The term is the latest of those used by Tony Blair's supporters to describe his political philosophy, and that of the re-invented centre-left in Europe and North America. The discussion is deemed important enough for Mr Persson to leave Stockholm only hours after the polls close in the country's general election.
But is it? From London the trip is being spun with gusto. To coincide with the seminar the Prime Minister will publish a Fabian Society pamphlet outlining his latest "third way" thinking. Selected leaks are likely to appear in the press before he boards Concorde.
Mr Blair will make two speeches, at the United Nations General Assembly and the New York stock exchange. At 4pm the seminar will begin under a title which cannot have been cleared by the spin doctors: "Strengthening democracy in the global economy: an opening dialogue". The audience at the NYU School of Law, of students, professors and journalists, will not be allowed to ask questions. The discussion is likely to be general, focusing on common problems: employment, welfare and the global economy. The beauty of the "third way", of course, is that all manner of political strategies can be pursued, providing they fall short of pure free-market economics on the one hand or dirigiste state socialism on the other. Whether the seminar will clarify what it means is another matter.
Critics argue that the "third way" is simply the latest buzz phrase being used to give some intellectual ballast to New Labour's rightwards drift; "first there was `stakeholding', then there was `communitarianism', now there is the `third way'", said one party insider. Mr Blair has, however, won intellectual brownie points by recruiting to the cause Anthony Giddens, director of the London School of Economics. In the United States there are advocates, too. Prominent among them is Sydney Blumenthal, the former political columnist who is now one of President Clinton's close advisers, (so close , in fact, that he features prominently in the Starr report). In May Mr Blumenthal told a meeting of the World Policy Institute: "With Great Britain we have forged a new special relationship, a 21st century alliance, as the President called it, based not only on all our traditional mutual interests but on our common conviction of the necessity for a new social contract.
"Blair is accused of accused of spin and waffling, lacking conviction, offering up a blur, just conservatism in disguise. But the emergence of a trans- atlantic one-nation politics of a new third way makes it increasingly clear that far more than personality is at stake."
It is the third such discussion between Messrs Blair and Clinton, and Ben Hall, research director at the Centre for European Reform and a former aide to Robin Cook, argues: "It is rather ironic that the third way conference is happening in New York when the impetus must be coming from continental Europe." Surely, goes the argument, Mr Blair should be trying to strike up common themes with his European partners as the left strengthens its grip on the continent. Which raises the interesting question of Lionel Jospin's absence.
According to one government source Mr Jospin turned down an invitation. The rumour was that the French Prime Minister felt snubbed because the organisers had not been swifter to contact him. Whatever the explanation his absence underlines the difference of emphasis between his government and Mr Blair's.
Mr Jospin has traditional European socialist roots, so much so that when he was elected, New Labour aides quipped that he was just the sort of figure who would have been expelled from their party. Since then there has been a rapprochement, culminating in Mr Jospin's visit to London, and to Mr Blair Sedgefield constituency earlier this year.
They seemed closer on policy too. In a set-piece speech in London Mr Jospin produced a soundbite much admired by Mr Blair's French-speaking press spokesman, Alastair Campbell: "Yes to a market economy, no to a market society".
In Germany, Gerhard Schroder, the Social Democrat challenger in this month's elections, has also deployed similar language, talking of a "new middle", although commentators find his political recipe vague.
While the rhetoric of the centre-left in Europe may be converging, it is hard to see a new, homogenous philosophy taking hold. As Dr Pfaller puts it: "In Great Britain it makes particular political sense because Old Labour was more leftist in its ideological leanings than, for example, the German Social Democrats or the Scandanavian socialists. But the third way means different things in different countries."Reuse content