What tax deductions do you give up for flat rate?

The flat tax is a longtime Republican hobby-horse that may appear to be gaining some actual legs.

Presidential candidates ranging from Ben Carson to Rand Paul are pushing the idea for the 2016 campaign, releasing plans with varying levels of detail about how they'd transform America's complex income tax system from one that's seen as progressive to a one-size-fits-all format. In Tuesday night's GOP debate, Carson pushed his plan as being "fairer" than the current system since "everybody should pay the same proportion of what they make."

The problem is, though, to actually make a flat-tax work, some beloved tax breaks would have to be discarded, ranging from the mortgage-interest deduction to charitable deductions. That's because to even have a chance of keeping federal tax revenue at the same level after reducing the tax rate on the biggest tax payers, who are now in a 39.6 percent tax bracket, deductions would have to go.

Losing the tax code's complicated system of tax credits, deductions and loopholes is partly what makes the plan so intriguing to both the candidates and some voters. Almost two-thirds of Americans say both corporations and the wealthy don't pay their fair share, according to the Pew Research Center. About one out of five Americans say the poor aren't contributing enough in taxes.

Given those feelings that others are gaining unfairly by leveraging the tax code's quirks, the flat tax may seem both fairer and simpler than the current system, at least to some voters.

"People's antipathy toward complicated taxes isn't because their own taxes are complicated, but they think it's full of loopholes that they think other people are taking advantage of," said Roberton Williams, the Sol Price fellow at the Urban-Brookings Tax Policy Center. "You think, 'Those other people are getting away with murder, and I have to pay a bigger tax bill.'"

Even if deductions and credits are eliminated, some flat tax plans would still lead to lower tax revenue, according to analyses from tax groups. Senator Ted Cruz's (R-Texas) flat-tax plan, which calls for a 10 percent rate on all income tax, would lead to a reduction of tax revenue of almost $800 billion over the next decade, while Rick Santorum's 20 percent flat tax would reduce tax revenue by $1.1 billion over the next decade, according to analyses from The Tax Foundation.

Even though deductions are often seen as the sacred cow of the tax system, about 44 percent of Americans polled by WalletHub said they believe a fairer system would include fewer deductions.

Still, the flat tax has a long ways to go before it wins over the hearts and minds of most voters, given that the WalletHub survey found that only 24 percent supported a flat income tax.

Below are some of the deductions that would be likely to be eliminated under a flat income tax. However, some candidates have said they'd maintain some deductions, such as Rand Paul, who reiterated in Tuesday's debate that his plan would keep breaks for mortgages and charitable donations.

Mortgage-interest deduction: One of the most widely used tax breaks, it enables homeowners to deduct the interest they pay on their mortgages. Between 21 percent to 26 percent of taxpayers take the mortgage-interest deduction, according to Taxpayers for Common Sense, and it is believed to help subsidize the cost of homeownership and entice many Americans to buy rather than rent. Carson acknowledged the attachment Americans have to the tax break on Tuesday, noting, "There are a lot of people who say, if you get rid of the deductions, you ruin the American dream."

It's also a costly tax break for the Treasury, given the Joint Committee on Taxation estimates the deductions for primary residences are responsible for $405 billion in lost taxes from 2014 to 2018.

Carson noted that Americans still bought homes before 1913, before the tax break was introduced. In 1910, the homeownership rate stood at about 45 percent, compared with about two-thirds of Americans today, according to Census data.

Charitable deductions: This long-term favorite allows Americans to deduct donations given to charities, ranging from money to household goods. Some believe that the deduction encourages taxpayers to donate to their favorite charities. The tax break will mean a loss of about $192 billion in tax revenue between 2014 and 2018 tied to donations to nonprofits, according to Bankrate.

Getting rid of the tax break won't hurt charities, Carson argued on Tuesday. "The fact of the matter is, I believe if you put more money in people's pockets that they will actually be more generous rather than less generous," he said.

Still, only half of wealthy Americans said they'd maintain or increase their giving if the deduction was eliminated, according to a 2014 Bank of America report on philanthropy.

Earned income tax credit: This credit is designed to offset payroll and income taxes for low- and moderate-income workers. In 2013, about 27 million families received the credit, which is based on income, marital status and children. The average EITC was $3,074 for a family with children in 2013.

Many economists believe the credit has been a success on two fronts: encouraging work, since it's based on earnings, as well as reducing poverty.

Still, it comes at a cost to tax revenue: an estimated $353 billion between 2014 and 2018.

Health insurance: While the government taxes compensation, it excludes some employer-provided benefits, including what employers pay for workers' health-insurance premiums.

The cost to the Treasury through 2018 will be a loss of revenue of $785 billion.

Pension plan contributions: Employers who make contributions to defined benefit plans are exempt from paying tax, and the plans are exempt from income tax as the funds gain in value. Employees, however, pay taxes when they receive their pension payments in retirement.

The cost of this tax break is estimated at $248 billion between 2014 and 2018.