Libby Garvey, a veteran Arlington School Board member who appealed to those seeking an independent voice on a County Board dominated by unanimous votes, won the Democratic nomination Saturday for the board’s open seat.

Garvey collected 44 percent of the vote with 1,915 votes to Melissa Bondi’s 966, Terron Sims’s 922, Kim Klingler’s 333 and Peter Fallon’s 178. Democrats voted in a two-day caucus Thursday night and all day Saturday.

Garvey, 60, said she thinks her 15 years on the School Board and her 35 years living in Fairlington convinced voters that they could trust her. She said she considers herself a team player but an independent thinker, evidenced by her willingness to be the sole no vote on several school issues.

On budget issues, Garvey said her guidelines are “at what cost, for whom and for what benefit.” “I had a lot to do with making our schools the best in the nation,” she said in an interview Sunday. “And I think [voters] liked my message that we need to set priorities in the county.”

Garvey said she would like a cost-benefit analysis of the proposed Columbia Pike streetcar, for example. whose cost has ballooned $100 million since 2007.She said she has concerns about the effect of the Columbia Pike redevelopment project on affordable housing and wants more information.about the county’s plans there.

She spent the day after her win at a Quaker meeting and at the Renwick Gallery for an opera recital. But she said she is not taking the March 27 special election for granted. She will face Green Party nominee Audrey Clement and Republican nominee Mark Kelly, the chairman of the local GOP. Both have lost previous races for the County Board, but both have received vote counts that could be significant, depending on turnout.

Although Democrats dominate Arlington County politics, “these small special elections are the ones Democrats lose in Arlington,” Garvey said.

Garvey was endorsed by two retiring state senators, Patsy Ticer and Mary Margaret Whipple, as well as the County Board member she seeks to succeed, Barbara Favola. Favola was elected to the state Senate in November. The County Board term expires at the end of 2012, which means the winner will have to run again in the fall.