53 Pa. Stat. § 30355
In the event that the mayor shall fail to appoint a deputy mayor in accordance with the provisions of this act, or, in the event that the person designated by the mayor to act as deputy mayor shall, for any reason, be unable or unwilling to act as deputy mayor, then and in that event, a majority of the heads of the departments of cities of the second class A shall designate the deputy mayor, who shall exercise all the powers and discharge all the duties of mayor except the power of appointing to or discharging from office in the city government. The following department heads shall be entitled to vote: City treasurer; city solicitor; director, department of public health; director, department of public safety; director, department of public works; and director, department of supplies. In the event of a tie vote, the president judge of the county in which said city of the second class A is situate shall vote for one of the candidates within a period of twenty-four hours after the city clerk has notified him in writing of the tie vote. For the purposes of this act, the city clerk shall act as chairman of all meetings for the purposes of designating a deputy mayor, but under no circumstances shall have the right to vote on the appointment of a deputy mayor. For the purposes of selecting a deputy mayor, four of the department heads shall constitute a quorum.
53 P.S. § 30355