The prospect that Christine Quinn will accede as the next speaker of the City Council represents an opportunity to build a more cooperative relationship between the mayor and the city’s legislature. Her accession was all but guaranteed with the concession last night of Bill de Blasio, and the word around City Hall is that she intends to try to work with the mayor. That would be a sharp contrast with her predecessor, Gifford Miller, who seemed, in his fevers of ambition for the mayoralty, to find it necessary to oppose the mayor even when, as has so often been the case lately, the mayor was taking a reasonable position.

In Ms. Quinn’s case, our sense of the situation is that it is not so much her ambition that one needs to worry about as her ideas. She is one of the leaders of the effort to block New Yorkers from access to the kinds of low-cost prices on goods that Wal-Mart has offered as a strategy to become the largest retailer in America. She is a proponent of spurning the twice-expressed will of New Yorkers to limit the terms of members of the council; Ms. Quinn wants to extend to 12 the number of years one can serve in the council and to do so through the maneuver of legislation, rather than taking the matter to the voters who installed the limits in the first place. She voted to override the mayor’s veto of the lead paint bill.

But there is a sense around City Hall that Ms. Quinn is someone who is prepared to work with the administration. She is said to have put in a call to the new deputy mayor, Kevin Sheekey, who had been Mr. Bloomberg’s campaign manager. We’re told it hadn’t been returned last night, but the fact that she placed it is an encouraging sign. If Mr. Sheekey doesn’t call her back, the mayor ought to do it himself, particularly since the word around City Hall is that the mayor preferred her to Mr. De Blasio. According to the Politicker Weblog, she has retained as a consultant Josh Isay, who had also been a consultant to Mr. Bloomberg’s re-election campaign. Certainly her professed willingness to work with the mayor is something that it would make sense for the mayor to test early.

Mr. Bloomberg has proven himself a lot more adept a politician than many predicted he would be when he set out on his mayoralty. But the council has stood off to the side as such a negative force in city life that serious people are wrestling with ways to reduce its power or increase representation within it of factions that have been cut out of city politics. The mayor’s own effort – non-partisan elections – was spurned by the voters, and, in our view, for good reason; political parties are a fundamental force of free expression. The nadir of the council may have been Mr. Miller’s abuse of his office through the use of huge amounts of public money to mail thinly-disguised campaign fliers to voters. Ms. Quinn has vowed to end such mailings from the speaker’s office. It seems she has not, or not yet, been infected with itch for higher office that ruined the tenure of Mr. Miller. If Mr. Bloomberg and Ms. Quinn can forge a working partnership, it could be sharp turn for the better in city governance.