New York Governor David Paterson’s appointment of Kirsten Gillibrand as Hillary Clinton’s replacement in the U.S. Senate has set in motion a three-dimensional political chess game. To date, most press attention has focused on the foibles of Caroline Kennedy, but the intersection of the senate appointment, this year’s New York mayoral race, and next year’s New York gubernatorial race has rearranged all three levels of politics. The big winner is the state’s senior senator, Chuck Schumer. The big losers are Mayor Michael Bloomberg and, to a lesser degree, Paterson.

Schumer backed Gillibrand, a moderate, fiscally conservative, anti-gun control Democrat, even when she was considered a dark horse to succeed Clinton. She’s the very model of the candidates with cross-party appeal whom Schumer recruited in 2006 to win Democratic control of the House of Representatives. Gillibrand appeals to the same moderate and independent voters who proved so important to Barack Obama’s presidential victory. For now, Schumer stands tall not only in New York, but on Capitol Hill as well.

At first glance, Paterson seems to have suffered a significant defeat. After 55 days spent dithering over Clinton’s replacement culminated in a nasty spat with the once-putative choice, Caroline Kennedy, Paterson stands exposed as an accidental governor, ill-organized and indecisive. His setback comes just as the state, which lost roughly 100,000 jobs over that same two-month period, slides into an economic and fiscal swamp. Paterson’s visible weakness might draw New York Attorney General Andrew Cuomo into the 2010 Democratic gubernatorial primaries. Paterson could have appointed Cuomo to succeed Clinton, thus eliminating him as a gubernatorial rival. But that would have provoked a battle with the state legislature over who was to succeed Cuomo as attorney general, setting up a showdown between the governor and Democratic Assembly Speaker Sheldon Silver, who was sure to prevail, and thus expose Paterson’s weakness.

Nonetheless, even at considerable cost to himself, Paterson showed that he was strong enough to deny the senate seat to heirs from two of the most powerful political clans. More importantly, though Gillibrand has drawn the ire of liberal Democrats—some of whom are already threatening to oppose her in two years, when she will have to run for her seat—the congresswoman’s appointment strengthens Paterson among upstate voters, whose support he will need should he face a strong GOP opponent in 2010.

By contrast, it’s hard to find an upside for Mayor Bloomberg. He placed a heavy bet on Kennedy, who through her ties to President Obama could have been the mayor’s prized connection to the new administration in Washington. The appointment of the pro-NRA Gillibrand is a slap in the face to the mayor, who has become the leading national supporter of gun control. A Senator Caroline Kennedy closely affiliated with Bloomberg would likely have kept Paterson at arms length from this year’s mayoral contest. But with Kennedy out of the picture, there’s little to prevent Paterson, who’s made no secret of his disdain for the mayor, from throwing his gubernatorial weight behind New York City Comptroller Bill Thompson’s mayoral bid.

The Gillibrand appointment also creates a problem for Long Island’s energetic Republican Congressman Peter King. King was primed to run against the feckless, simplistically liberal Kennedy for the Senate. But Gillibrand’s moderation makes her a much tougher target, and King may now be thinking of a gubernatorial run against Paterson instead—assuming that Rudy Giuliani doesn’t jump into that race.

And if all of this wasn’t enough, the Gillibrand appointment this morning was followed by this afternoon’s announcement that former State Senate Majority Leader Joseph Bruno, a longtime New York political powerhouse, has been indicted. Bruno’s indictment follows what journalist Jacob Gershman describes as the Albany crime spree, in which 11 major figures in Albany have, over the past six years, been caught up in criminal activity. And to close the circle, Gillibrand’s father was long a close business associate of Bruno, a connection that helped pave her way into Congress.

This extraordinary moment has exposed the decay of New York State’s political culture, in which clan membership seems, at times, to be a prerequisite for higher office. At the same time, those who criticize the Gillibrand appointment will have to explain why the state’s 26-member congressional delegation (sure to shrink in 2010) has so few players who’ve made any impact in Washington. The best known and most powerful member, Congressman Charles Rangel, is caught up in a series of corruption scandals of his own. This is the leadership vacuum that created the brief Caroline Kennedy boom. In its aftermath, the Gillibrand appointment will resonate through the city and state for many years to come.

Fred Siegel is a contributing editor of City Journal and a professor of history at the Cooper Union for Science and Art.