The first round of the second Democratic presidential primary debate began Tuesday night with a lengthy back-and-forth over how the candidates hoped to improve health care. (Well, actually, the debate began with a lengthy introductory sequence and a commercial break. But who are we to be catty?) Should the country embrace a complete overhaul, switching to a centralized system? Is it enough, instead, to refine Obamacare to provide better coverage to more people?

There are a number of intricacies to the conversation and a number of pits into which the debate can quickly stumble. Sen. Bernie Sanders (I-Vt.) at one point accused CNN’s Jake Tapper, one of the debate moderators, of leveling a Republican talking point at him. It’s fair to discuss the economic effects of massive shifts in federal programs, but Sanders was right that “how will we pay for it” is a common rejoinder from an opposition party that embraced a tax cut that helped spike the deficit.

While that debate bubbled, it was worth remembering an important subtext to the fight. In part it was about a vision for the future of health care in the country. In large part, though, it was about trying to figure out just how progressive the eventual Democratic nominee can be without sabotaging the party's ability to beat President Trump.

Sanders and Sen. Elizabeth Warren (D-Mass.) advocate not only for dramatic progressive policy proposals but also for the utility of those overhauls.

“I don’t understand why anybody goes to all the trouble of running for president of the United States,” Warren said at one point, “just to talk about what we really can’t do and shouldn’t fight for.” She was responding to former Maryland congressman John Delaney, whose campaign is predicated on a more moderate vision of where the party should be. Policies like those Warren and Sanders espouse, he said, were essentially “fairy tales.”

There’s truth in Delaney’s comment that derives more from the political reality of a Republican-controlled Congress than anything. To the idea that the party should avoid more progressive policy proposals to head off Republican attacks, South Bend, Ind., Mayor Pete Buttigieg suggested that their opponents would call the field “a bunch of crazy socialists” even if they adopted a conservative policy platform.

But, again, note what all of this is orbiting the question for Democrats: How do we win?

FiveThirtyEight’s Nate Silver, weighing in on the debate on Twitter, noted that there is a robust body of research showing that moderate candidates are more likely to win elections. The operating theory for decades has been that primaries are fought closer to the poles, to appeal to hardcore partisans. When the general election begins, the candidates move back toward the center, with the hope of peeling away less ideological members of the other party. Stake out a position at the far left and a more-centrist Republican could either win over moderate Democrats or get them to stay home, indifferent about who wins.

Whether that calculus still holds true in 2019/2020 is another question.

Consider the 2016 election. Donald Trump staked out a moderate economic position that he coupled with an extremely conservative position on immigration. At no point did he shift his positions to appeal to a general election audience, choosing instead to keep stoking the energy of his early supporters, many of whom embraced his immigration message. He ran against a candidate, Hillary Clinton, who explicitly tried to appeal to moderate Republicans in a mirror-image of the scenario outlined above.

Trump received fewer votes than Clinton but squeezed past her in Michigan, Pennsylvania and Wisconsin, thanks in part to being the more popular candidate among voters who disliked both candidates — a group making up a fifth of the electorate. More than 4 million people who voted for Barack Obama in 2012 didn’t vote at all in 2016.

Trump’s appeal to his base was enough to get the votes he needed. Clinton’s more traditional path was not. One can debate the role that the electoral college played in disrupting the cleanliness of this narrative, but it’s clearly the case that Trump’s unusual strategy was not prohibitive to his chances.

Hence the dispute among Democrats. Given Trump’s success and given the number of 2012 voters who stayed home, is it possible to put together a campaign that energizes infrequent Democratic voters, doesn’t turn off those Democrats who vote regularly — and doesn’t further energize Republicans? Can the Warren-Sanders strategy of whipping up the progressive left deliver the White House? Is the era of the moderate advantage over?

