Mankiw explains his theory

Here.

The idea is that if markets are free enough, then people will mostly advance on their own merits. If we limit government to the minimum needed for free markets, then limited government will mostly protect free markets. But free markets will mostly be dominated by those who do well, and none of the less successful will tax themselves to protect a market they do not gain from.

The causality goes in reverse, if we mostly tax people who do well then they will insure that government is limited and mostly protects free markets. The evidence backs me up, central government gets smaller when progressive tax rates get higher.

I say he still has a theoretical problem, he never captured the entanglement between government and traders. The real solution is to reserve high progressive taxes for central government and encourage local government to go on a flat tax.