At the New York Times, Josh Barro argues that Donald Trump is a moderate Republican.

Here's the argument: Trump's affect is much more confrontational than his (occasionally self-contradictory) policy pronouncements. Trump opposes cuts to Social Security and Medicare, hasn't signed Grover Norquist's anti-tax pledge, believes single-payer health care works well in other countries, and is skeptical of free trade.

"Trump is offering an unusual combination of extreme language, moderate policy and rudeness, and so far it’s connecting with Republican voters," Barro writes.

I think Barro's onto something, but it's not that Trump is a moderate Republican. It's that he's a moderate, full stop. And he's the kind of moderate that really exists, not the kind of moderate Washington likes to pretend exists — which is to say, his policy ideas, such as they exist, are often extreme, but they can't easily be classified as left or right.

And there's a market for that.

Why we mistake extremists for moderates

Moderates often aren't moderate at all. They're just inconsistent. And that lets them be more extreme.

This makes them different from loyal Democrats and Republicans. Partisans tend to adopt the positions held by their parties, and parties tend to adopt positions that are popular, achievable, and workable. So voters who follow their parties end up pushing ideas in the political mainstream.

But voters who aren't as interested in politics and who don't attach themselves to a party push the ideas they actually like, irrespective of whether they're popular or could attract 60 votes in the Senate or would be laughed at by policy experts. Those ideas are often pretty extreme, but because they fall both on the left and the right, pollsters often mistakes them for moderates.

The way it works, explains David Broockman, a political scientist at the University of California Berkeley, is that a pollster will ask people for their position on a wide range of issues: marijuana legalization, the war in Iraq, universal health care, same-sex marriage, taxes, climate change, and so on. The answers will then be coded as to whether they're left or right. People who have a mix of answers on the left and the right average out to the middle — and so they're labeled as moderate.

But when you drill down into those individual answers you find a lot of opinions that are far from the political center. "A lot of people say we should have a universal health-care system run by the state like the British," Broockman told me in July 2014. "A lot of people say we should deport all undocumented immigrants immediately with no due process."

One of those people, obviously, is Trump, who has both lavishly praised national health-care systems and called for mass deportations.

Trump's mishmash of ideas is part of his appeal

In a fascinating paper, Broockman and Doug Ahler look at the results of a survey that gave people seven policy options that ranged from extremely liberal to extremely conservative on 13 different issues.

On some issues, the most popular position in the one smack-dab in the middle. This is true for the environment, and for gay rights. But on most issues, the "center" of public opinion is often off-center — sometimes substantially so.

On marijuana, the single most popular position was full legalization. On immigration, it was "the immediate roundup and deportation of all undocumented immigrants and an outright moratorium on all immigration until the border is proven secure."

These are the kinds of voters Trump could appeal to: voters who hold a basket of opinions that aren't quite represented by either party. Voters who want to deport all unauthorized immigrants while also spending more money on Social Security, or voters who are skeptical of free-trade agreements even as they're virulently anti-abortion. As my colleague Matthew Yglesias wrote, these voters definitely exist:

The Trump worldview isn't just a grab bag of popular issues. It holds together. Political scientists Donald Kinder and Cindy Kam have shown that Medicare and Social Security are more popular among highly "ethnocentric" white voters, while anti-poverty spending is less popular among this demographic. Those "ethnocentric" whites are precisely the ones who are most hostile to immigrants and likely the ones who are most friendly to the anti-Obama "birther" messages that made Trump a political sensation in the first place.

Trump's ideas are sometimes very liberal, sometimes very conservative, and sometimes completely incoherent. And that's true for a lot of voters, too.

This speaks to the problem with Washington's fetishization of moderate voters, which is more often a projection of what political elites wish nonaffiliated voters wanted than a serious engagement with what people ill-served by the two parties actually want. After all, now that someone is finally representing all those moderates out there, the political establishment doesn't seem all that happy about it.