AMES, Iowa — Mitt Romney won Saturday's nonbinding presidential straw poll of Iowa Republicans with nearly a third of the vote, but his chief rivals weren't here, and neither were a lot of voters.

Both former New York City Mayor Rudy Giuliani and Arizona Sen. John McCain decided earlier this year to skip the daylong event that serves as a fund-raiser for the Iowa Republican Party.

Their names were still on the ballot, though, along with another no-show, likely GOP challenger, actor and former Tennessee Sen. Fred Thompson, and the eight candidates who did appear at the Iowa State University Hilton Coliseum.

The vote doesn't count for much other than as a test of a candidate's organizational abilities in Iowa, where residents are the first in the nation to name their presidential primary picks in a caucus vote that this election season, could come as soon as mid-December.

The big surprise Saturday was a second-place finish by former Arkansas Gov. Mike Huckabee. Kansas Sen. Sam Brownback, who pushed to position himself as Romney's toughest competition here, came in third, followed closely by Rep. Tom Tancredo, R-Colo.

With no presence at the fairlike event Saturday aside from a pair of Texas A&M students handing out bumper stickers, Fred Thompson came in seventh, ahead of Giuliani, who was eighth, and McCain, who was 10th.

Romney eagerly claimed victory. "People of this great state sent a message to America and that is, change begins in Iowa," he told cheering supporters shortly after the vote was announced Saturday evening.

Later, he told reporters that the low turnout was expected, given the day's extreme heat and humidity, which felt like triple-digit temperatures. The state party reported 33,000 people attended the straw poll and more than 14,000 voted.

As for his absent competitors, Romney said it was "too bad the other guys weren't competing here. If they thought they could have been successful here, they would have been here."

Kelly Patterson of Brigham Young University's Center for the Study of Elections and Democracy said Romney did what he had to do in the straw poll. "He had to do well and show he was capable of winning," Patterson said. "He won and he won by a huge margin."

Huckabee, a Baptist minister, said getting more than 18 percent of the vote "validates the importance of coming to Iowa because the people here weren't influenced by media or by money. They were ultimately influenced just by message and their own heart and will. ... Today shows we can win."