Those who think Mr. Bloomberg would want to build a similar kind of organization, be it No Labels or something else, are assuming that the growing power and disaffection of independent voters who identify with neither Democrats nor Republicans make a third party more viable than it has ever been. In fact, though, the rise of the independents represents a movement in exactly the opposite direction — away from party organizations altogether.

This isn’t so much a political phenomenon as it is a cultural one. In the last decade or so, the Web has created an increasingly decentralized and customized society, in which a new generation of voters seems less aligned, generally, with large institutions. MoveOn.org and the Tea Party groups, for instance, were born as protests against the establishments of both parties, and they empowered citizens to create their own agendas, rather than relying on any elected leadership.

What the current moment might offer, then, as Mr. Bloomberg surely knows, is an unprecedented opportunity not for a new party, but for an independent candidate who represents a break from the dictates of any party organization, mainstream or otherwise. In the current environment, the less of a party apparatus an independent candidate carries, the better his chances of success may be.