Cal. Government Code § 31523.1

(a) In the event of a vacancy in the second, third, fourth, or eighth member position on a board of investments established pursuant to Section 31520.2, the board of investments shall cause an election to be held at the earliest possible date to fill the vacancy. The vacancy in the second, third, fourth, or eighth member position shall be filled for the duration of the current term except that, if the remaining portion of the current term on the date of the election is six months or less, a single election may be held to fill the vacancy for the remainder of the current term and to fill the position for the succeeding term. (b) If an election has been called on the expiration of the term of office of any member, or to fill a vacancy for the second, third, fourth, or eighth member position of a board of investments, and only one candidate has been duly nominated in accordance with the rules established for the holding of that election, the board of supervisors shall order that no election be held and shall direct the clerk to cast a unanimous ballot in favor of the candidate.