Should presidential-debate moderators do double duty as fact-checkers, too? With the first showdown between Hillary Clinton and Donald Trump coming up tonight at Hofstra University in New York, this argument is hot again.

Ari Fleischer, who was a press secretary for George W. Bush, argues that it’s the job of the other candidates, not the moderators, to correct any whoppers one of the debaters might tell.

Others disagree, believing that the moderator’s job is analogous to what a boxing referee does — policing violations of the rules, which in the political arena means sticking to something resembling the truth.

Former debate moderators Jim Lehrer and Bob Schieffer advocate something of a middle-ground policy. Moderators should give the other candidate a chance to rebut an obvious falsehood, but Schieffer thinks that “if he (or she) doesn’t, then you should step in.”

The answer on this issue may depend on what we think debates are for. If they are combat to determine who should sit in the Oval Office, then firm rules faithfully enforced are a must. But presidential debates don’t have the job of controlling that; nor should they.

It makes no sense for any voter to make these events central to his or her decision process. Debate skills are narrow and technical, and have at best only loose connections to the skills that presidents need. After all, formal debates do not resolve foreign clashes, for example, nor disputes with Congress. Nor is the ability to deliver pre-planned zingers important to the functioning of the presidency.

This doesn’t mean debates are unimportant. Many people watch them, and even more wind up exposed to post-debate media coverage. So the events are one important way for voters to learn about the candidates and the campaign, even if this information doesn’t affect their choices.

The debates are also internally important to campaigns. Candidates must be prepared with coherent answers to likely questions, pushing them to take positions on public policies they might prefer to remain neutral on. Politicians are thus pushed into making promises to voters that affect how they govern.

If the debates are therefore about representation, then it’s wrong to say that a moderator is like a referee enforcing the rules. Instead, his or her job is to nudge the candidates toward topics that lead to promises, both on the issues and on how they intend to behave as president. The moderators may not succeed, but they can push in that direction.

What if a candidate states something that is glaringly untrue? In that case, the course that Schieffer suggested — correcting it, if the opponent in the debate does not — is probably the way to go. Since debates are about giving voters information, it’s better to avoid blatant misinformation. But candidates should be the main fact-checkers on the debate stage.

Off the stage, of course, the press covering the event should do its usual fact-checking.

Jonathan Bernstein is a Bloomberg View columnist. He taught political science at the University of Texas at San Antonio and DePaul University.