The board of directors of a district which lies entirely within one county may submit to the qualified electors, at a general election or a special election called for that purpose, a proposition to increase the number of directors from three to five. By initiative ordinance the electors of such a district may adopt legislation providing for the increase of the number of directors from three to five. The initiative proceedings shall be conducted in all respects as prescribed by general law for the initiative by electors of counties. If a majority of the electors voting at the election vote in favor of the proposition, the district shall have five directors elected at large.