Laws that relate exclusively to local matters within one senatorial district may be enacted by the legislature or by the affirmative vote of a majority of the members representing that district. The legislature shall define the local matters that may be the subject of laws enacted by the members from the respective senatorial districts, laws enacted through initiative by the voters of a senatorial district under article IX, section 1, regulations promulgated by a mayor under article VI, section 3(e), or local ordinances adopted by agencies of local government established under article VI, section 6(b).