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WASHINGTON - President Bush won re-election, took a majority of the popular vote for the first time in 16 years and added to his party's majority in both houses of Congress for the first time since Franklin Roosevelt did in 1936. What more could he want?

A mandate.

''America has spoken,'' Bush said, his eyes on a bold second-term agenda that would overhaul the nation's tax code, partly privatize Social Security, reshape America's courts and assert U.S. military power abroad regardless of world approval.

''President Bush ran forthrightly on a clear agenda for this nation's future and the nation responded by giving him a mandate,'' said Vice President Dick Cheney. Bush voters echoed that sentiment, saying their majority is strong and clear: Godspeed and full steam ahead.

Democrats, however, insist that Bush won no such endorsement from Americans to pursue such an aggressive second-term agenda. His victory was narrow, they said, and any claim to broad national support would deny the voices of 55 million Americans who voted for John Kerry.

The question of whether he has a mandate is important given Bush's ambitions, particularly since he won an election in which the choice was clear and the stakes were high. Earlier turning-point elections with such stark differences between the two major parties - such as those in 1932, 1964 and 1980 - all led to significant changes in the government. All those winning presidents also claimed mandates.

''It gives a president greater confidence. It's more intimidating to Congress,'' said historian Robert Dallek.

But what defines a mandate, and to what does it apply? History suggests that's up to the winner.

Woodrow Wilson won a narrow re-election in 1916, running on a platform of keeping the United States out of World War I. Yet he used his second term to enter the war and then try to reorder international affairs with a League of Nations.

John F. Kennedy won 49.7 percent of the vote in 1960, but claimed a mandate to bear any burden and pay any price to win the Cold War. He ratcheted up the confrontation with the Soviet Union, but wasn't able to get major proposals to cut taxes or expand civil rights through Congress.

Ronald Reagan got 50.7 percent of the vote in 1980 and claimed a broad mandate to cut taxes and confront the Soviet Union. He got a bigger vote in his 1984 re-election, but did less in his second term.

Bill Clinton never won a majority - winning 43 percent in 1992 and 49.2 percent in 1996, owing to third-party candidate Ross Perot - but claimed a mandate to overhaul health care and cut the federal budget deficit.

Was Bush's 51 percent of the popular vote enough to claim a mandate?

For voters, it can depend on the issue.

Exit polls of voters on Election Day indicated that Bush has a mandate to protect against terrorism and work on health care - 71 percent of voters said they are worried about terrorism; 70 percent said they are very concerned about the cost and availability of health care.

On Iraq, the will of the people is less clear. Polls showed 51 percent thought the war was the right thing to do, but 52 percent also think the war is going badly now.

Ask about abortion, and there's no clear mandate: 21 percent want it always to be legal, 38 percent want it mostly legal, 26 percent want it mostly illegal, and 16 percent want it always to be illegal.

The same goes for gay marriage: 25 percent want it legalized, 35 percent want to legalize civil unions and 37 percent want no legal recognition.

Ditto for Bush's tax cuts: 41 percent said they were good, while 32 percent said they were bad.

''It's not just the number. It's the sense of the people,'' said Mary Beliveau, a lobbyist from York, Pa., who voted for Bush and believes the majority wants Bush to appoint conservative judges, limit abortion and help religious groups do more to help the needy. ''He has a mandate to do exactly what he said he was going to do.''

Maryanne Spooner, a nurse from Parma, Ohio, voted for Bush and believes his majority support gave him approval to pursue his entire agenda. ''Look at the majority vote. A majority went with Bush,'' she said. ''That tells you what people are thinking. They want morals and values. They want homeland security. They backed him in Iraq.''

James Hooper, a retiree from Jackson Township, Ohio, also voted for Bush, hoping that the president would reverse what Hooper called the country's moral decline in everything from abortion to the coarseness of popular entertainment. But he said Bush's mandate wasn't open-ended.

''It depends on what your definition of mandate is,'' Hooper said. ''If it means he can do whatever he wants to do, I don't accept that definition.''

Kerry voters definitely don't accept the idea of a Bush mandate, especially a broad one.

''I heard him say that America had spoken. Well, nearly one-half of the country didn't vote for him,'' said Dorie Vazquez-Nolan of Macomb, Mich. ''He barely won. I don't consider that a mandate. Maybe if he had won 60 percent of the vote. But not with 51 percent.''

To please voters such as Vazquez-Nolan, Bush would have to pull out of Iraq, increase taxes on the wealthy, support affirmative action and back unequivocal abortion rights.

But she acknowledged that that's virtually impossible. On taxes, she said with a shrug, ''I guess he can do what he wants to do.'' On everything else, she said, the best she can hope for is that he makes some concessions to her side.

Dallek, the historian, said that presidents who claim big mandates could be tempted to overreach. Roosevelt did so in his second term, proposing a scheme to pack the Supreme Court with allies. Johnson did so in his second term, plunging the country deeper into the Vietnam War.

''There's always a mandate to govern, no matter how much you win by,'' said Leon Panetta, a former White House chief of staff for Bill Clinton. ''But if someone says they have a mandate to implement a party ideology, that's a different question.

''You have to be careful not to read too much into a win. Power produces arrogance. The more power you think you've got, the more arrogant you become. The public can always turn on you. It's smart to understand there is a short leash here.''