At the last official estimate, the population of Greater London was 7,512,400. So quite how the greatest city in the world found itself with a choice between Ken Livingstone, Boris Johnson and Brian Paddick to serve as mayor is a mystery. Many Londoners feel that they have the unenviable task of choosing between a whining, boozing and not-so-unreconstructed Marxist, a braying shambolic Old Etonian and a smug, self-righteous non-entity. Yet London's success or otherwise has a bearing on the fate of everyone in the country, in economic, social and environmental terms. The influence of the world's most cosmopolitan capital is felt well beyond Britain's shores.

Any contest in which the incumbent has been in place for two terms and is seeking a third will inevitably be, in large part, a referendum on that person's performance. Public office is given on a leasehold, not freehold, basis. Change is natural and generally healthy. Yet there are also times where the effectiveness of the person in charge is such that it would be churlish to assert that a new figure is needed for the hell of it. Richard Daly Jr, the Mayor of Chicago, for example, has been viewed as a public administrator of the highest calibre and has been rewarded by six successive election victories. His is a story that Ken Livingstone openly aspires to emulate.

Whether he has a record to match that of his Chicago counterpart is much more contestable. It should be acknowledged, frankly, that he has been a better mayor than was generally expected, not least by this newspaper, when he stood and when an independent eight years ago. He has not been the crude anti-capitalist that he was when at the helm of the Greater London Council in the early 1980s. He has forged a surprisingly amicable working relationship with the City of London and the business community. Upon returning to the Labour fold for the 2004 mayoral contest, he also developed an unexpected empathy with Tony Blair.

He also has a set of accomplishments that he can highlight. Despite arriving in office hostile to any “Napoleonic” model of the mayor, he appreciated that his objectives would never be realised if he did not build up his own position. In the competition between the centre and the boroughs, he has reinforced the centre and acquired the unlikely support of big business for that shift as he did. The congestion charge is not universally adored, but it was a bold decision that has reaped some rewards in terms of a reduction in congestion. The innovation of the Oyster card was, similarly, one that could have ended in tears but proved successful. The mayor was a passionate and persuasive advocate of London's bid to host the Olympics. He found the right words to express the defiance of Londoners after the terrorist outrages that occurred on July 7, 2005. He has made himself the public face of the capital.

All of that, however, is some distance in the past now. The blunt truth is that the returns on his tenure have been diminishing rapidly over the past two years. If he seems tired today (and he certainly does), then the fatigue that may well be manifest shortly into a third term is not an enticing prospect. The mayor has done little in the course of his re-election effort to imply that be can provide anything but more of the same.

And that means proportionately more of the side of Mr Livingstone that is deeply repellent. It includes his tendency to ignore the faults of his immediate cronies and the inadequacies of his extended family of intimates (such as Sir Ian Blair, the hapless Metropolitan Police Commissioner). It involves his willingness to engage in appalling gesture politics such as his ludicrous formal accord with Hugo Chávez, Venezuela's quasi-dictator, and his readiness to embrace a variety of extremists because they are anti-American, even if those people loathe the social diversity in London that the mayor normally lauds. As Mr Livingstone's energies waned, once re-elected, he would be less inclined to set out new ideas and more at ease promoting old, mistaken, causes. It has to be concluded that two terms are enough.

Democracy, nevertheless, requires an acceptable alternative. In theory, the Liberal Democrats had an unusual opportunity this year. They have been strengthening steadily in the capital and a liberal message is one that should have appealed to those who favour a dynamic mayor who sticks to the job, not crass symbolism. The selection of Brian Paddick as their contender has not, it must be stated bluntly, been an inspired move. He has at no second offered compelling reasons why he should be in the mayor's chair. Instead, he has taken every opportunity to underwhelm.

That leaves Mr Johnson. Is he up to it? If the answer to that question were an unalloyed “yes”, then the mayor would be clearing his desk already. It is only because there is uncertainty in this regard that the theme of “time for a change” has not swept all before it. By dint of his bumbling public persona and unconventional background for executive management, Mr Johnson has invited the charge that he himself is the sole remaining argument for re-electing his rival.

There is plainly an element of risk in backing Mr Johnson. Newspapers have fretted about endorsing him precisely because journalists know Mr Johnson, a fellow journalist, so well and they know he has a history of letting people down. But there are grounds for suspecting that the gamble is not as wild a wager as it might appear.

The Conservative candidate is an enormously intelligent man. His eccentricities are, it should be remembered, basically harmless and inoffensive whereas Mr Livingstone's various attempts to summon up the political spirit of 1968 and cosy up to political thugs and merchants of hate most definitely are not. The thrust of Mr Johnson's policy suggestions on crime, transport and planning are sensible. His candour is welcome. His energy, enthusiasm and appetite for the role are much needed, particularly as London's economy heads into a testing few years. He is alive to Londoners' very deep concerns about drugs, stabbings and gangs, disappointment about persistent poverty and housing shortages, as well as their frustrations at traffic jams, empty bendy buses and an Underground network that is held to ransom by Bob Crow and the RMT. The responsibility of office will discipline Mr Johnson and will soon convince him, as it did Mr Livingstone, that a strong mayor who is more than the plaything of the boroughs is vital if the capital is to be prosperous.

If he does not, then London and the country will have learnt something of immense value. Mr Johnson is not the only Old Etonian with a sense of entitlement and a pretty modest understanding of truly ordinary people who intends to put himself up before the electors at some moment. A Johnson mayoralty would allow voters everywhere to reach a judgment on whether charisma, style and an easy elevation to prominence can be matched by the intelligence, steel and the commitment to be a leader in the interests of the many and not merely a well-entrenched few. If the experiment succeeds that will bode well for the credibility of a modernised conservatism. If it fails, voters in London and Britain will be wholly entitled to draw broader conclusions from it too.