Hardly anyone likes the alternative minimum tax, the provision that ended up costing Donald J. Trump an additional $31 million in federal income taxes in 2005 that a banquet of deductions would have otherwise enabled him to avoid paying.
At its most basic, the A.M.T.'s goal is simple: In a tax system with enough loopholes to fill a macramé tapestry, the idea was to ensure that the richest taxpayers were not able to skip out on paying altogether. A version was introduced in 1969 after Congress discovered that — are you ready? — 155 taxpayers with taxable incomes over $200,000 paid no tax.
But critics across the political spectrum have long complained that it has failed to live up to the promise. BothMr. Trump and the House Republicans' proposed overhaul of the code would eliminate the individual and corporate alternative minimum taxes. During his Democratic presidential campaign, Senator Bernie Sanders of Vermont suggested replacing the A.M.T. with a flat 28 percent rate on deductions for high-income households. Even the National Taxpayer Advocate within the Internal Revenue Service once called it the most serious problem facing taxpayers.
The minimum tax has gone through several iterations, but the essential intent has not changed: to limit the amount of deductions available to the richest Americans. Over the years, though, inflation has eaten away at its effectiveness — as has the exclusion of interest and dividend income, which insulates the richest Americans.
About 30 percent of households earning $200,000 to $500,000 in 2016 are being hit by the minimum tax, as are 63 percent of those earning $500,000 to $1 million, according to calculations from the nonpartisan Tax Policy Center in Washington. But only a fifth of the total earn more than $1 million and face the minimum tax.
Of the 4.7 million filers paying the A.M.T. in 2016, most either have large families (and therefore are entitled to several personal exemptions) or live in high-tax states (and can deduct the state and local taxes they pay), said William G. Gale, co-director at the Tax Policy Center. "That's not the kind of egregious tax sheltering that we think we're going after," said Mr. Gale, a member of the Council of Economic Advisers under President George Bush. "Despite its existence, some very high-income people are paying no taxes."
Kyle Pomerleau of the conservative Tax Foundation agrees that "it's not typical that the very, very wealthy pay any A.M.T."
Yet while policy makers on both sides of the aisle want to get rid of the alternative tax, their proposed solutions would have opposite effects. President Trump and congressional Republicans want to eliminate the alternative minimum tax in the context of lowering tax rates — especially for those at the top of the income ladder. The richest would benefit the most. By contrast, Senator Sanders's plan to ditch the A.M.T. is part of an effort to raise rates on the wealthiest Americans.
What is interesting about the impact of the alternative minimum tax on Mr. Trump's 2005 tax return, however, is that it does not illustrate either side's criticisms. Rather, it seems to be a rare case where the alternative minimum tax functioned exactly as it was meant to: to require a wealthy multimillionaire to pay more of a fair share. In Mr. Trump's case, he paid 25 percent of $153 million in taxable income instead of the less than 4 percent that he would have paid without it.
"Trump seems to have been hit by the A.M.T.," Mr. Gale said. "At least in that one case, it seems to have worked as intended."