When George Bush was running for president in 2000, there was a sales pitch in his stump speech that never failed to offend my European ears. "I'm a leader," he would boast, with a particular emphasis, as though this entitled him to the top job without further explanation.

He never, in my hearing, said he was qualified to be a leader because he had a Harvard MBA, though he did. Nor did I ever hear him refer specifically to his co-ownership of the Texas Rangers baseball team, though that might not have been irrelevant. Every now and again he did mention his job as Governor of Texas, although he had campaigned for that job with the same sense of leader's entitlement as he was now employing to win the presidency.

He seemed to treat leadership as an innate and self-perpetuating quality, something innate, rather than inculcated through education or training which, given his lineage, might have been a reasonable assumption. But it was also a quality that appeared to be hugely in demand in the United States.

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Whenever I received CVs from someone hoping for an internship in this newspaper's Washington office, the application invariably contained a paragraph about the candidate's leadership skills, right before one saying what a splendid "team player" they were. Obviously, any American CV had to hedge its bets, while a US president is supposed to lead – even if leadership ability is to be judged, as it surely is, less by the leader than the led.

Given where George Bush's leadership ability took the United States, it is perhaps unsurprising that neither of his would-be successors claimed "being a leader" as their forte. That might also be because, as senators, their experience was not primarily in an administrative role. The absence of "leadership" boasts from that campaign, however, has not halted an ever louder and more urgent clamour for "leadership" since, not just on the national scale, but, as is even more striking, globally.

Take last week. When President Obama delivered his long-awaited address on Afghanistan policy, there were countries where real, practical, actions would be determined by what he had to say. It was, after all, not just the US military that had been awaiting its orders, but the Nato allies, starting with Britain, France and Germany, who needed to know what would be asked of them. Then there was Afghanistan – the government, the regions and the Taliban – all waiting to hear what direction the US would take.

Yet it was not only these countries, governments, military commanders and, indeed, rebel groupings, that seemed to be keenly awaiting what the US President had to say – and periodically asking what was taking him so long. The expectation, and the frustration, went far wider. A large part of the world seemed to be waiting for Mr Obama as the acknowledged standard-bearer of the globe. When he said, as he did in his speech, that the only nation he was interested in building was his own, the disappointment was palpable, as though a US President, whose election had been hailed around the world, was somehow guilty of poverty of ambition.

Such disappointment is at its most acute where the US President is concerned. His early speeches, not least the one to the Muslim world in Cairo, were widely interpreted as evidence of benevolent global reach, rather than a desire to right wrongs in US relations with a particular part of the world. There is a sense in which the award of the Nobel Peace Prize – which Mr Obama will receive in Oslo on Thursday – was itself an expression of that early hope that Barack Obama's soaring eloquence would be matched by action on the same sweeping scale.

Similarly, his decision to travel to the Climate Change summit at all, and then for the end rather than the opening, is interpreted as something of a talisman. It has been hailed as a sign that the Copenhagen meeting – historic, global, you choose the adjective – could actually succeed in helping to save the planet.

But similar, if more modest, hopes are applied to other political leaders. During Germany's election campaign, the Chancellor, Angela Merkel, was repeatedly challenged about her supposed unwillingness or inability to lead. The fact that Germany's awkward coalition had held together for its whole four-year term was not considered counter-proof enough.

In Britain, Gordon Brown is repeatedly assailed with complaints that he lacks leadership ability – the comparison being with his predecessor, Tony Blair. But is there perhaps confusion here between leadership ability and charisma, even demagogy? Taking people along with you may include the capacity to inspire, perhaps to deceive. But might it also include the less exciting ability to persuade with a compelling argument?

A debate was very nearly, but not quite, had over leadership and what it means, as the recent appointments to the top posts in the European Union were finalised. There was plenty of public noise and advocacy in advance. But behind the scenes the 27 national leaders reached a consensus about the qualities they wanted in their president and high Representative, which explains the low-key choices made. The 27, it appears, wanted people capable of bringing others together and facilitating acceptable solutions. They did not want a high-profile standard-bearer who, in that celebrated expression, would "stop the traffic in Beijing". But who is to say that this quieter concept is not leadership, too?

The interconnectedness of the world, thanks to instant communications, has surely contributed to the idea that a single, inspirational leader would be an asset: a "take me to your leader" syndrome. But perhaps, in the cacophony of competing national and sectional voices, the opposite is now true. This need not mean world governance by cumbersome committee, but a recognition that the promise held out by a single inspirational individual is likely to be vain amid so much difference. Boring it may be, but effective chairmanship is a much underestimated strength – and one that might have made history look more kindly on George Bush.

m.dejevsky@independent.co.uk