AMERICANS ARE deeply divided politically, so much so that polarization itself has become an issue that may overshadow the specific substantive disagreements among parties and candidates. After all, if partisan animosity renders the government machinery dysfunctional, then it hardly matters who the people choose to operate it. So one of the big questions hanging over Tuesday’s voting, not only in our area but also in other states, was whether voters would send a clear signal in favor of pragmatic, as opposed to ideological, governance.

New Jersey Gov. Chris Christie’s reelection suggests that the answer is at least partly “Yes.” This was not necessarily foreshadowed in the first year or two of Mr. Christie’s term, which began in 2009. The Republican governor made a national name for himself by confronting opponents, sometimes in angry language. But the issues he tackled — educational and pension reform — were genuine. And when the time came to legislate, he proved capable of working with Democrats. His embrace of President Obama when Superstorm Sandy hit his state during the waning days of the 2012 campaign may have infuriated GOP leaders, but it was in his constituents’ interest. You don’t have to be a fan of Mr. Christie to be impressed by his victory, just someone who believes that the entire two-party system would benefit if more Republicans were to follow his more inclusive brand of politics rather than the tea party variant.

Next door in New York City, Public Advocate Bill de Blasio, a Democrat, was elected mayor by a huge margin after campaigning on a rather different theme. An unabashed liberal populist, Mr. de Blasio spoke of a “tale of two cities ” and promised to focus on the plight of the 46 percent of New Yorkers who live on incomes equal to 150 percent of the federal poverty line or less. After 12 years of centrist, nonpartisan government under Mayor Michael R. Bloomberg (I), city services run more efficiently, school reform has advanced and crime has plummeted. Yet economic inequality represents the unfinished business of Bloomberg-style centrism — as, indeed, it remains a major issue nationally. Mr. de Blasio has promised to tax the rich to pay for preschool and to abandon the “stop-and-frisk” policing methods that Mr. Bloomberg credited for curbing crime — but that also alienated minority youth who bore the brunt of these tactics.

If Mr. Christie has made himself the new hero of mainstream Republican conservatives, Mr. de Blasio is the champion of those on the Democratic left who are disillusioned with President Obama and eager to implement their undiluted ideas on the Big Apple’s big stage. With unions already lining up to press for fatter contracts, the new mayor’s challenge will be to husband the city’s resources and use them to cut inequality and expand opportunity — without forfeiting the gains in safety and livability that New York made during Mr. Bloomberg’s time.