Even after a third-place showing in South Carolina on Saturday, Ted Cruz is one of three Republican presidential candidates — along with Donald Trump and Marco Rubio — who still has a relatively straightforward path to the nomination. But by nominating someone who is among the most conservative members of the Senate (and is perceived as such), would the GOP be setting itself up for defeat in November?

For the Cruz team, the answer is a clear “no.” Cruz staffers argue that they can win by prioritizing mobilizing the conservative base over appealing to swing voters. In their telling, Mitt Romney’s 2012 campaign targeted chimerical swing voters and missed the true prize: conservatives. As Eliana Johnson reports in National Review, “Cruz and his team have talked endlessly about the power of these missing conservative voters, and their theory remains the subject of considerable skepticism in the political class.” Count me among the skeptics.

There is a logic underpinning the base-focused strategy. In a polarized age, there simply aren’t many swing voters up for grabs, and each party has a large and reliable base with millions of voters whose main choice is whether or not to go to the polls. A recent article by political scientist Corwin Smidt confirms the endangered status of contemporary swing voters.

Still, whether candidates can win by focusing on base voters depends on their relative capacity to mobilize their base and to persuade undecideds. And thanks to math, persuasion has a built-in advantage over mobilization in two-party contests: When you persuade a voter, you reduce an opponent’s vote total while increasing your own. When you mobilize a voter who would never have backed the opposition, you add a vote to your own tally without touching your opponent’s.

Even with that math, it’s in some ways a false choice. Campaigns almost always engage in both persuasion and mobilization. But Team Cruz’s critique of the Romney campaign — and of the GOP establishment — is that it should have put more stock in mobilizing conservatives. In part, they point to John Sides and Lynn Vavreck’s data showing that voters in 2012 saw Romney as closer to them ideologically than Obama. In this view, to pursue base voters is simply to follow Obama’s 2012 road to victory.

To justify a base strategy, the Cruz camp also seems to draw on RealClearPolitics analyst Sean Trende’s argument that 2012 saw a drop-off in voting by non-Hispanic whites. That echoes Rush Limbaugh’s post-election take as to why Romney lost: “My best guess at what happened was, why the white vote stayed home, they didn’t think the Republican Party was conservative enough.” As Trende notes, though, it is one thing to say that whites stayed home, and quite another to say that conservative whites stayed home. And that’s an empirical question, so let’s go to the data.

One way to determine whether demobilized conservatives cost Romney the 2012 election is to look at the Institute for the Study of Citizens and Politics panel that Diana Mutz and I have been conducting with other colleagues. The nationally representative panel allows us to observe the same Americans from the 2008 primaries to the 2016 primaries. The data includes respondents’ vote histories, so we can look at how turnout varies by ideology and election year.

In the chart below, I plotted the share of respondents who voted in the 2008, 2010 and 2012 general elections (y-axis) by their self-reported 2008 ideology (x-axis). Ideology is reported on a seven-point scale, from “extremely liberal” (1) to “extremely conservative” (7). Each dot shows the average turnout. The vertical bars show 90 percent confidence intervals. They are much wider at the ends of the spectrum, because there are relatively few “extreme” liberals and conservatives in the survey. Consistent with other research, there are more respondents who are conservative than who are liberal.

Let’s start with the left panel, which plots the ideology-turnout relationship in 2008, when John McCain ran against Barack Obama. In general, we see the expected U-shaped pattern: Just like people who don’t care much about the outcome of a baseball game are less likely to go, people who are more moderate ideologically are less likely to vote. As Jan Leighley and Jonathan Nagler show in a recent book, perceiving that the parties differ is a motivation to turn out. The 3 percent of the sample who identify as extremely conservative do appear to vote at a lower rate than other conservatives, but the sample size is so small that we are very uncertain about the precise estimate.

In 2010, the tea party midterm, the results look a bit different — the traditional “U” shape is skewed, with conservatives showing markedly higher mobilization than liberals. For conservatives, the first two years of the Obama presidency were powerfully mobilizing. Even though 2010 was a midterm year, overall turnout dropped in this sample by just 8 percentage points, and among conservatives, it was down just 3 percentage points.

In 2012, the “U” shape becomes more symmetrical. But notice that turnout among the 19 percent of respondents who deem themselves “conservative” is 80 percent, which is notably higher than the 74 percent notched by liberals. Overall, it seems plausible that McCain’s nomination in 2008 kept some conservatives home, but there is no such evidence for Romney in 2012.

Another way to approach this question is to look at the geography of voter turnout. I focus on Iowa for two reasons. For one, its first-in-the-nation status gives us an unusually clear picture of where support for conservative candidates lies. In 2012, the Iowa GOP caucuses were so close that former Sen. Rick Santorum’s tight victory over Romney wasn’t clear for days. What’s more, Iowa was a heavily contested swing state in the general election, meaning that both the Romney and Obama teams worked hard to mobilize voters there.

The chart plots the share that right-leaning candidates won in the caucuses on the x-axis and shows each county’s general-election turnout on the y-axis. Each dot represents a county. As it makes clear, there isn’t a strong relationship between the counties where support for conservative candidates — Santorum, Michele Bachmann, Rick Perry and Newt Gingrich — was higher and low voter turnout. In fact, accounting for the counties’ total number of GOP caucus voters, turnout was higher in the places where right-leaning candidates did better. That relationship holds even if we deem only Santorum and Bachmann to be right-leaning. The survey evidence doesn’t back up the base-focused strategy, and neither do election returns.

Of course, the attraction of the turn-out-the-base strategy isn’t just about winning in November. The base strategy also has another appeal: It denies that there is any trade-off between taking more extreme positions and competing in a general election. In that, it provides cover for activists on both sides to push the policies they’d like to see. So it is a powerful strategy to justify stances that aren’t in line with the median voter. It’s just not as compelling in actually winning elections.

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