Harris County officials are scrambling to resolve a mistake involving the May primary election for trustees of the Harris County Department of Education, less than a week before early voting begins for a runoff election. The county relied on outdated district boundaries when it distributed ballots for the school trustee primary elections in May, which means some voters could have cast ballots in the wrong district and others who should have had a chance to vote were excluded. The mistake only affected the school trustee elections, said Doug Ray, an assistant Harris County attorney. John Sawyer, the appointed superintendent of the department, said he expects that a judge ultimately will void the elections. He said his agency, which provides educational services to local school districts, would contest the election if no one else does. “I will tell you that ultimately we would contest them because I don’t think they (the boundaries) were legally drawn, and I’m not going to be responsible for swearing in candidates that may not be elected legally,” Sawyer said. “I just can’t do that.”