Historically, third-party presidential candidates have appealed largely to disaffected voters of a single major party. These candidates can't win, but they affect the outcome by siphoning enough votes from that major party's candidate to guarantee his defeat.

Take TR as the Bull Moose candidate. People who had not voted for him as a Republican weren't going to vote for him this time either. He split the Republican vote and ensured the Democrat victory.

John Anderson's candidacy in 1980 was less consequential because he was trying to split the difference--running between Reagan and Carter ideologically. Many of his initial supporters drifted to one of the major party candidates between the conventions and the general election, and Reagan ended up with a majority of the popular vote and 489 electoral votes.

In 1992 Ross Perot drew his support primarily from disgruntled Republicans. Perot couldn't win, but he enabled GHW Bush's defeat and Clinton's victory. In that election, most states were won by plurality instead of majority. The combined vote totals of Bush and Perot exceeded Clinton's vote total everywhere except AK, DC, MD, and NY. Perot rearranged the electoral picture more comprehensively than any other third-party candidate.

In 2000, Ralph Nader's campaign openly admitted that one of the primary purposes of his campaign was to punish the Democrats for drifting too far to the right. The 32,000+ votes that he got in Florida were more than enough to tip the election.

Bloomberg's appeal would be primarily to northeastern and west-coast liberals in states that Kerry won in 2004, and which would presumptively go Democrat in 2008. I doubt very much that he would do well in flyover country. This implies that he siphons votes from the Democrat candidate, possibly enough to tip some key states (like Wisconsin and Pennsylvania) that were only marginally blue in 2004, and also to shore up states like Ohio and Iowa that were only marginally red.

One other interesting note: all of these third-party candidates except Nader vanished from electoral politics after their third-party campaigns. If Bloomberg runs, and ends up costing the Democrats the election in 2008, he'll be done. The hatred for him from the Democrats will eclipse anything directed at Nader in 2000. Of course, he can always console himself with a bathtub full of $100 bills.