Last week, Pew Research published a “political typology,” a schema of nine voter categories it had invented, on the basis of a national poll of political attitudes, to capture the ideological state of the nation. Pew has been doing this every few years for three decades, modifying the types every time. On this round, the big finding was that the country’s political polarization continues; the Republican base and the Democratic base live almost entirely separate lives, geographically, socially, and ideologically.

But Pew’s data also made clear why both parties are having trouble holding their coalitions together. “Country First Conservatives,” who look a lot like the explanation for Donald Trump’s having mowed down his primary-season opponents last year, are anti-immigration and isolationist, while “Core Conservatives” are not. “Opportunity Democrats” don’t dislike corporations as much as “Solid Liberals” do, “Disaffected Democrats” mistrust government, and members of the “Devout and Diverse” category usually vote liberal but are deeply religious.

Most people running for office try every possible technique to win, but, to make life neater than it actually is, there are two main strategies for a campaign: motivation and persuasion. Motivation means firing up the base, with the goal of increasing turnout among people who were never going to vote for your opponent. Persuasion means pulling undecided voters over to your side. A deeply polarized country would seem to be friendlier to a motivation strategy; maybe that was why Hillary Clinton used one in 2016. But the Pew data open up lots of possibilities for the two parties to employ persuasion—not by moving to the center, exactly, but by looking for commonalities with opposition voters. Where do they live? Where do they pray? How are they doing economically? How does the future look to them? There are not dispositively Republican or Democratic answers to these questions. A year ago, The New Yorker, working in partnership with Pew, published an interactive game that encouraged users to play with changing the loyalties of twelve groups of voters. That was an implicitly persuasionist exercise.

Back in 1960, the great Southern liberal historian C. Vann Woodward published an essay in defense of populism. Woodward was motivated by the alarm that was then prevalent among liberals about what they took to be the essential and irredeemable impulses of conservative voters. In a phrase that would not need much editing to sound contemporary, Woodward wrote, “By one or another the Populists are charged with some degree of responsibility for Anglophobia, Negrophobia, isolationism, imperialism, jingoism, paranoidal conspiracy-hunting, anti-Constitutionalism, anti-intellectualism, and the assault upon the right of privacy—these among others.”

Woodward felt that the writers he was arguing against—people like Richard Hofstadter, Peter Viereck, Edward Shils, and Talcott Parsons—had been comfortable with populist sentiment as long as it was an element in the electoral coalitions supporting Presidents Franklin Roosevelt and Harry Truman. But, now that a Republican was President and the country’s leading populist had been (until he died, in 1957) Joe McCarthy, populism looked menacing to them. It was an impulse to be conquered, because no good could come of it. Although Woodward had no illusions that populist voters were calmly well-informed, he saw them as a necessary check on élites; they could “shock the seats of power and privilege and furnish the periodic therapy that seems necessary to the health of our democracy.” So, Woodward wrote, “the intellectual must not be alienated from the sources of revolt. . . . The intellectual must resist the impulse to identify all the irrational and evil forces he detests with such movements because some of them, or the aftermath or epigone of some of them, have proved so utterly repulsive.” The forces he was thinking of were the racial and ethnic hatred, propensity to violence, and attraction to mob rule that his contemporaries were ascribing to populism.

It’s easy to take the result of the last election cycle as a sign that the Republican Party has organized the same irrational and evil forces into a smoothly operating political machine, but the Pew study ought to remind us of possibilities that aren’t so neat but are more encouraging. Low-income, low-education voters sit inside both parties, waiting for an appeal that feels directed at their lives. The same goes for small-town and rural voters, and religious, Southern, and union voters. Barack Obama’s electoral success with many Americans who later voted for Trump is proof of that. In a two-party system, each party has to pull together a diverse coalition whose members want very different things from government. It’s possible to do that by appealing to the best in people, even people who also have proved capable of voting for candidates who appeal to the worst in them.