WASHINGTON — One of the numbers that jumped out of a new Washington Post-ABC News poll of Iowa voters came from 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 percent of likely caucus participants cited the former New York mayor, putting him behind Republicans Mike Huckabee, Mitt Romney, Fred Thompson and John McCain. At the same time, 31 percent cited Giuliani as the strongest leader in the field, well ahead of all his rivals except Romney, who was at 30 percent.

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 likability?

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

This year, Clinton and 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 Mark McKinnon, who did the ads for Bush in 2000 and 2004 and now works for McCain, said Wednesday: “You usually don’t like people you don’t trust.”

Mark Mellman, who was Kerry’s pollster in 2004, said other attributes are more important than a candidate’s likability and have been in past elections. “I think likability 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,” Andrew Kohut, who directs the Pew Research Center, wrote in his e-mail response to my question about this. “In this case, people see a failure of leadership in the Bush years, and that’s why strong leadership image may be trumping ‘likability.’ “

Whit Ayres, a Republican pollster, said likability still matters and pointed to Huckabee’s rise in Iowa as evidence. He said respect matters more than likability, 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.”