the former, even though in the latter case the standard deviation of the sample mean must converge with increasing sample size to zero, and in the former case it remains infinite.
The resolution of this paradox lies in the fact that as the variance of a distribution that has a finite variance becomes larger and larger, the rate of convergence of sample means becomes slower and slower. For the Cauchy distribution truncated at +/- X and a sample size of N, for large X and N the variance of the sample mean is proportional to X/N. If we take the limit of this as X goes to infinity, we get infinity, independent of N. If we take the limit as N goes to infinity we get zero, independent of X. The behaviour found when both X and N are finite will depend on which is bigger. When X is very large, even the entire population (conceived as a sample from an underlying data-generation process) may not give a good estimate of the distribution mean.
Taleb and Douady's point is that for a power law distribution, wealth owned by the top 1% is subject to this phenomenon. A larger population will explore more of the tail of the distribution, and unlike the normal distribution, the tail is fat enough to give a different value for the statistic. The "true" distribution does not have to actually have infinite support, for the entire population of a country to be insufficient to explore the tails.
The authors draw the implication that as both population and technological development grow, the top 1% will be found to have larger proportions of the wealth, not because of any change in the mechanisms of society to favour them, but because more of the sample space is being explored. "So examining times series, we can easily get a historical illusion of rise in wealth concentration when it has been there all along." (Presumably one could quantify the effect and correct for it.)
A possibility that the paper does not raise is that instead of calculating the actual wealth held by the actual top 1%, you could estimate the Gini coefficient from the whole population, and calculate a theoretical 1% wealth. This may be substantially more. The authors suggest that Pareto's empirical observation of the 80/20 rule, which implies 53% wealth held by the top 1%, might actually correspond to a figure of 70%.
This could be spun in opposite ways. If you want to boom freedom and boo levellers, you can point to this and say there's always more room at the top. If you want to boom equality and boo the rich, you can say that the true situation is even worse that the 1% figure says, indeed that the figure is a systematic underestimate, a piece of evil propaganda used by the rich to conceal the true extent of the inequality inherent in the system.
Take your pick.
No, I think the argument Eugine is refering to is that more companies in the SAP 500 weren't there 50 years ago then corresponding European indexes. It's a data driven argument. I'm however not sure that it measures "equality".
Me neither. Turnover in companies isn't the same as turnover of CEOs....and the relationship between CEo stability and oligarchy, in the polsci sense, is rather murky too.