For the purpose of complying with Section 50271 of the Government Code, each mayor shall designate a member of the city’s legislative body to attend and vote in his or her place and as his or her representative if the mayor is unable to attend any meeting of the city selection committee to be held pursuant to this article. If a mayor does not make this designation within 10 days preceding a meeting of the city selection committee, the legislative body shall designate one of its own members to represent the city.