WASHINGTON — There was a time when ticket splitting was common. Voters would support one party’s candidate for president and the other’s for Congress. At its peak in 1972, ticket splitters represented 30 percent of voters, reports political scientist Alan Abramowitz of Emory University. Since then, the practice has gone into eclipse. In 2012, only 11 percent of the electorate were ticket splitters.

And yet.

To bring this nasty and bizarre campaign to a meaningful conclusion, what this country needs is an outburst of ticket splitting. Republicans should vote for Hillary Clinton, and Democrats should back Republican House and Senate candidates. This will strike most people as counterintuitive, if not foolishy, but there are three good reasons for doing so.

The first is to make a statement about the outcome. Neither party deserves complete victory. Both nominated widely distrusted candidates. In the latest NBC/Wall Street Journal poll (taken before last week’s final debate), only 40 percent of respondents viewed Clinton positively; a mere 29 percent felt that way about Donald Trump. Parties shouldn’t be rewarded when their popular support is so thin.

The second reason is related: to avoid misinterpretation. Assuming Clinton wins, she and others will claim that the Democrats have a “mandate.” They don’t. Her triumph would be more a repudiation of Trump than an endorsement of her policies. Just because Trump’s bad behavior was extraordinary — routinely crude, hateful and uninformed — does not make Clinton a beloved figure with a compelling agenda.

The same point holds true for Republicans. Retaining control of the House and, possibly, the Senate would not signal the popularity of their political philosophy, whatever it is. The election’s message for Republicans would seem devastating. Losing the White House for the third consecutive time — and five of the last seven elections — would show how out of touch with political reality they are. Their support is mostly defensive: fear of Democratic one-party rule.

The final reason is the most consequential — and the most hypothetical. Divided government, driven by ticket splitting, might actually produce better government.

How could that be? Superficially, the opposite would seem more likely. Divided government would mean paralyzed government; it’s more gridlock. Clearly, that’s possible. It happened during the Obama years. We could have a repeat performance.

But that’s not inevitable. For starters, we would have a new cast of characters. Clinton, House Speaker Paul Ryan and Senate Majority Leader Mitch McConnell are all “transactional politicians” — they want to get things done — as well as being fierce partisans. They also know that the gridlock of the past eight years hasn’t done either party much good. All this creates reasons to reach mutually acceptable agreements.

Well, we’ve tried ideological politics and we’ve learned one thing: It doesn’t work. It doesn’t produce consensus, and it doesn’t produce working majorities, either of the bipartisan or one-party variety. Because parties strive to differentiate themselves, cooperation become harder. On both the right and the left, power has flowed to the political fringes, who excel in rhetorical self-righteousness and flunk in legislative accomplishment. Major legislation needs bipartisan support; for confirmatin, see Obamacare.

The overriding need of the next president and Congress is for both parties to rebuild their political centers, which — almost certainly — still command the backing of public opinion. Revitalized centrist politics does not guarantee good legislation, but it stands a better chance of producing publicly acceptable legislation. Even this may be a long shot, but it’s our best shot.

Robert Samuelson is a columnist for The Washington Post. ©2016 The Washington Post Writers Group.