Of course, there is much to be said for a second referendum. It is now clear that Britain’s most colossal decision in a century was taken after a campaign marred by lies, personal ambition and possible Russian manipulation. Meanwhile, new facts have emerged about the cost and consequences of leaving. If the facts have changed, minds may have too, right?

Yet there are very good reasons not to go down this route, too. There is probably no better way to anger people than by suggesting that their first vote was OK, but not quite good enough. A referendum that welcomes any outcome, as long as it is “yes”, would be deeply problematic. How democratic is it to ask the public to revise their opinion until it satisfies the elite? A second referendum sounds like the best way to undermine trust even more, divide the nation even further and risk another dirty campaign.

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As Iain Walker of newDemocracy in Australia wrote to me this week: “The line of thinking can be distilled as: ‘We just did something monumentally stupid. Now we demand to do it twice!’”

He is right. The problem with the Brexit referendum was not Brexit, it was the referendum. How could such a drastic decision be taken through so primitive a procedure in the first place – a one-round popular referendum based on a simple majority? Two years on, it still feels like David Cameron was trying to outsource political open-heart surgery to a passionate crowd wielding the blunt axe of the referendum. Why would a new blow produce surgical precision this time?

Yet there is a way out. Britain does not need a second referendum, it needs a preferendum. The preferendum is a little known but powerful tool for public decision-making on controversial issues. Imagine you’ve just walked into a restaurant and the landlord shouts at you: “Food or no food?” That’s pretty much what a referendum looks like. Now imagine being handed a menu and some time: you read the list, evaluate the dishes and pick the ones you like.

The method of the preferendum was refined by the French mathematician Jean-Charles de Borda in 1770. Today, it is used in the US by Major League Baseball to determine the player of the year. The Eurovision song contest uses a similar procedure: rather than picking out the best song, juries are invited to give points to a range of artists, so that the cumulative effect of individual voting gives a final ranking of competing candidates.

This procedure could be applied successfully to the UK. In the polling station people would not just receive the classical yes/no question, but a list of 30 proposals on Britain’s future relationship with the European Union. They might include ideas such as: “The status of Northern Ireland and the UK should be the same, even if that implies a harder border with the Republic of Ireland”; “Only Britain should be able to regulate who enters the country”; “Migration can only be tackled if Britain works with its European partners”; “Travelling to the EU should not require a passport.” Et cetera.

In the run-up to the preferendum every voter would receive a brochure with the arguments for and against each proposal, as is already common practice in Switzerland. In the voting booth citizens would be invited to rate the proposals (to show how strongly they agree or disagree) and rank them (pick a top three).

The preferendum would grant every citizen a more meaningful say on Brexit than a referendum. It resembles the vote compass tools popular online that place you in a grid according to your answers to political questions. But whereas these connect citizens to politicians, the preferendum connects politicians to citizens. It allows them to hear what citizens value the most. The outcome is a list of shared priorities rather than a broken country.

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Of course, the key question is: who writes the proposals? Leaving this in the hands of political and social elites might not be the best idea. Instead this should be entrusted to a random sample of citizens representative of the British population. Much can be learned from the Irish citizens’ assemblies, where groups of 99 citizens drafted by lot came together one weekend per month for half a year to advise on whether gay marriage and abortion should remain unconstitutional. In the UK, a representative sample of people would include hard Brexiteers, soft Brexiteers, remainers and proponents of a second referendum. They should meet in London for a number of weekends, not to shout at each other, nor even to change their minds. The only thing they need to agree upon is which proposals should be presented to the public.

The preferendum is a smart tool that could satisfy both camps. Remainers would have what they’ve always wanted: a final say. Leavers would get what they never expected: a chance to be taken seriously. And UK politicians would receive what they no longer dare to dream of: a clear answer. The preferendum is not a gimmick to bully the victors. The result might still be a very hard Brexit. But at least that decision would be taken consciously, through a proper procedure, on the basis of more precision than has hitherto been the case.

• David Van Reybrouck is the author of Against Elections: The Case for Democracy. He is a founding member of DemocracyR&D, a global network for democratic innovation