(CNN) -- With less than a month until the first votes are cast in the presidential campaign, the Republican race is wide open for the young voters, a survey shows.

Former New York Mayor Rudy Giuliani is the top pick for 26 percent of young GOP voters.

Among young Republicans, more are undecided than those who have made up their minds. Just 13 percent of young adults who say they are Democrats are still undecided, according to the survey.

The national poll by Harvard University's Institute of Politics questioned about 2,500 18- to 24-year-olds between October 28 and November 9.

Among decided GOP voters, former New York Mayor Rudy Giuliani leads the pack, and Illinois Sen. Barack Obama is the top pick for Democrats, the survey shows.

But candidates from both parties have reason to court the youth vote, according to the institute's polling director, John Della Volpe.

More than 40 percent of young adults polled said they would "definitely be voting" in a primary or caucus, and 61 percent said they would definitely vote in the general election for president, according to the survey, which has a margin of error of plus or minus 4 percentage points.

The young voters could be the "wild card," Della Volpe said, adding that in the 2004 presidential election, more votes were cast by people younger than 30 than those older than 65.

Young people could easily swing enough votes to make a difference in the early contests, he said.

But that will be determined by how many young voters actually go to the polls. A similar institute survey in October 2004 found that 81 percent of the respondents said they were "definitely" going to vote, but turnout in that age group was a little less than 47 percent, according to Census Bureau figures.

The first votes in the 2008 presidential race will be cast on January 3, and 30 percent of young Republicans polled said they still have not selected their candidate.

Giuliani is the top pick for 26 percent of those surveyed. His numbers are down from 6 months ago, when 31 percent chose him. See who young voters want in the White House »

Rounding out the rest of the GOP slate, 15 percent of those polled said they would pick Arizona Sen. John McCain; 9 percent chose former Tennessee Sen. Fred Thompson; former Massachusetts Gov. Mitt Romney and Texas Rep. Ron Paul both came in at 6 percent; and former Arkansas Gov. Mike Huckabee was close behind with 4 percent.

Obama is the top pick for 38 percent of young voters who say they are Democrats. Thirty-three percent picked New York Sen. Hillary Clinton; 7 percent chose former North Carolina Sen. John Edwards; and 3 percent would vote for Ohio Rep. Dennis Kucinich.

Young Democrats are solidifying behind their candidates more than Republicans, Della Volpe said.

More than a third of all young Republicans voters are dissatisfied with their current crop of candidates, compared to just 18 percent of the young Democrats surveyed.

But, Della Volpe said, "it's a month away from the first caucus and young people have a lot to think about before they actually cast their first vote."

And the young voters are spending time thinking about the campaign and its top issues, the survey shows.

The war in Iraq is the most pressing issue for 37 percent of young Americans, according the poll. Health care at 10 percent is the second most important. The environment, the economy, immigration and foreign policy are also priorities for the youngest members of the electorate, the poll shows.

Additionally, most young adults said they think the country is headed in the wrong direction. More than 60 percent said the country is on the wrong track, while just 15 percent said the country is headed in the right direction.

Young people want change, Della Volpe said, and now, "they see the efficacy of their vote and their participation," he said. E-mail to a friend

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