Correction to this article

JUST for this week, indulge in a fantasy. Everything you think you know about next year's presidential election in America might be wrong. You think you know that the candidates will be Barack Obama and Mitt Romney, or perhaps one of the non-Romneys such as Newt Gingrich. But, just possibly, Americans will be presented with a far wider choice next November. This might even be an election more like the race of 1948, which produced a dazzling array of candidates and a deliciously unpredictable result, when Dewey did not, after all, defeat Truman.

The reason for entertaining this idea is the universal belief that America's politics are “broken”. From the tents of Occupy Wall Street to the firesides of Georgetown, the cry goes up that the ideological polarisation of the political parties leaves the great bulk of the electorate unrepresented. This newspaper cares very much about this “missing middle”. But is it just the middle that has gone missing? Many Americans lament what they consider the missing right, and some complain of a missing left as well.

Indeed, start with the left. Barack Obama is not facing a primary challenger from his own party, but he almost did. For all the Republican nonsense about the president being a “socialist”, a group of deep-pocketed Democratic donors is so disappointed by what they see as his timid centrism that they trawled the country for a candidate willing to take him on from the left. The name on some lips was that of Russ Feingold, a former senator from Wisconsin. In the event, nobody was willing to run. But that, says one corporate titan involved in the effort, was only because no Democrat dared to risk bringing down the country's first black president. Had he been white, it would have been different.

What about the missing right? It is not missing at all, say those Democrats who think that the tea-party movement has wormed its way into the brain of Republicanism, taking it over and driving it mad. But tea-partiers will consider all the worming and the takeover to have been for naught if a candidate from the right of the party fails to win its presidential nomination. So it is not at all fantastical to think that if Mr Romney secures the nomination a more authentic conservative will decide to go it alone.

The fact that Mr Romney has so far failed to win over more than a quarter of Republican voters suggests that his nomination would leave a tempting gap in the ideological market—too tempting, perhaps, for Ron Paul, a Texan libertarian, to resist trying to fill it. Though Mr Paul is running as a Republican, in 1988 he was the presidential candidate of the tiny Libertarian Party. He has an avid following, but it is small, and he must know that he will never be president. All the same, by staying in the race under a different banner he could continue what is probably anyway his real goal, namely to educate Americans about the evils of the Fed, the madness of foreign entanglements and so forth.

As for the missing middle, next year will see an innovation. In June 2012, well before the Republican convention in Florida and the Democratic convention in North Carolina, an organisation calling itself “Americans Elect” will hold an online nominating convention of its own. Its plan is not to create a third party but to use the internet to choose a presidential candidate from any party (who will in turn have to pick a running-mate from a different one) and put this non-partisan ticket on the ballot in every state. The outfit has already collected more than 2m of 3m or so signatures it will need to satisfy every state's ballot requirements.

Americans Elect has the benefit of rich sponsors (one of its promoters is Peter Ackerman, a philanthropist who made his fortune in the finance industry) and good timing. Polls suggest that Americans are heartily sick of the established party machines and a system of primary elections that forces candidates to pander to the extremes instead of reaching for the centre. It is not completely impossible that it could attract a big name with bags of money as its candidate. Michael Bloomberg, the post-partisan billionaire mayor of New York City, claims right now not to be interested in a presidential run. But he could change his mind, especially if the Republicans plump for one of their scarier ideologues—Mr Gingrich?—instead of the pliant Mr Romney, thus creating an opening in the centre.

Better the duopoly you know?

Precisely because it is more than a quixotic fancy, Americans Elect is controversial. In the Washington Post, Norman Ornstein of the American Enterprise Institute and Thomas Mann of the Brookings Institution have highlighted the pitfalls. Even a strong independent from the centre would be hard put in a three-way race to win a majority of the 538 votes of the electoral college. But such a candidate might also prevent the others from gaining a majority. The constitution would in that case leave the final vote to the (highly partisan) House of Representatives. In the unlikely event of the third candidate winning, how would he or she govern with no party allies in Congress? And what if a third candidate merely attracted enough centrist voters away from Mr Obama to give victory to a far-right Republican nominee?

The doubters are probably right. Gridlock in Congress is arguably the biggest obstacle to effective government, and there is no attempt to form a third party there. Besides, third parties and independent candidates have had a lousy record. In 1992 Ross Perot won 19% of the popular vote but not a single vote in the electoral college. In 1912 Theodore Roosevelt, a former Republican president running as a Progressive, won 27% of the popular vote and outpolled his Republican successor, William Howard Taft. But that only handed victory to the Democrats' Woodrow Wilson. Even so, just think: Obama versus Romney versus Paul, or Obama versus Gingrich versus Bloomberg. That has to be a lot more fun than a straight two-way race, doesn't it?

Economist.com/blogs/lexington

Correction: A previous version of this article omitted William Howard Taft's first name. This was corrected on December 8th 2011.