In this work we give a careful mathematical treatment of two majority voting procedures in which a voting agenda is utilized: sincere voting and sophisticated voting. We elaborate and expand on work by Banks (1985), Miller (1977, 1980), Miller, Grofman and Feld (1986), and Shepsle and Weingast (1984). We discuss algorithms to obtain these two decisions under such procedures, the location of these two decisions in the underlying majority tournament, the relative locations of these two decisions in the voting agenda, and the possibility of an alternative which is both of these decisions.