A popular Facebook and Twitter game asks friends to post an unpopular opinion. Here is an unpopular fact: Tax reformers cannot deeply cut income taxes for lower-income families, because they already pay no collective income tax.

Tax reform is intended to bring simplification and economic growth. Yet many commentators seem interested in only redistribution.

This explains the teeth-gnashing over the Tax Policy Center estimate that the Republican tax blueprint would save the median family $420, but a family in the top income quintile $10,610.

While that sounds unfair, consider this: The top-earning 20 percent of households currently pay 88 percent of all federal income taxes. So even a proportional income tax cut will save them the most money.

In 2013 (the latest data year available), the top 20 percent of households paid $1.2 trillion in income taxes. The next 20 percent paid just $175 billion. The bottom 60 percent collectively paid $0. Actually, the IRS paid them $17 billion, thanks to refundable tax credits.

Put another way: Household income tax bills averaged $47,000 for the top income quintile, $7,000 for the next quintile and negative $200 for the bottom 60 percent.

How are tax reformers supposed to target most income tax savings to those with no income tax burden?

Obviously, some wealthy families escape taxes and some poorer families face painful tax burdens — which should be addressed. However, the aggregate tax savings will align with the aggregate tax burden.

By the way: In anticipation of knee-jerk dismissals of “right-wing lies and propaganda,” all this data is publicly available from the nonpartisan Congressional Budget Office (the same group cited as gospel in the recent health coverage debates). The Obama Treasury produced similar data, which no serious economist has challenged. It cannot be wished away simply because it conflicts with populist narratives.

Nor can this extreme progressivity in our tax code be dismissed as the inevitable result of the rich earning all the income. We can adjust for income inequality by comparing the ratio of taxes paid to income earned.

The richest 1 percent pays 38 percent of all income taxes while earning 15 percent of all pre-tax income. Thus, their share of the income taxes is 2.6 times their share of the income earned. For the top 1 percent and top 20 percent of earners, this ratio has grown steadily since the 1980s — meaning their share of the income taxes has grown significantly faster than their share of the income earned (surprisingly, the top 1 percent’s share of the income remains at 1998 levels).

In fact, the Organization for Economic Cooperation and Development in 2008 showed that the United States had the most progressive tax code of all 24 countries measured. And that doesn’t even count America’s 2013 upper-income tax hikes, or Europe’s steep value-added taxes, which each widen America’s progressivity lead over Europe.

European governments tax the rich more heavily than America does — yet Europe’s tax burden is flatter because it also slams the non-rich with a VAT and high income (and payroll) taxes. By contrast, America has steeply cut taxes for the non-rich.

Actual tax returns show that the top 1 percent and the top 20 percent pay average effective income tax rates of 23 percent and 16 percent, respectively — nearly the same as in 1979. Yet the average rate paid by the bottom 80 percent of families has fallen from 5.4 percent to 0.1 percent. Millions of low-income families were removed from the income-tax rolls by the expanded Earned Income Tax Credit, refundable child credit and reduced, 10 percent bracket (thank you, George W. Bush).

Yes, families pay payroll taxes — often exceeding their income tax burden. But payroll taxes finance the Social Security and Medicare systems, which these families will benefit from later (and cutting payroll taxes means fewer benefits at retirement). Should the entire rest of the federal government be funded by only 20 percent of families? Ten percent?

Adding all federal taxes together, the top-earning 20 percent fund 69 percent of all federal revenues.

The point is not that progressivity is harmful or should be reversed. Rather, it mathematically limits the low-income taxes left to cut.

It’s easy for politicians, populists and panderers to pretend that the middle class pays all the taxes, and thus deserves the largest tax savings. But the first assertion is demonstrably false, which makes the second mathematically impossible. Champions of progressive income taxation have won. The bottom 60 percent have seen their collective income tax reduced to zero. In tax reform, there are no more winnings left for them to claim.

Brian Riedl is a senior fellow at the Manhattan Institute.

Twitter @Brian_Riedl