notes-politics-progressiveIncomeTaxWithFewFreeParameters

It would be nice to have an income tax rate that went up with income, but according to a single formula instead of having various tax brackets set by the legislature. How could this work?

One simple idea is to have the tax be a power law which is superlinear in income; eg tax = 0.1*income^1.5 or something like that. A problem with this is that income^1.5 is not scale-free; that is, the amount by which the high-income people are taxes more than the low-income people depends not just on the proportional gap but also on the value of $1.

One solution would be to change units from dollars to something like the poverty line, which is presumably set in some quasi-objective fashion.

Another solution is to change units to the sum of all reported incomes.

A third solution is to change units to the greatest gap between any two reported incomes, after sorting all incomes.