OK, so, I think this has helped me pinpoint the root of the disagreement here: we have different beliefs about what the relevant statistical population is. Here are four possibilities, in increasing order of expansiveness.
1. The statistical population is whatever big sample one can get one's hands on.
2. The statistical population is the literal population of (working-age? adult?) people in a place of interest at a given time.
3. The statistical population is that implied by "a truncated power law", with its bounds "placed at the limits of what is possible".
4. The statistical population is that implied by a power law with only a lower bound.
(1) is what E_N apparently believes I endorse, even though it's obviously a stupid choice based on confusing sample & population. I actually contend (2). You propose (3). T&D seem to assume (4).
I introduced (3) to demonstrate that it has almost the same observational properties as (4). If the bounds are drawn widely enough that no member of a population of the given size drawn from the full distribution is likely to exceed the truncation, then that population has exactly the same properties as if drawn from the full distribution.
The proper concept of "population" is an important issue in statistics, the two main concepts being "all actually existing examples" (your (2)) and "all hypothetical examples that could be produced by the causal process responsible for creating the existing examples, in the proportions that they would be produced" ((3) and (4)). Each of these concepts has its uses, but both are called "the population". This can produce confusion. There is no such thing as the "right" concept, only the concept that is relevant to whatever the context is.
I believe that some statisticians argue that the "hypothetical" concept of population is moonshine, but I don't know if that view has a serious following. (I am not a statistician.) WWJS? (What Would Jaynes Say?)
If you just want to describe the existing population, e.g. finding what proportion of the wealth is currently owned by the currently richest 1% of the population, then you are talking about the first. If you want to make predictions about other populations, e.g. what proportion of the wealth will be owned by the top 1% if the population doubles and the Gini coefficient remains the same, then the hypothetical concept is involved: you have to calculate the expected value of the top centile on the basis that the new population is a random sample from the full distribution.
The practical point made by the Taleb and Douadi paper, put in terms of observations of actual populations, is that for a fixed value of the Gini coefficient, as the population grows, the actual top 1% will come to own an increasing fraction of the total wealth. This will happen not because of any change in the causal mechanisms by which people acquire differing wealth, but just because the population is larger and is statistically likely to explore more of the fat tail. Observing such an increase therefore cannot be used to argue that the rich are being increasingly favoured, unless a correction is first made to account for this effect.
As a footnote, I also note that the paper does not consider the issue of how accurately the power law fits the distribution of wealth, especially at its extremes. By definition, if the entire population of the country has only explored a certain way into the tail, it provides no evidence for how far the power law distribution continues beyond that point. One might justify the use of the power law as being some sort of maxent prior (I don't know if it is), but that amounts to the same thing: a profession of maximal ignorance about the whole distribution, conditional on having observed the actual population, and one would have to be willing to update to a different law on discovering that the tail actually stopped. If one was doing science, and had a well-understood mechanism that could be demonstrated to yield a power law distribution, then one would have more solid grounds for applying it.
I agree with every paragraph there but one. Unfortunately the paragraph I disagree with is the important one.
...The practical point made by the Taleb and Douadi paper, put in terms of observations of actual populations, is that for a fixed value of the Gini coefficient, as the population grows, the actual top 1% will come to own an increasing fraction of the total wealth. This will happen not because of any change in the causal mechanisms by which people acquire differing wealth, but just because the population is larger and is statistically likely to explo
Politics as gymnastics for rationalists. No one one Less Wrong is quite sure why politics is a taboo topic or how things got to be that way. What we do think we know is that politics is a great way to bring out the irrationality in people. So why not take advantage of that and use politics as a way to measure rationality? Since politics brings out the most irrationality, it should provide the strongest signal. Since there aren't useful objective metrics of how a political discussion went, we'd have to use subjective judgements by neutral third-party raters, kind of like they do in gymnastics. (In the comment thread for this post, feel free to find fights that you have no dog in, improvise a rationality rubric, and grade participants according to your rubric... let's see how it goes.)
Be a sheep. This is probably the exact opposite of what you were taught in your high school civics class. But if my friend Jane is more intelligent, more informed, and less ideological than I am, it seems like voting however Jane is going to vote is a strict improvement over voting however I would naively. It also saves me time, and gives Jane an incentive to put even more time in to carefully considering political issues since she now controls two votes instead of one. Done on a large scale, this could provide an interesting twist on representative democracy. Imagine a directed graph where each node represents a person and an edge is directed from person A to person B if person A is auto-copying person B's votes. There's a government computer system where you can change the person you're auto-copying votes from at any time or override an auto-copied vote with your own personal guess about what's best for society. Other than that, it's direct democracy... all bills are put before all citizens to vote on. Problems this might solve: