If Mayor Bloomberg is interested in making politics more competitive in New York City and enfranchising the city’s roughly 1.3 million registered non-Democrats, as he and members of his Charter Revision Commission so often say, there are better options than instituting nonpartisan elections. For many calculate that eliminating party primaries and replacing them with a first round of elections in September and a runoff between the top two vote-getters in November would tend to produce a general election in which two Democrats face one another. It’s hard to see where that’s a win for the people of New York.

The mayor has already incurred the wrath of the city’s two major parties, several smaller ones, and organized labor. But now, as our Benj. Smith reported this week, the big question is whether Hizzoner will spend from his own fortune to push through his scheme. But there’s another way for the mayor to spend to produce a more diverse ballot — putting some of his money into supporting candidates for City Council who are running under the banner of the party the mayor ran under to gain City Hall, namely the Republicans.

It wouldn’t be hard to double the size of the Republican delegation in the City Council. At the moment, it consists of but three members out of 51. Yet there are some competitive races. In District 19 in Queens, where a Republican, Philip Ragusa, is challenging an incumbent Democrat, Anthony Avella, the demographics give Mr. Ragusa a good shot. In Disctrict 43 in Brooklyn, a Republican, Pat Russo, is challenging another incumbent Democrat, Vincent Gentile, who betrayed the anti-tax campaign on which he won his council seat. In District 5 in Manhattan, a Republican primary is heating up between Douglas Winston and Jennifer Arangio to determine who will challenge Speak er Miller.

A relatively modest amount of money could make a big impact in these races, where, like in nearly all local races, name recognition is the biggest hurdle. If there’s one thing that can be purchased with cold, hard cash, it’s name recognition. In the medium term, New York City’s Republicans simply need more money to spend on political clubs and grass-roots organizing. Whether Mr. Bloomberg is prepared to come to the aid of his party, however, is doubtful, and that gets to the nub of the contradiction in the mayor’s reform.

Consider, for example, the North Shore of Staten Island, whose District 49 poses a classic problem for Mr. Bloomberg. There, a Staten Island Democrat, Michael McMahon, who voted for the mayor’s 18.5% property tax increase, will be challenged by an anti-tax Republican, Lisa Giovinazzo, who until recently was a reporter for Bloomberg Television. Last time out, while Mr. Bloomberg was running for mayor, he gave money to Mr. McMahon, snubbing the Republican in the race. It illustrates the fact that the mayor, while nominally a Republican, is a Democrat at heart.

Only a few months ago the mayor caused a delegation of Staten Island Republicans to storm out of a dinner party when he promised to support Democratic candidates who had voted for his property tax increase. He has already said he’d vote for the speaker of the council, Gifford Miller. In the race on the North Shore of Staten Island, the question will be laid bare: Does Mr. Bloomberg stand with Democrats and higher taxes or with Republicans? If he can’t bring himself around to supporting a fellow Republican and former employee, voters will know all they need to know about just how much the mayor really wants to empower those parties that have supposedly been driven out by partisan politics in New York.