IF SOMETHING is impossible, it does not happen. If a country votes to make two plus two equal five, this "democratic decision" will eventually be overridden by the rules of arithmetic, no matter how large the majority or how loudly "the people have spoken".

This is the story now playing out in Britain as British Prime Minister Theresa May's government stumbles towards the final act of the Brexit tragi-comedy.

In 2016, the British people voted to leave the European Union while keeping "the exact same benefits" that they enjoyed as EU members. David Davis, Mrs May's former minister responsible for negotiating Brexit with the EU, used that phrase repeatedly in Parliament, and it was then taken up enthusiastically by Mrs May herself. The promises by former foreign secretary Boris Johnson, the chief Brexit campaigner, were even more fulsome: Britons would have complete freedom to live, work, and study throughout Europe; untrammelled access to the EU single market; and full participation in whatever political institutions a post-Brexit government might feel like cherry-picking from the EU orchard. In short, the 2016 referendum was a vote for two plus two equals five.

The consequences of this self-delusion are now becoming obvious, as Britain's government finds itself unable to get a parliamentary majority for any realistic Brexit plan. If this situation persists, Britain will have only one alternative: another referendum to reconsider the impossible result of the 2016 vote.

The Times now estimates that there is a 50 per cent probability of such a referendum. When Justine Greening, one of Mrs May's recently sacked Cabinet ministers, became the first senior Conservative to propose this option, the objections raised to it were no longer about the principle of a second referendum, but about the difficulty of deciding the right question and method of casting votes.

A new referendum is rising to the top of Britain's political agenda because of the self-defeating behaviour of the Conservative Party's hardline Brexiteers. When Mr Davis and Mr Johnson resigned from Mrs May's Cabinet, chaotic parliamentary rebellions - from both the Eurosceptic and pro-European factions of the party - ensued. As a result, the main opposition Labour Party now sees a realistic chance of bringing down Mrs May's government and triggering a general election by uniting with either hardline Brexiteers or pro-European Conservative rebels to kill whatever Brexit plan that Mrs May ultimately puts to Parliament. Labour opposition makes every Brexit option almost certain to be blocked.

Start with the threat of a "no deal" rupture, whereby Britain would crash out of the EU with no agreement at all on a new relationship. This is now totally implausible, because all of Britain's opposition parties - plus the clear majority of Conservative MPs whose primary loyalty is to business interests - would block it.

Almost as improbable is a "hard Brexit", in which Britain and Europe agree to an orderly separation, but with no preferential arrangements for future trade. This, too, would be voted down by all the opposition parties, along with dozens of centrist Conservatives. Some of the Brexit hardliners also would oppose any such agreed separation, because it would force Britain to pay a large EU exit fee and to follow European rules for an open border with Ireland, in exchange for no commercial privileges at all.

Mrs May's latest plan for a more cooperative "soft Brexit" now also faces insuperable opposition from Mr Johnson and Mr Davis, plus several dozen followers. These hardliners have denounced Mrs May's new plan as "Brexit in Name Only" and a plot to turn Britain into an EU "vassal state". Labour is now willing to enter an unholy alliance with them in the hope of precipitating a government collapse.

This leaves one final option: a parliamentary rebellion to stop Brexit. "Exit Brexit" is the official policy of the Liberals, the Greens, and the Scottish National Party. But all serious Brexiteers, plus the vast majority of Conservative MPs and the Labour leadership, who feel obliged to follow the "instructions" of the 2016 referendum obviously will not support this option.

If Mrs May finds herself unable to muster a parliamentary majority for any version of Brexit, resignation and a general election will not be her only recourse. One goal unites all the Conservative factions, regardless of their views on Europe: to avoid a general election and the risk of Labour winning power. This means that Mrs May could attach a referendum proposal to her preferred version of Brexit, justifiably claiming that Parliament's response to the 2016 referendum should either be ratified or rejected by another popular vote. The criminal investigations launched recently into illegal spending by Mr Johnson's official Leave campaign, and allegations of Russian funding for former UK Independence Party leader Nigel Farage's parallel campaign further justify a final referendum.

The Labour leadership would probably oppose a new referendum, because it would derail their efforts to force a general election. But, crucially, the Liberals and Scottish Nationalists would enthusiastically support a referendum as long as it offered voters the option of keeping Britain in the EU. As a result, Mrs May would have no trouble assembling a parliamentary majority for a legislative package that bundled her Brexit plan with a referendum to decide between it and the status quo alternative of remaining in the EU.

Logic suggests that such a referendum would reverse the 2016 decision to leave the EU, because any specific Brexit proposal presented by the government would be far less attractive than the utopian delusions that managed to secure only a narrow majority two years ago. But, by next year, the British people could be so angry with Europe that they vote Leave again. If so, Brexit could go ahead on whatever terms Mrs May negotiates, and nobody could complain about the consequences or costs.

Whatever the outcome, voters would have made an honest choice between genuinely and properly articulated options. That would be true democracy, instead of the demagoguery of two plus two equals five. PROJECT SYNDICATE