Mayor Michael R. Bloomberg, the billionaire founder of Bloomberg L.P., who spent $74 million of his own money in 2001 to gain an office few thought he could win and $85 million more in 2005 to keep it, has become a singular figure in American politics. He ran as a nominal Republican, blending a liberal outlook on many social issues with bottom-line pragmatism developed in the private sector. He has been frequently mentioned as a potential presidential candidate for 2008 - a notion that grew when he dropped his affiliation with the Republican party in June 2007. He has insisted that he will not run, but his aides continue to promote the idea.