The two candidates were the top vote-getters in the June 8 election, but a candidate for a supervisor seat must win 50 percent of the vote, plus one, to win the election.
The count as of June 14 shows Mr. Horsley with 30,154 votes, or 39 percent of the vote; Ms. Vargas, 18,271, or 23.6 percent; Jack Hickey, 12,588, or 16.3 percent; Matt Grocott, 11,045, or 14.3 percent; and Michael Stogner, 5,168, or 6.7 percent.
The candidate who wins in November will replace Rich Gordon of Menlo Park, who won his race June 8 in the Democratic primary for the District 21 state Assembly seat. The winner will take his or her seat on the five-member Board of Supervisors in January.
Mr. Horsley, a resident of Emerald Hills, currently serves as president of the Sequoia Healthcare District Board. He served as county sheriff from 1993 to 2007, and as a member of numerous law enforcement and public service commissions and boards.
Ms. Vargas, a resident of Montara, served a four-year term on the Midcoast Community Council from 1999 to 2003, and has served on several county governmental committees. She also served for two years as legislative advocate for the environmental group, Committee for Green Foothills.
The five-way contest was an anomaly for a supervisor race in San Mateo County, which for years has not seen a race between viable candidates for a board post.
In District 2, appointed incumbent Carole Groom of San Mateo took 75 percent of the vote. Her only challenger, Daniel Kaul of San Carlos, appeared to lose interest in the race, and announced at one point that he would neither actively campaign nor give interviews to the press.