Whenever county bonds are voted or a special tax is levied for paving a county highway, and the natural course of such highway runs into or through any city, the board of supervisors shall pave within such city that portion of the highway which is designated by the chief executive of the city and the county supervisor in whose district such portion is located. Such highway portion shall be constructed to standards equal to those of the highway approaching such city. If such chief executive and such supervisor do not agree as to what street will be thus designated, then the chairman of the commission shall designate the street and his judgment shall be final and conclusive.