Janet Brown, executive director of the Commission on Presidential Debates, doesn't think it's a good idea for moderators to act as fact-checkers.

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"The commission asks independent, smart journalists to be the moderators, and we let them decide how they’re going to do this. But I have to say, in our history, the moderators have found it appropriate to allow the candidates to be the ones that talk about the accuracy or the fairness of what the other candidate or candidates might have said," Brown said on CNN's "Reliable Sources."

"I think, personally, if you are starting to get into the fact-check, I’m not sure what is the big fact, and what is a little fact. ... Does your source about the unemployment rate agree with my source?

"I don't think it’s a good idea to get the moderator into essentially serving as the Encyclopedia Britannica. And I think it’s better for that person to facilitate and to depend on the candidates to basically correct each other as they see fit."

The discussion over what role a moderator should play in a debate was reignited following criticism of Matt Lauer's appearance at a presidential forum earlier this month.

He faced criticism for not pushing back on Republican presidential nominee Donald Trump Donald John TrumpBubba Wallace to be driver of Michael Jordan, Denny Hamlin NASCAR team Graham: GOP will confirm Trump's Supreme Court nominee before the election Southwest Airlines, unions call for six-month extension of government aid MORE's claim that he has always opposed the Iraq War, a statement that has been widely debunked.

Democratic presidential nominee Hillary Clinton Hillary Diane Rodham ClintonJoe Biden looks to expand election battleground into Trump country Biden leads Trump by 12 points among Catholic voters: poll The Hill's Campaign Report: Biden goes on offense MORE and Trump will face off in their first presidential debate together Monday.