Last weekend’s vote in the West Bank and Gaza Strip drew praise from many quarters, not least from the White House where President Bush called it “a historic day for the Palestinian people and for the people of the Middle East.”

The White House is looking ahead to an even more closely watched exercise in democracy, the elections in Iraq scheduled for the end of January.

Both votes raise the same question: Is holding an election the benchmark of democracy? The answer depends on whether the election yields a government that is legitimate in the eyes of the majority of its people.

The best measure of legitimacy is competitiveness and voter participation. Does an election offer real choice? And how many voters come to the polls? On both counts, the picture in the occupied territories is a mixed one — and even more so in Iraq.

When it comes to the Palestinian territories, Bush’s description is factually wrong on one key point. “The election is not historic, by any means,” says Middle East scholar Shibley Telhami.

Palestinians have held several elections, including a 1996 presidential vote. In that truly historic first, Palestinian leader Yasser Arafat got 90 percent of the vote against a single, nominal challenger. Despite a call for a boycott by Islamic militants, the turnout was exceptionally high — 90 percent in the Gaza Strip and 85 percent on the West Bank.

This time around, competitiveness improved but turnout slipped, notes Telhami.

The winner, Mahmoud Abbas, received just over 62 percent of the vote, according to preliminary official results, with his main rival garnering about 20 percent. But there was never any question that Abbas, the candidate of the Palestinian establishment, would be the victor. The outcome was predetermined when the Palestinian leadership, backed by Arab governments, put tremendous pressure on popular jailed radical leader Marwan Barghouti to withdraw his candidacy.

“Elections are often about deals among elites rather than legitimate expressions of popular opinion,” said Georgetown University Middle East scholar Daniel Byman.

The certainty of the result may have pushed down voter participation. Turnout was reportedly about 65 percent, down even from municipal elections held some months ago. So few voters showed up early in the day that Palestinian officials extended voting for two hours.

“Still, people will accept that this is a legitimate election,” believes Telhami, a close observer of the region. Though the militant Islamist group Hamas called for a boycott on the grounds that any election held under Israeli occupation was unacceptable, it has agreed to acknowledge the government that emerges.

The Iraqi election poses much greater challenges. Most parties and leaders representing Sunni Arabs — at least 20 percent of the population — refused to run for election to Iraq’s new parliament. Voter turnout among Sunnis is likely to be very low, mostly because they see the entire process as illegitimate.

Among the majority Shiites and the Kurds in the north, there is greater enthusiasm for the election. The most popular election slates represent those populations well. But even they may balk at voting because of intimidation ahead of balloting and a lack of security at polling places.

Iraqi and U.S. officials stress that Sunni participation is necessary for the vote to be considered legitimate. But the findings of a poll conducted last month by the State Department’s Bureau of Intelligence and Research shows that only a third of Sunnis are “very likely” to vote and that only 12 percent consider the election legitimate. The poll probably overstates Sunni participation as it did not include some major centers of resistance.

The poll showed that the threat of violence would keep as many as 88 percent from voting, according to press reports. Roughly 38 percent of Shiites — who account for 60 percent of Iraq’s population — would stay home if there is violence at polling stations.

The government that emerges from this election will be slightly more legitimate, says Byman, a former intelligence analyst. But the danger, he says, is that “Sunnis will increasingly see the system as stacked against them and the rebellion will intensify.”

That prospect has prompted growing calls to postpone the Iraqi election, an option that most experts consider unrealistic at this point. Elections will go ahead. Legitimacy may have to wait a while.