I asked a couple years ago, Who Pays Taxes? Are They Doubly-Progressive?
On Paying Our “Fair Share” : The Freeman: Any set of progressive tax rates is arbitrary. If the set 10%, 20%, and 30% is unfair, would the set 20%, 30%, 50%, and 90% be fair? How could anyone ever know? It’s all a matter of opinion—or a matter of politics. It’s therefore difficult to see how any progressive tax can be justified at all. There is certainly no scientific rationale for such a tax. Teddy Roosevelt and Barack Obama to the contrary notwithstanding, a progressive income tax is unfair precisely because it is deeply and unavoidably arbitrary. Applying the same percentage tax rate to all taxpayers, in order to raise a given amount of tax revenue, is indeed also an arbitrary rule. But it is a whole lot less arbitrary than imposing any one of an infinite set of progressive tax rates that could raise that same tax revenue.
Who Pays Taxes? Is It Fair?