A second vote could actually undermine faith in British democracy.

One reason political scientists are so skeptical of referendums is that leaders tend to turn to them as a sort of political theater. They give the appearance of democracy happening when those leaders are unable to get what they want through the regular legislative processes.

“A referendum is not a form of direct democracy,” Nadia Urbinati, a Columbia University scholar of democracy, said. “A referendum is used when a representative system decides that it wants to have the support of the people.” And usually, it’s for something the government has already decided to do.

That can backfire, though, as Prime Minister David Cameron learned in 2016 when he called for a Brexit vote. Mr. Cameron did so not because he was curious what voters thought, but because he believed they would vote to remain, shoring up his position within the Conservative Party, political analysts widely believe.

If a second referendum results in a narrow majority for remaining in the European Union, then the nearly half of the country that still wants to leave could reasonably conclude that the political establishment ginned up a new vote to suppress the popular will that was expressed in 2016.

But if the public once again votes to leave, then the people who wish to remain — and thought that a second referendum would deliver that — may doubt whether the outcome was truly democratic. After all, polls have shown for some time that a slight majority favors staying in the European Union.