IN ONE corner of Michael Bloomberg's open-plan City Hall offices, near the digital clock counting down his final days as New York's mayor, hangs a large cartoon cut-out of a helicopter. Hanging from its cockpit window is a towel bearing the word "Bermuda." This is a somewhat edgy gag. Thanks to the financial-information empire that he founded, Mr Bloomberg is one of the richest men in the world: Forbes puts his wealth at $31 billion. Naturally, he owns a real-life helicopter and a weekend home in Bermuda. It is not known just how often he flies to the balmy island to play golf. Though the mayor has brought transparency to once-murky city government (a favourite Bloomberg motto is: "In God we trust. Everyone else, bring data"), he does not feel a politician's urge to share his inner life with voters. New Yorkers have weathered a dozen eventful years with their mayor, spanning the aftermath of terror attacks, the financial crash and Hurricane Sandy. They elected him three times, first as a Republican, then as an independent, after campaigns of stupendous, lopsided expense (Mr Bloomberg shovelled more than $100m of his own money into his final re-election). His wealth frees him from corrupting special interests: he never has to beg for campaign donations. It has also spared him the usefully humbling experience of having to beg a truculent city for its love. He is a chief executive, not a leader who makes voters swoon. Barred by term limits from running again, Mr Bloomberg has mere weeks left in office. Under his tenure New York has become safer and cleaner. His attempts to make New Yorkers healthier (a smoking ban in public places, calorie counts on menus) have been embraced after some grumbling. Schools have improved, albeit patchily. Real incomes have stagnated, however, and the gap between rich and poor has widened alarmingly. Visiting the mayor at City Hall, Lexington pondered a narrower question: whether Mr Bloomberg's experiment with self-funded, data-driven rationalism has broader lessons for American politics. Mr Bloomberg is sometimes called a centrist, but that is not quite right. He is a social liberal on issues from gay rights to the folly of imprisoning so many Americans. But he upsets liberals too, when he defends frequent police searches of young black and Hispanic men. "Stop-and-frisk" has cut crime, he says briskly: "Scaring the kids to not carry guns is one of the integral parts of it." There are city programmes to help young minority males, he adds: his foundation gave them $30m. That combination of liberalism, conservatism and philanthropy works in a city like New York. But it has no large constituency in national politics - as Mr Bloomberg tacitly conceded when he shut down half-formed thoughts of a presidential run in 2008. Now New Yorkers are ready for change. The outgoing mayor talks of Americans "voting with their feet," visiting his city as tourists in record numbers, moving their children into its public schools and applying to work for the city in lines "a zillion miles long." Even income inequality is the result of hard work to attract the "ultra-rich," who patronise shops and restaurants and pay lots of tax, Mr Bloomberg suggests. But election day on November 5th will almost certainly see a thumping win for a more left-wing Democrat, Bill de Blasio, who has run as the anti-Bloomberg, vowing to raise top income-tax rates and playing to voter angst about a glittering city that feels unaffordable to many. Outside New York in conservative circles, the mayor is held up as a sinister, Bond-villainish scold, dropping millions on political campaigns to foist big-city values on middle America. Favourite Bloomberg causes, from education reform to gun control, have drawn him into electoral fights nationwide. Bloomberg-funded attack ads helped derail a pro-gun Democrat trying to win a party primary in Illinois, and have pounded the pro-gun Republican running to be Virginia's next governor. The tycoon's cash is not always welcome. Colorado's Democratic governor, John Hickenlooper, recently hinted that he would prefer a Bloomberg-funded group, Mayors Against Illegal Guns, to stop helping him fight gun-rights advocates, saying that folk in his state dislike outside "meddling." Supporters say that Mr Bloomberg is a pioneer of a new politics. Books with such titles as "If Mayors Ruled the World: Dysfunctional Nations, Rising Cities" argue that cities have almost magical powers to transcend partisan gridlock. To boosters, cities encourage pragmatic problem-solving, because mayors are accountable for tangible tasks like collecting rubbish, fighting crime or fixing schools. They quote a former New York mayor, Fiorello LaGuardia, who said: "There is no Democratic or Republican way of fixing a sewer." They look forward to Mr Bloomberg going global as a mentor to mayors, via such bodies as C40, a network of big cities taking steps to reduce greenhouse-gas emissions. Mr Bloomberg seems to side with the boosters. National and state governments must wrestle with tasks such as redistributing wealth from haves to have-nots, he says. Washington looks "broken and shut down and hopelessly partisan." In happy contrast, "Good mayors across America are doing innovative things." Resist the scourge of golf But not all mayors are good, or immune from rows about wealth-sharing. Whoever is New York's next mayor, the unions will demand new, generous and retroactive contracts. Ask union members - or the taxpayers who must foot the bill - whether fixing sewers has partisan aspects. It is true that dynamic American cities attract the sort of rich folk willing to spread their wealth a bit if that is the price for walking the streets in safety, as opposed to living in a gated, guarded suburb. But that is an observation about politics, not about processes of government. Mr Bloomberg has done a lot for New York. Cheer if he devotes his coming years to helping cities, rather than to golf. Alas, his success is not much of a guide to fixing America.