> The billionaire pays less on $10 in marginal income than a poor person, because the taxes and benefits phase outs result in absurdly high marginal rates on the poor.

This is just patently false. The highest marginal income tax rate is 37%.

If you've read articles claiming that billionaires pay some absurdly low tax rate, those articles are counting their capital gains as income. Which is just a flat out lie, since those gains don't actually get taxed until the gains are realized, and the value of that capital can go down.