I must confess, you have an astonishingly good idea there, Doctor. —Soviet ambassador Alexi de Sadesky to Dr. Strangelove, 1964

Bernie Sanders has proposed that Democrats and Republicans debate each other during the Presidential primaries. PHOTOGRAPH BY DANIEL ACKER/BLOOMBERG VIA GETTY

Bernie Sanders is not a doctor, and, unlike President Merkin Muffley’s crazed science adviser, he is not in favor of having the government build a luxurious bombproof underground hotel/brothel to insure that white male American officials will be in a position to repopulate the world after a nuclear holocaust. But Sanders, the junior senator/senior citizen from Vermont, does have an astonishingly good idea: interparty campaign debates during the primary season.

“Chuck, we need a lot more debates in this campaign," Sanders said a few Sundays ago, addressing the host of “Meet the Press.” “I hope very much that we can begin with the Democratic candidates at least as early as July, and also Republicans in those debates as well.”

Emphasis mine, but Sanders’s, too. The day after his “Meet the Press” appearance, he upped the idea from offhand suggestion to formal proposal. In a letter to Debbie Wasserman Schultz, the chair of the Democratic National Committee, he observed that “having debates between Democratic and Republican candidates during the primary process” would “engage large numbers of voters who typically do not pay attention to the process until much later, when the general election begins to come into focus.” This, he said, would “get people to participate at higher levels.”

Sanders offered another plus: “These inter-party debates,” he wrote, “would put in dramatic focus the shallow and at times ridiculous policies and proposals being advocated by the Republican candidates and by their party’s platform.”

That’s his opinion, of course, and I may agree with him, but it’s not an argument likely to persuade Republicans. It fell to Rachel Maddow to point out that Democrats aren’t the only ones who think that the other side’s ideas are shallow and ridiculous. So why not, she asked,

have Democrats and Republicans mix it up—have Democrats and Republicans in some combination start debating each other? Not as the official nominees of their parties but as people who want to be the nominees of their parties, and who want to make the case that they ought to be that nominee—in part by showing off what they can do to guys on the other side of the aisle. All right? Pick me, Democratic Party! Pick me to be your nominee, because this is what you’ll get if you put me up against the Republicans! The same goes on the Republican side. Hey, Republican Party, pick me as the nominee! Watch how I take apart these Democrats in the debate!

I’m sure you can think of a million reasons this is extremely unlikely to happen. I certainly can. Just for fun, though, let’s imagine that it’s a few months from now. Things have begun to settle down. The five Democrats—Clinton, Sanders, Martin O’Malley, Lincoln Chafee, James Webb—are still in the running. The Republican clown car is still full, but it has become obvious which of its occupants are remotely imaginable nominees and which are not. Put the five top plausible Republicans—Jeb Bush and Marco Rubio, for sure, Scott Walker, maybe, plus two or three from the Paul/Kasich/Cruz/Perry/etc. grab bag—on one side of a New Hampshire stage. Put the D-5 on the other. And ring the starting bell.

My guess is that, for the voting public, the biggest benefit of an interparty debate would be its effect on the participating candidates. The dynamic of such a debate would create some interesting incentives, most of them healthy.

A typical debate among, say, five Republicans or five Democrats is a five-sided free-for-all, and the game is zero-sum. A debate with five Republicans and five Democrats would have ten players, each with his or her own individual interest, but, in important ways, each player would be on a side—a team, if you like. This might encourage a certain discipline. The members of each side would be reminded that what distinguishes them from one another is less important than what distinguishes them from the members of the other side. Nobody would want to be the one whose jab at a teammate provides an opportunity for real-time gloating by the other side. (“I have to agree with Mr. Chafee about Secretary Clinton’s scandalous speech fees.” “Senator Rubio said it better than I could about Jeb Bush’s mediocre record in Florida.”) Everyone on the stage would have to be conscious of an electorate beyond his or her own party’s base. All would have to demonstrate an ability to handle challenges from those who differ from them in ways that go beyond the details of their own party’s ideological orthodoxy. The narcissism of small differences might give way to a clash of larger visions.

Of course, no one can really predict what would happen, which would be part of the fun. But the television audience would be huge—a lot bigger, I suspect, than for any of the Republican-only or Democrat-only debates. The sheer novelty would be a magnet for eyeballs. Anyway, when the Yankees play the Red Sox, it’s a lot more riveting than watching one or the other take batting practice. And, of course, the fans can still decide who they think is their team’s M.V.P.

I know, I know. Ain’t gonna happen. But, given the wide-openness of the Republican field, with no clear favorite, I don’t see why five G.O.P. candidates couldn’t be persuaded to participate. And, while Hillary Clinton, as an undisputed front-runner, doesn’t have a lot to gain from lots and lots of sparring sessions with her four Democratic rivals, a debate with Republicans in the mix might be a different story. It’s hard to imagine her fellow Democrats trashing her under those conditions, especially on so-called “character” issues. For reasons of party loyalty, ideological affinity, civic responsibility, and—let’s be frank—simple gallantry, they might even be inclined to have her back.

Well, one can dream. That idea of Sanders’s may sound a little strange, but there are those of us who love it.