Republican presidential candidate Donald Trump, speaking at a Dec. 12 town hall meeting in the Convocation Center on the University of South Carolina. (Richard Shiro/AP)

Donald Trump is one of the most extreme presidential candidates to gain widespread support in contemporary American politics. Despite championing policies like the end of birthright citizenship, mass deportation of undocumented immigrants, and a registry of Muslims living in the United States, Trump has consistently polled atop the Republican field since July. A popular perspective thus attributes Trump’s success to a “right wing fringe” of GOP voters.

But this conventional wisdom misses something important: Trump meets the textbook definition of an ideological moderate.

Trump has the exact “moderate” qualities that many pundits and political reformers yearn for in politicians: Many of Trump’s positions spurn party orthodoxy, yet are popular among voters. And like most voters — but unlike most party politicians — his positions don’t consistently hew to a familiar left-right philosophy.

At Tuesday night’s debate, for example, Trump flanked the Republican party on the right and left — calling for killing civilians and saying the Iraq war was a mistake because it diverted money from domestic spending priorities. CrowdPAC thus lists Trump as far more moderate than the other Republican candidates.

How can Trump be both a moderate and an extremist? Our research has shown why support for extreme policies and so-called “ideological moderation” often go together — people who appear “moderate” on a left-right ideological spectrum often have extreme views on individual issues.

Here’s how this works: Measures of voters’ left-right “ideology” primarily capture the frequency with which their opinions fall on the liberal or conservative side on different issues. Many Americans’ policy opinions are mixed bags of liberal and conservative positions, earning them the distinction of being called “ideological moderates.” Just like Trump.

But, as Trump shows, holding ideologically mixed positions across issues, which political scientists call “ideological moderation,” doesn’t guarantee that those individual policy views are moderate at all. Donald Trump — and, we will show, his supporters — thus illustrates an important lesson: We should not confuse moderation in the general ideological sense with moderation on actual issues.

Indeed, when we have investigated ideologically moderate voters’ views on particular issues, we often found these views far from moderate. The very same people who support extremely conservative immigration policies also often favor extremely liberal policies on taxes and social spending, yet these people are called “moderates” because their extreme positions aren’t consistently on one ideological side.

In a recent working paper, we show that these ostensibly moderate American voters don’t care much about whether candidates are ideologically moderate per se. What they do want is politicians to represent the contents of their own mixed bags of views. As others have noted, our research has long made the case that many voters want a candidate with eclectic but extreme positions on key issues, especially the very ones where Trump has staked out extreme stances.

When we wrote our paper there weren’t many candidates out there who took the extreme issue positions we argued were popular among voters, so we had to rely on experiments and artificial candidates instead. Skeptics wondered whether a candidate that appealed to a mix of the extreme views on the left and right could really gain much support.

Now that Donald Trump has arrived, we can see how well our ideas explain an actual extreme candidate’s support. To do so, we surveyed Americans in October and computed a measure of respondents’ left-right ideology based on their pattern of responses across issues. We also asked questions about two policies where Trump has departed from party orthodoxy: immigration and taxes.

The results showed that the ideological extremists in the Republican party are not more likely to support Trump’s extreme candidacy; in fact, if anything Trump supporters are more likely to be ideological moderates, just like the candidate himself.

But, despite this pattern, moderate views on actual issues do not fuel Trump’s support. On the contrary, we find (as did Michael Tesler) that conservatism on immigration strongly predicts Trump support.

Surprisingly, however, so do liberal views on taxes. Although it’s unclear exactly what Trump’s tax plan is, Trump’s soak-the-rich rhetoric and failure to sign a pledge saying he won’t raise taxes have led many to characterize him as more liberal than his party on this issue. And indeed, Republican voters with liberal views on taxes are more likely to be Trump supporters.

These patterns underscore a central implication of our work: It is misleading to call politicians “moderate” or “in touch with public opinion” based simply on their position on a left-right ideological spectrum or whether they break with their party. This has a few important implications.

First, voters do not inherently care where candidates are located on a left-right ideological spectrum or whether they break with party orthodoxy. If voters primarily cared about these qualities, Trump and his libertarian rival Senator Rand Paul should have more similar levels of support because they both espouse ideologically mixed (or “moderate”) platforms and break with their party on many issues.

But Trump’s popularity, just like the popularity of his positions on particular issues, far outstrips that of Sen. Rand Paul (R-Ky.). It’s probably no accident that the issues where Trump, unlike Paul, has broken with the Republican Party are the very issues where his positions are more popular than the party’s orthodoxy. The candidates’ positions on individual issues like these is what voters examine, not candidates’ left-right ideology or whether candidates simply break with their party at all.

More fundamentally, the fact that Trump and his supporters qualify as moderates on a left-right scale illustrates just how misleading popular definitions of ideological moderation are. This misleading definition of moderation has led many who are concerned by polarization to recommend amplifying the voices of ideologically moderate voters and empowering ideologically moderate candidates.

However, the very candidates whose positions and supporters appear “moderate” in terms of left-right ideology might not be so moderate on actual issues. Empowering ideological moderates might just empower more Trumps.

As a corollary, pundits should not be so quick to assume that existing ideological moderates like Olympia Snowe are particularly well-attuned to general public opinion, either. Like ideologically moderate voters, ideologically moderate politicians can have wildly differing political views on different issues which may or may not reflect what many Americans want. Ideological moderation just doesn’t mean much.

It remains to be seen whether Republican party elites will keep Donald Trump from winning their party’s nomination. But as they struggle to do so, an irony bears note: The very elites so often lambasted for pulling politics to the ideological extremes now represent a main line of defense against extremism reasonably defined.

Doug Ahler is a PhD candidate at the University of California at Berkeley. David Broockman is an assistant professor at the Stanford Graduate School of Business. This post draws on their paper “Does Polarization Imply Poor Representation?” Replication material for this post is available here.