Bloomberg is hardly a win for the Republicans.
Why do you say that. I dont follow NYC politics so I really know nothing about him.
NYC doesn't really have much of Republican party outside of Staten Island and some enclaves elsewhere. Furthermore, none of its stalwarts has any chance of ever being elected to any citywide office - not even the Chief Dogcatcher of NYC, were they to establish such a sinecure in the next Charter revision. Therefore, there isn't really much of a competition in party primaries - no heavyweight wants to be a whipping boy.
In contrast, the Democratic party is full of ambitious local politicians. Winning a Democratic primary without having paid one's dues to the organization for decades is nearly impossible. Hence, there is a respectable tradition for ambitious outside politicians (as well as for some unsuccessful long-timers) to reregister as Republicans with an explicit purpose of being nominated. This is exactly what a life-long Democrat Bloomberg did before running for Mayor. Actually, this is also what Giuliani did right before he ran the first time (he lost then to Dinkins, but won 4 years later). The strategy is surprisingly successful: faced with a choice between a fresh and energetic face and a tired party hack, oftentimes New Yorkers are willing to vote for a nominal Republican.
Of course, once they become elected Republicans people like Giuliani and Bloomberg try to be reasonably loyal to the national and state parties (they don't have to do much for the local Republican party, since there ain't any). So they donate money or organize fundraisers, etc. In these respects they are indeed quite loyal, at least to Republican incumbents: being friendly with national and state Republicans helps having things done. Still, they don't really change their issue positions much on anything - they'd be (politically) dead in months if they did.
