Like the Praetorian Guard of Ancient Rome, they derive significant power and wealth from the fact that they take orders directly from the elites. But since they are not the actual elite, they must endure intense vetting and culling at every level, and work hard often in harsh conditions (also like the Praetorians of old).

So the comparison in the original PDF is not exactly apples to apples.

Usually the claim is that the people at the top inherited their position rather than earning it, and that others didn't have a fair shot at getting it.

Obviously the latter claim is a far better narrative.

We're talking about the "New Aristocracy". In extremis that's where you're either in the elite, or barely subsisting. It doesn't matter how meritorious the admissions to the upper class are - it's an awful way to live for nearly everyone, and where it's been implemented it's been marked by abuse and stagnation.

From a motivational standpoint, of course the incentives of a great reward matter. But there has to be a reason for everyone from 2nd place downward to participate.

You are conflating inequality with poverty. To recognize that they aren't the same thing, come visit the highly equal society of India or Bangladesh.

Also, the more you make a curve convex (and increasing), the more incentives it creates for everyone. Proof: convexity = u''(x). Increasing u''(x) increases u'(x)=int u''(x) dx. Since u'(x) is incentive, the proof is complete.

https://en.wikipedia.org/wiki/List_of_countries_by_income_eq...

And while alleviating absolute poverty is great, the point I'm making is that a large middle class is a tremendous driver of many positive societal outcomes - politically, economically, and socially.

You can't just take a steepening reward structure out of that context.

India UNR/P = 8.6, WB Gini = 33.6, CIA R/P = 8.6, CIA Gini = 42.8

USA UNR/P = 15.9, WB Gini = 41.1, CIA R/P = 15, CIA Gini = 45

I have no idea what you mean by "middle class" - there are many possible definitions.

Now that your claims about incentives and your conflation of poverty and inequality are debunked, you still believe that inequality is somehow bad? What facts (if any) would cause you to reject this belief?

And you really believe that you've "debunked" my claims by referencing what happens to a pure mathematical abstraction? I'm not even sure how to address that. You can't honestly believe that models have influence over reality, and not the other way around?

And I'm not claiming that inequality is bad. It's necessary, for example, to accommodate risk. All I've said is that it matters how much inequality there is, and having too much distorts things. The only claim I've made as to what constitutes too much is the level found in aristocratic societies.

Are you arguing the opposite, that the degree of inequality has no great effect on a society? Or that the repercussions aren't negative as a country approaches the level that is marked by the formation of an aristocracy?

You made a mathematical claim about a mathematical construct (incentive): From a motivational standpoint, of course the incentives of a great reward matter. But there has to be a reason for everyone from 2nd place downward to participate.

I gave a mathematical response. If you don't believe that incentives govern behavior, then why did you bring them up and make incorrect claims about them?

The only argument I make is that I've seen no convincing evidence that inequality matters much. At best I've seen a few cross-country correlations between inequality and other bad things. Even left wing types don't find such evidence very convincing, or at least they don't after I replace the X axis with "% single mothers" or "% black people" (increasing both the r^2 and social unacceptability of the conclusion).

You argue that, by mathematical definition, a steepening Pareto curve will increase motivation for everyone on it, and that: "Now that your claims about incentives and your conflation of poverty and inequality are debunked[...]"

Have you considered the possibility that in the actual world the curve doesn't strictly conform to the mathematical one? That it flattens early, or that the whole thing is translated downward? Or that it's not a Pareto curve but one that is similar? Or that (as has a lot of evidence behind it) that socially-based incentives are sensitive to relative inequality, not absolute? I pointed to an abstraction for illustration, and you made claims based on that abstraction and called it proof of the real world.

This is economics: there's no such thing as "debunking", there's no such thing as "proof". There's evidence, and there's models that maybe explain some aspects of it better than others, from a very narrow view. Models can't demonstrate anything, all they can do is suggest experiments to be carried out in the actual world, at which point what happens there trumps any claims that they may have made.

The only thing we really have is comparative studies, across nations and through time. Everything else is just fooling ourselves with our own metaphors.

So when you discard the only thing that we've got as "a few cross-country correlations between inequality and other bad things", what exactly are going going to replace that with, your theories? It must be nice to live in such a simple world.

No, I didn't. The pareto curve is not the reward curve, which is what we were discussing.

Have you considered the possibility that in the actual world the curve doesn't strictly conform to the mathematical one?

I was explicitly assuming your hypothetical was true, and showing it doesn't support your conclusion. That's a conditional claim.

I pointed to an abstraction for illustration, and you made claims based on that abstraction and called it proof of the real world.

No, I called it proof that your argument is bunk. If you want to make an argument based on some complicated theory of socially-based incentives, you need to actually cite such things.

So when you discard the only thing that we've got as "a few cross-country correlations between inequality and other bad things", what exactly are going going to replace that with, your theories?

Tell me; if I can dig up a graph with a better r^2 and a different label on the X axis, will you change your views on inequality? I.e., if I show you this graph, will you say "oops, I'm wrong, inequality is not the issue, I guess $new_x_axis_label is the real problem here?" (Note that I will of course make $new_x_axis_label something socially unacceptable.)

If not, then your argument is simply dishonest. You are criticizing me for being unpersuaded by evidence that you would also find unpersuasive.

Scaling u''(x) doesn't change inequality anyway (as defined by measurements of u(b)/u(a) or the Gini index) so it's a poor stand-in for the kind of convexity people are complaining about.

Inequality is most definitely NOT defined by ratios of a utility function. The convexity of the OP was in the utility function; he seemed to believe that convexity of reward (and hence of utility, assuming u(reward) is monotonic) would only increase the reward for those at the top.