A precise restatement and extension of Black's theorem on voting orders

Duncan Black originally suggested that ‘the later any motion enters the voting, the greater its chance of adoption.’ We formalize this reasoning as a theorem, which we prove. We then specify the implications of this theorem for agenda control. If the social preference is known and there is no majority winner, one is best off choosing a specific voting order, which may or may not have one's most preferred alternative last. If the social preference is unknown, the optimal agenda is one in which voting is in reverse order of one's preferences.