“While Fiorello! is the most successful Broadway musical about a New York mayor, it’s not the only one. Jimmy, about La Guardia’s predecessor Jimmy Walker, had a short run in 1969, as did Mayor, about Edward I. Koch (sample song: ‘How’m I Doin’ ‘), in 1985. Could Mr. Bloomberg be next? We asked three musical-theater composers to imagine song-and-dance numbers from the life of our current three-termer.”