I objected (mildly) to the underlined:

"Tom's talking about a regressive tax rate “where the relative tax rate or burden increases as an individual’s ability to pay it decreases” (by wikipedia, of course). That’s the mathematical consequence of a flat tax rate"

I don’t understand the concept of a regressive “mathematical consequence” of a flat tax based on all income.

Did anyone else have to read the wiki definition twice? I think an example might be a good idea.

Consider a state which only has a sales tax. The tax applies to food. To make it easier imagine the citizens only buy food and nothing else.

A poor family could easily spend 25% of their income on food.

A family with a $100,000 income probably spends more on food because they can. They go out to dinner a few times a week, like to entertain, buy choice cuts of meat etc. But percentagewise they spend 18% of their income on food.

The “wealthy” family is taxed only on 18% of their income while the poor family pays tax on 25% of theirs.

Since they are both taxed at the same rate, they pay 18% and 25% in state taxes respectively. If the wealthy family ate the same food that the poor family did, their effective tax rate would drop to 6%.

The sales tax is even more regressive because the poor family probably spends their entire annual income. If there were no exemptions like there are in the real world, they would pay taxes on 100% of their earnings.
The wealthy family likely puts money in savings and investment accounts. The more they save the less they pay in taxes.

There are plenty of examples of regressive taxes; car tabs, taxes on utilities, cigarette taxes, and gasoline taxes.

The reason why people call a flat income tax ‘regressive’ is the fact that most flat tax proposals exclude capital gains, interest and dividends from taxation.

That’s insane in my opinion. Doubt Romney would think so.

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(I’ve never heard of a proportional tax. As far as I can tell it’s that same thing as a flat tax.)