Recent political polls have shown that the slice of Americans who consider themselves independents is about the same size or bigger than those who consider themselves Republicans or Democrats. If that's the case, then why should the candidate who wins the November election surround himself exclusively with members of his own party?

There's only one answer: tradition.

That's not a good answer for anything in the first decade of a new century, and if it were, all your daughters would be spending the summer being taught to mend and tend and fix, preparing them to marry whomever Papa picks. (I speak on authority as someone who never had the right, as master of the house, to have the final word at home.)

So now we have, perhaps for the first time ever, two apparent nominees who have shown disregard for their parties' orthodoxies and traditions, who speak about reaching across the partisan aisle, who have said that the old ways of doing things just won't do. Will Sen. John McCain, whose views on campaign finance and the influence of business lobbies horrify Republicans, and Sen. Barack Obama, whose willingness to inch toward the center and consider Republican ideas is sending ripples of fear among Democrats, pledge to put together a government of the best men and women -- regardless of party?

For all the talk of the strong political movements that have placed Sen. Obama and Sen. McCain on the verge of nomination, a third political movement has quietly been taking shape in the nation this year -- one that is urging Americans, and especially American political leaders, to move beyond party to address the serious economic and national-security questions that face the United States today.

There have been, to be sure, a handful of members of the opposition party in American administrations in the last several decades. C. Douglas Dillon, the Republican chairman of Dillon, Read, was treasury secretary under John F. Kennedy, a Democrat. John Connally, the former Democratic governor of Texas, served as treasury secretary under Richard M. Nixon, a Republican. William S. Cohen, former GOP senator from Maine, served as defense secretary under Bill Clinton, a Democrat. For five years, Norman Y. Mineta, a longtime Democratic congressman from California, served as transportation secretary for George W. Bush, a Republican.

But those are singular examples. No president in modern times has assembled a truly bipartisan Cabinet. Increasing numbers of former political figures are arguing that now is the time to change that.

"Usually one or two of the other party are chosen as a nod to nonpartisanship," Angus King, an independent who served as governor of Maine from 1995 to 2003, said in a telephone conversation. "You can't tell me that the very best people in the country, except for one, in 1999 were all Democrats but then, suddenly, two years later, all the best people in the country, except for one, were Republicans."

Mr. King says he realized after being elected that he had a remarkable advantage as an independent. "If the country is a third Democratic, a third Republican and a third independent, a Democratic president who appoints only Democrats has eliminated two-thirds of the public from consideration," he says. "I could appoint anybody. It was a great luxury."

Often supporters of nonpartisan government point to the example of Lincoln, who brought his greatest adversaries into his government -- an act that, if repeated today, would display what historian Doris Kearns Goodwin in The New York Times called "that rare combination of humility and confidence required to perform wisely at the highest level." Mr. Obama has read "Team of Rivals," Ms. Goodwin's book on the Lincoln Cabinet, two times and has discussed the book with the author.

Another example: the National Government assembled by J. Ramsay MacDonald in Great Britain during the Depression. That Cabinet included four Conservatives, four Laborites and four Liberals. It called itself a Government of Cooperation, with a simple goal -- "to deal with the national emergency that now exists."

Earlier this year, former Democratic Sen. David L. Boren, now the president of the University of Oklahoma, assembled a group of top officials, including former senators such as Republicans John W. Danforth of Missouri, Bill Brock of Tennessee and Mr. Cohen and Democrats Gary W. Hart of Colorado, Bob Graham of Florida and Sam Nunn of Georgia. Together they explored the limits of partisan government and the potential that a nonpartisan approach might hold.

Mr. Boren was elected with a large group of centrist senators in 1978, including Mr. Cohen and Nancy L. Kassebaum of Kansas, both Republicans, and J. James Exon of Nebraska and Howell Heflin of Alabama, both Democrats. The new senators had regular potluck suppers with their spouses, rotating from house to house, and they prided themselves on their bipartisan impulses. At the time the Senate was under the sway of a tradition that was named for the former Senate majority leader, Mike Mansfield of Montana, which discouraged senators from traveling to their colleagues' states to campaign against them. That custom has withered -- along with the vestiges of civility that prevailed in that time.

"The world has changed fundamentally, and our system has not been able to adapt to these changes," former Sen. Charles S. Robb, the Virginia Democrat, said at the Oklahoma conclave. He urged that Americans demand "the kind of reaching across the aisle that all of us believe is necessary."

Only once before in American history has more than one sitting senator run in a general election for president. That was in 1836, when three of them, including Daniel Webster, ran. All of them lost. This time two sitting senators are in contention, which despite the frustration many Americans may have with Washington may in fact be an advantage. Both Mr. McCain and Mr. Obama are running from a legislative position that requires compromise, even in the Senate. They know that they cannot get their way alone, and they know that the great legislation in American history, from Social Security to the Reagan tax overhaul, have had bipartisan support.

"Major legislation requires -- demands -- a lot of bipartisan voting," Mr. Boren, who is a member of the Obama foreign-policy team, said in a conversation the other day. "Even if we have a landslide in the congressional elections, we have to have a good 10 or 15 of the other party who are ready to join legislation or you are not going to get anything done."