Yet there are times when such concessions backfire. Britain’s fight over Brexit is one.

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Two years after Britain voted to leave the European Union, there is a clear case for a second referendum. It’s not just that yanking Britain out of its most important trading relationship will be costly. It’s that yanking Britain out won’t deliver the promise of “taking back control” that Brexit supporters cherish. The deal now emerging is likely to require Britain to continue to abide by at least some European rules. It will involve some kind of payments to Brussels. It will cause stresses in the relationship between mainland Britain and Ireland, and perhaps between England and Scotland. It will not make Brexiteers happy.

Because the emerging deal is a mess — a dog’s Brexit, the wags say — it may well be blocked in Parliament. Purist Brexiteer “headbangers” in the ruling Conservative Party denounce what they see as an insufficiently clean break, and there may be enough of them to prevent passage. If that happens, Britain could leave the European Union without a deal, which would disrupt everything from auto supply chains to peace in Ireland. Alternatively, Britain could put the question to a second referendum, allowing voters to choose among three options: the compromise negotiated by the government, a no-deal hard break or remaining in the European Union.

To populists and their appeasers, a second referendum is anathema. The first was billed as the most important vote in a generation, and 72.2 percent of the electorate turned out, the highest share in a national contest in more than two decades. In the face of that mandate, the argument goes, elites have no right to tell people to vote again so they can deliver the “right” answer. Besides, if a second referendum went in favor of Remain, Brexiteers would argue that this merely made the score 1-1, so there ought to be a tiebreaker. Maybe this is men’s Grand Slam tennis rather than women’s? Why not five referendums?

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This objection would be compelling if Brexit voters were being deprived of something they dearly wanted. However, the fact that the most enthusiastic Brexiteers are poised to vote against the exit deal suggests otherwise. Top Brexit standard-bearers, notably former foreign secretary Boris Johnson, have resigned from the government to protest the emerging compromise, with one saying it would make Britain a “vassal state.” Most Brexit voters still want out of Europe, but they feel let down by the convoluted way it’s happening.

That leaves the second objection to a fresh referendum: that it would be hard to organize. Enabling legislation would have to go through Parliament. The phrasing of the questions would take time, all the more so because there would be three options for voters — the leave compromise, the hard break and the Remain U-turn. Preparations would extend beyond the Brexit deadline next March, so the European Union would have to agree to postpone B-Day.

But these objections, too, are underwhelming. Europe would have every incentive to agree to a postponement: Brexit will mainly hurt Britain, but it will also hurt its neighbors. And while a referendum with more than two options may sound complex, it’s not impossible. In 1977, Australia used a referendum to select one national anthem out of four. An alternative-vote system, in which the second choices of the bottom-ranked option are added to the tallies of the top two, offers an intuitively fair way to determine the outcome.

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The truth is that Britain has no easy way forward. If Brexit is derailed, Brexit voters will feel cheated and the backlash could be serious. But if a dog’s Brexit is served up, Brexit voters may still feel unsatisfied and Remainers will be disgusted. And because Brexit will crimp tax revenue and constrain government spending on hospitals and schools, its effect over the long run will be to make everyone angrier.

An alternative-vote referendum could plausibly yield victory for any of the three results. But at least it would avoid the suspicion that the nation had stumbled into a fudge that pleases nobody because political leaders handled the negotiations incompetently. If populism shows that mainstream politicians have not listened enough to regular voters, there is no shame in asking voters to express their views a second time.