[yummyfajitas]

Because the wealthiest 10% paying a larger share of the total taxes is compatible with each of those wealthy individuals paying a relatively small individual percentage of their income in taxes...

Did you read the linked article? It measures the ratio (% of taxes paid) / (% of income earned). In this US, this ratio is 1.35%. In Norway, it's 0.95. Inequality would increase the denominator, not the numerator. With a flat tax (at 35%, 47% or 59%), this ratio would always be 1.

Perhaps you are confusing overall tax burden (taxation levels) with progressivity (the derivative of tax rate w.r.t. income)?

As for positional/signalling goods/status (e.g., a Porsche that no one else owns), they are always a zero sum game. There is no avoiding this. The most you can do is equalize incomes and allow status to be unequally distributed via other mechanisms (good looks, athletic ability).

[rwl]

> Did you read the linked article? It measures the ratio (% of taxes paid) / (% of income earned). In this US, this ratio is 1.35%. In Norway, it's 0.95. Inequality would increase the denominator, not the numerator.

Right, sorry, I should have been more clear. Yes, inequality increases the denominator. But what I meant was that I would expect the numerator to grow faster than the denominator, at least some of the time, as both inequality and regressivity increase. So I would expect the ratio to be higher for some countries with higher inequality and relatively less progressive taxes (it seems likely that the U.S. is one example). Thus, one should not necessarily understand a higher ratio as indicating a more progressive tax system, which is what the original commenter was claiming.

[yummyfajitas]

But what I meant was that I would expect the numerator to grow faster than the denominator, at least some of the time, as both inequality and regressivity increase.

Not possible. Define P = progressivity index = tax rate for top 10% / tax rate for bottom 90%. Define R = income of the top 10%, B = income of the bottom 90%, and inequality I = R/B. Tax paid by the rich = RP x tax rate for bottom 90%.

% of taxes paid by rich = RP / (RP+B) = IP/(IP+1). (Tax rate for bottom 90% factors out)

(% tax paid by rich) / (% income earned by rich) = [IP/(IP+1)] [(R+B)/R] = P(I+1)/(IP+1)

Simple calculus shows this quantity always increases with increasing P and decreases with increasing I. So a higher ratio implies either a) a more progressive tax system or b) less inequality.