British Prime Minister Theresa May's position on Brexit is clear: Damn the torpedoes, full speed ahead.

Unfortunately, it looks like the torpedoes are going to hit.

May refuses to revisit the question of whether Britain should leave the European Union. But there's increased chatter from her own party that she should reconsider. Parliament is nearing open revolt against her government. Why? Because the Brexit deal May hammered out likely can't pass, meaning the maximum-chaos scenario of a no-deal Brexit is more likely than ever.

The solution is obvious: May should swallow her pride and have a second referendum on Brexit.

May has held firm thus far to the apparently sacrosanct "no do-overs" tenet of democracy. "Let us not break faith with the British people by trying to stage another referendum," May said in a Monday statement reiterating her position. "Another vote which would do irreparable damage to the integrity of our politics, because it would say to millions who trusted in democracy, that our democracy does not deliver."

"Another vote ... would further divide our country at the very moment we should be working to unite it," she continued.

Would it really be so bad to hold a second referendum? Are the people not allowed to change their minds? If a second referendum yielded a vote against Brexit, that would be equally as legitimate as the original vote in favor of Brexit. And the key thing, either way, is that the decision would still rest with the people. This wouldn't be Britain's elitist ruling class overruling the people. It would be lawmakers asking the people for confirmation. This thing you said you want to do seems increasingly bad. Are you sure you want to go through with it?

Democracy should be an iterative learning process: The people vote in governing coalitions, get to experience the results, and then bring the lessons of that experience to their choices in the next election. Indeed, the relatively straightforward majority-rule of the British parliamentary system is advantageous over America’s relatively veto point-ridden system. Majorities actually get to pursue their agendas, giving the voters something concrete to assess.

Voters asked for Brexit, and two years into the process it's become increasingly clear that a sensible divorce from the European Union just isn't in the cards, for good or ill. It also appears British voters are absorbing the implications of that. A study in September found that 2.6 million people who voted for Brexit have since changed their minds. That would be more than enough to flip the vote in favor of "Remain" should a second referendum occur.

No one likes the deal May hammered out with the EU, and the general sentiment is that it can't pass Parliament. May had to cancel a vote on the measure last week, and then faced a parliamentary vote of no confidence that would have dissolved her leadership. The vote failed, but Labour Party leader Jeremy Corbyn is already threatening another round. Meanwhile, reports are circulating that two of May's deputies and a number of other officials from her own Conservative Party are discussing a second referendum, though they've publicly distanced themselves from that story so far.

Earlier this month, European courts ruled that Britain could unilaterally cancel Brexit if it wants to. If May needs an extension of the March 29 deadline to actually get the referendum done, she could probably get it from the EU if the explicit purpose was to put Brexit up for a second vote.

Plus, canceling Brexit would give Britain a chance to address its actual problems.

The Brexit campaign was shot through with racism and nativism. But dig a bit and you'll see the complaints from the pro-Brexit camp were largely economic: an undersupply of housing and health care, stagnant wages, and insufficient jobs. Those are all real problems. It's just that the culprit isn't immigration; it's the British government's turn towards budget cuts and tight money in the aftermath of the 2008 crisis. Indeed, one of the things that's so politically poisonous about austerity is how it creates precisely the kind of economic scarcity that reactionary nativists then blame on immigrants.

Britain is bizarrely fortunate in that all this was an entirely self-inflicted wound. Unlike Greece or Italy, Britain still controls its own currency, and isn't subject to the monetary and fiscal straightjacket of the eurozone. If Britain wants to rebuild its working class and equitably share its economic prosperity again, it can just do so; it doesn't need to smash its way out of the EU common market first.

In fact, canceling Brexit could open up a broader conversation about the actual causes of Britain's doldrums. Under the best circumstances, Britain could become a demonstration project that rising living standards for all are perfectly compatible with large immigration flows.

All this said, there are risks to another Brexit referendum: A second vote could make it even less clear which side in the Brexit debate has a democratic mandate. "Suppose we had another referendum. Supposing the 'remain' side won it by 52 to 48, but it was on a lower turnout — entirely possible," Britain's International Trade Secretary Liam Fox explained to the BBC. "People like me will be immediately demanding it's best of three. Where does that end up?"

But Brexit is consuming British politics. It seems unlikely that the verdict in a second referendum, however it went, would come in with a sufficiently lower turnout to question the vote's legitimacy relative to the previous referendum.

Meanwhile, the potential payoff to taking that risk is the British people would get to exercise their democratic will, learn from their past experiences, and possibly save May and the British government from having to go through with the whole sordid mess.