This is a complicated question that involves a lot of moving parts. We can and should discount anecdotal examples of how to win presidential races like that offered by former Chicago mayor Rahm Emanuel simply because presidential races are unique contests that happen after (relatively) long gaps and for which we have only a limited number of precedents. (Since the election of John Kennedy, there have been only 14 presidential races — fewer than there were House races in Pennsylvania last November.) What’s more, those who’ve been involved in political races (like Emanuel) tend to assume that, if they won, the way they won is the way all campaigns should be won. That doesn’t work very well.

Writing for The Post earlier this month, Emanuel did raise the good point that Democrats are more heavily moderate than Republicans. That’s true — but there’s been a dramatic shift in recent years.

What’s more, there’s been an increase in how heavily ideology overlaps with partisanship. There used to be a big middle occupied by members of both parties. Now most Democrats are more liberal than the median Republican and most Republicans are more conservative than the median Democrat.

In June, the Niskanen Center, a D.C.-based think tank, interviewed two political scientists to assess the extent to which moderates still retain a political advantage. One of the scientists, Andrew Hall of Stanford University, argued that the rise in polarization in politics derived to some extent from fewer moderates actually running for office. Stephen Utych of Boise State University, however, compiled data showing that the moderate advantage had been erased in recent elections.

This is the central chart of Utych’s analysis. The top of the chart indicates more success winning elections; the bottom, less success. The line that begins at lower left represents more ideological candidates. The line that starts at upper left represents more moderate ones.

In 1980, moderates had a lot more luck than ideologues. By 2008, the two were about equivalent.

"Individuals are much better ideologically sorted into their preferred party today than they have been in the past,” Utych writes in his paper exploring his research, “leading to an increased correlation between ideology and party.” In other words, the above animation showing how the parties have moved apart represents one of the factors in more ideological candidates having more success.

For Democrats, though, there’s an additional concern: turnout. Democrats often turn out less heavily than Republicans, in part because factors that correlate to regular voting — age and income in particular — are factors that tend to skew Republican.

Analysis by the New York Times’s Nate Cohn suggests that an increase in turnout in 2020 wouldn’t necessarily benefit Democrats as much as past trends would indicate. But perhaps targeted turnout gains would. Those 4.4 million 2012 voters who didn’t vote in 2016: How do you get them to come out? What’s more, how do you get them to turn out without also spurring Republicans to turn out more heavily? If Democrats nominated Warren, for example, would anti-Warren Republicans be more inspired to come out and vote?

"Studying the House,” Stanford’s Hall told Niskanen, “what we find is that when you nominate these more extreme candidates an important part of why they seem to do worse in the general election is that their party goes on to have a lower share of the turnout in the general election, in particular voters of the other party seem to turn out at a higher rate in response to an extremist nomination.” What’s more, he added, the turnout benefit from a more ideological candidate wasn’t as big as expected.

It’s important to note the recent increase in negative partisanship. Members of one party tend to view the opposing party with increased skepticism, dampening the likelihood that they’d cast a vote across party lines. (In 2016, partisan votes heavily aligned with the party’s candidates, as has generally been the case in recent years.) Independents that vote with one party often do so more out of hostility to the other party than affection for the one they support.

Hall notes, though, that his research focused on House races, not presidential ones.

Speaking to Niskanen, Utych raised an important point: The moderates-are-more-electable idea may be somewhat self-fulfilling.

“When a candidate is moderate, people tend to believe they’re more likely to be elected than a candidate who’s ideologically extreme,” Utych said. “That does have some impact on how they’ll vote. It’s these ideas of yeah I think this candidate will win.”

If you need evidence of that, listen to cable-news pundits and more-moderate Democratic candidates.

The problem with presidential elections is that they are both extremely important and often hard to predict. Is it possible that a moderate Democrat will have a better chance at beating Trump? Former vice president Joe Biden has wider margins against Trump in head-to-head polls than his opponents right now, and Biden’s running as a moderate. But, then, on July 31, 2015, Clinton had a 15-point lead over Trump in the RealClearPolitics polling average.

Trump’s strategy, such as it was, overcame that.