LEXINGTON once asked America’s most successful centrist to explain the strength of the two-party system, in a country that views those same parties with scorn. The problem is tribal loyalties, replied Michael Bloomberg, then in his final days as mayor of New York, in late 2013. Running for national office as an independent is “just not practical”, explained Mr Bloomberg, a technocratic billionaire who looked into, then decided against, a non-party presidential run in 2008. Such a big share of the population “will vote the party line no matter what your policies are”, he sighed. “That may not be good, but that is true.”

Now the Michael Bloomberg of early 2016 hears calls to think again. For the main parties may be about to pick presidential nominees who repel all but the most tribal voters. The chances are rising that Republicans will choose either Donald Trump, a snarling demagogue, or Senator Ted Cruz of Texas, a glib and calculating tribune of the hard-right. The presumed Democratic front-runner, Hillary Clinton, is struggling to hold off her leftist rival Senator Bernie Sanders of Vermont, whose plans would by his own admission require a political revolution.

Bloomberg-boosters see a chance to remake national politics. In a true three-way race, they reason, winning the White House does not require a majority of voters: about 38% of the electorate in the right states would do. Mr Bloomberg, who is 74, does not have long to decide: he must launch a campaign by early to mid-March to get his name on the presidential ballot in all 50 states. Allies see a path ahead for him if Republicans pick Mr Trump or Mr Cruz and Democrats choose Mr Sanders. They also see a way to win if Mrs Clinton looks like prevailing, but has been weakened and driven to the left (or if she faces the real danger of an indictment for mishandling government e-mails as President Barack Obama’s first secretary of state). The din and fury of this year’s presidential primary season actively encourages Bloomberg-backers. They argue that most Americans abstain from such party contests. Studying polls, they spy a “new silent majority” that is fed-up with the status quo, but is not ready to burn it down.

Mr Bloomberg certainly breaks the two-party mould. He served at first as the Republican mayor of a mostly Democratic city, then became an independent. A Republican could not be elected president with Mr Bloomberg’s record. Raised Jewish in a blue-collar suburb near Boston, he is a secular big-city liberal on social issues, backing gay marriage and abortion rights. He tried to ban the sale of large sugary drinks and backed government action to curb climate change. The right loathes him for funding gun-control campaigns across the country. But Mr Bloomberg would also struggle to run as a Democrat. He clashed with teachers’ unions over school reforms. He angered the left by defending “stop-and-frisk” police searches which often involve non-whites. Such searches cut crime, he argued as mayor, in part by “scaring the kids to not carry guns”. When he defended the ultra-rich as valuable taxpayers those livid about inequality fumed.

Mr Bloomberg can be cranky. Asked by pollsters if they would want to spend Thanksgiving dinner with their then-mayor, nearly 60% of New Yorkers said no. Supporters say that Mr Bloomberg need not be loved: he just needs to be an acceptable third option for voters facing an otherwise appalling choice. The idea of Mr Bloomberg in a presidential television debate fills fans with nerdish joy. The self-made founder of a financial-data empire, he is worth an estimated $40 billion, or nine times more than Mr Trump, a rich man’s son—indeed, as a philanthropist, Mr Bloomberg has given away almost as much money as Mr Trump is thought to possess. Most of all, supporters say, he would stand out for knowing how the global economy actually works.

Frank Luntz, a Republican messaging guru (who is not working for any presidential candidate), says Mr Bloomberg offers voters a unique combination. He funds all his political campaigns from his own pocket, unlike Mr Cruz, Mr Sanders and Mrs Clinton. Unlike Mr Trump, he has a governing record. Lastly, he can appeal to both Democrats and Republicans, unlike any of his rivals. A poll taken by Mr Luntz in January saw Mr Bloomberg drawing more than a quarter of all votes in hypothetical matchups against Mr Trump, Mr Cruz and Mrs Clinton—though it is true that Democrats view him more favourably than Republicans do.

Steve Schmidt, a senior adviser to Senator John McCain’s Republican presidential campaign in 2008 (but unaffiliated this time) describes the two traditional parties as in a “state of collapse”. He sees in that a chance for innovation, as Mr Bloomberg would have the funds to invest in high-tech targeting of voters, driving tactical voting in his favour, including in the 30-odd states that usually have no impact on White House races.

Still a long shot

Alas for Bloomberg-boosters, there are reasons to be sceptical, too. The ex-mayor is a defender of free trade and immigration in a time of haul-up-the-drawbridge populism. Moreover, America’s established parties will fight hard to defend their duopoly. Democratic leaders have already urged Mr Bloomberg to stay out, fearing that he will mostly hurt their party. Republicans gleefully agree, and are urging him to run. Even the electoral rule-book helps traditional parties. Presidential contenders win by securing 270 or more electoral-college votes. If no candidate reaches 270, then the president is chosen by the House of Representatives. The next House will almost certainly be Republican-held. Especially with a Supreme Court vacancy at stake after the death of Justice Antonin Scalia, it can be expected to vote on party lines.

Mr Bloomberg may run anyway, drawing the support of millions of reasonable people. Yet if after some months it becomes clear that he will lose and help elect a President Trump, hope that he drops out. Being a true moderate is a responsibility, as well as an opportunity.