Do you want the next president to be somebody who brags about not being a politician?

Think about that for a minute. “Politician” isn’t a popular term right now. But claiming that you’re not one when you run for president is a little like applying for a job as brain surgeon by announcing, “I am not a physician.”

This week we acquired three new candidates for the Republican presidential nomination. Two are running on the not-a-politician line. That would be Carly Fiorina, the former head of Hewlett-Packard, and Ben Carson, a retired --- yes! --- neurosurgeon.

The third is the former Arkansas governor Mike Huckabee. We have met Huckabee before, and we will have many future opportunities to discuss his remarkable transformation from poor country lad to governor of Arkansas, from likable conservative candidate for president in 2008 to the rather mean right-winger we’re stuck with now.

But today let’s consider Fiorina and Carson, who want you to elect them to the highest office in the land because they have never held elective office.

Carson (“I’m not a politician”) became a Tea Party hero when he began denouncing Obamacare (“the worst thing that has happened in this nation since slavery”), comparing American society to Nazi Germany and claiming the president resembled “most psychopaths.”

Some political experts believe he is the kind of Republican who can do well in Iowa. Is that true, Iowa? I would rather think better of you.

Fiorina is running as the anti-Hillary. (“I think if Hillary Clinton faces a woman opponent, she will get a hitch in her swing.”) She is the kind of person who tells you that when she went to college she studied philosophy, ancient Greek, Latin, French and German, then adds that she also took Italian, “But that was just for the fun of it.”

That last bit comes from her memoir, which chronicles her rise to head of Hewlett-Packard in 1999, followed by a rather inglorious firing in 2005 for reasons that she most definitely feels were not her fault.

In her first campaign video, she’s shown watching Clinton’s announcement. We now have videos of candidates attacking other candidates’ videos. Soon we will drop debates entirely in favor of tweet-offs.

“Our founders never intended us to have a professional political class,” Fiorina says, turning to the camera.

Virtually every elected president in American history --- not counting the occasional military hero --- made his way to the top by getting elected to other offices first. There are a couple of exceptions who just served in the cabinet, like Herbert Hoover. We can all look forward to hearing a candidate vow to return us to the golden days of the Hoover administration.

Fiorina’s answer is to go back to men like Thomas Jefferson (state legislator, governor, diplomat, secretary of state, vice president), who she says believed strictly in “citizen government.” The founders may not have liked the idea of a political class, but they picked presidents who were part of one. Public men, whose experience in private enterprise frequently involved running a plantation into the ground.

Fiorina, whose tenure at Hewlett-Packard included a controversial merger deal and the layoff of about 30,000 employees, is actually an excellent example of why we don’t want the country to be run like a business. The American people aren’t just shareholders. They would like their government to be efficient, and they would like the budget to balance. But they also want a lot of other stuff --- protection from evildoers, compassion for the needy, assistance in retirement, highways without potholes, good schools, a healthy environment.

Who gets what first is a political question. One that preferably would be resolved without having any internal crises so exciting that the chief executive gets tossed out of office.

People who run for president boasting that they aren’t politicians are frequently just trying to compensate for a lack of political skill. Carson (who presumably wants to run government like an operating room) is going to appeal to the folks who think the military is plotting to take over Texas, but otherwise, his only political gift seems to be for making outrageous statements. Fiorina ran for the Senate in 2010 and was beaten by Barbara Boxer, who was thought to be a vulnerable incumbent until Fiorina got hold of her, racking up a grand total of 42 percent of the vote.

On the plus side, Fiorina’s campaign produced one of the all-time great attack videos, in which her more moderate primary opponent was depicted as a Demon Sheep, portrayed by a man crawling across the grass with what looked like a wooly rug over his back and a piece of cardboard on his face. After that it was downhill all the way.

If you’re shopping for candidates with no experience in the business they want to lead, I’d say at least go for the one with the Demon. But really, there are smarter buys.