WASHINGTON — One of the numbers that leaped out of the new Washington Post-ABC News poll of Iowa voters came on the question of which candidate voters see as honest and trustworthy. On that quality, Republicans in the Hawkeye State don’t think much of Rudy Giuliani.

Just 4% of likely caucus participants cited the former New York mayor, putting him behind Mike Huckabee, Mitt Romney, Fred Thompson, and John McCain. At the same time, 31% cited Mr. Giuliani as the strongest leader in the field, well ahead of all his rivals except Mr. Romney (who was at 30%).

A similar though less striking relationship occurred among the Democrats. Hillary Clinton was judged by third of Iowa Democrats to be the strongest leader in the field, but half as many called her the most honest and trustworthy.

The findings seem to raise an obvious question: What ever happened to likeability?

Mr. Bush was seen as a more likable candidate than Vice President Gore in the disputed election of 2000. Mr. Bush had an even greater edge on that attribute in a 2004 election that was fought on terrain that in many respects favored Senator Kerry.

This year, Mrs. Clinton and Mr. Giuliani, the two candidates who lead the national polls, get lower ratings on trust and honesty than they do on strength and leadership, and as a campaign advertising manager who did the ads for Bush in 2000 and 2004 and now works for McCain, Mark McKinnon, said Wednesday morning, “You usually don’t like people you don’t trust.”

One of Kerry’s pollsters in 2004, Mark Mellman, who was said other attributes are more important than a candidate’s likeability and have been in past elections. “I think likeability is vastly overrated,” he wrote. “It is just one dimension of personality to which voters react.

“Bush didn’t win in ’04 because he was more likable,” he added. “In part, what voters may be reflecting is a reaction to what they have seen over the past eight years. Given Bush’s low approval rating and the harsh assessments of the administration’s competence in managing the war in Iraq and the Katrina aftermath, there’s no doubt that voters are looking for more than likeability in their chief executive.

“I think that what voters want in a candidate depends on the voter’s verdict on the president in office” and the “state of the nation,” the director of the Pew Research Center, Andrew Kohut, wrote in an e-mail. “In this case, people see a failure of leadership in the Bush years, and that’s why strong leadership image may be trumping ‘likeability.'”

A Republican pollster, Whit Ayres, said likeability still matters and pointed to Mr. Huckabee’s rise in Iowa as evidence. He said respect matters more than likeability, but the key to a truly successful presidency is having both. Ayres cited Dwight Eisenhower, John F. Kennedy and Ronald Reagan as three who combined both.

“If you can only have one, respect goes farther in politics,” he wrote. “I think that’s particularly true in a time of national challenge like terrorism, and I think that helps to explain both Giuliani’s and Clinton’s strength so far.”