It is proper that there be nine men who will listen and respond to the entire repetition.‎{&&}‎1 How many people need to be finished with their amida in order to assume you have nine listening? This is a good question. In any case, the minhag is to allow the chazan to start the repetition with nine who have finished the amida, even if we have reason to suspect that some of them are preoccupied with other activities.‎{&&}‎2 The Mishna Berura suggests that, in such a case, the chazan should mentally stipulate that if nine aren’t concentrating, his tefilla should be accepted as an extra, voluntary one.
The Shulchan Aruch,‎{&&}‎3 in discussing the requirements for a minyan, says that we may count one person who is davening or sleeping, rather than listening, for the minyan. The Taz‎{&&}‎4 wonders how a sleeping person can be included, but, nonetheless, the Shulchan Aruch’s ruling stands.
The Mishna Berura‎{&&}‎5 suggests that, according to the Shulchan Aruch’s approach – that presence without participation is sufficient, even more than one preoccupied person may be included. However, his conclusion is that we may be lenient only with one preoccupied person. The distinction between one and more emanates from the Haghot Maimoniot.‎{&&}‎6 The gemara‎{&&}‎7 lists opinions that hold that a minor counts for the tenth man of a minyan. The Haghot Maimoniot claims that even those who are stringent not to count a minor agree that an adult, who usually can count for a minyan, provides the necessary level of kedusha for devarim sheb’kedusha (matters which require a minyan) even if he is sleeping or davening. However, as we cited above in the name of the Mishna Berura, this leniency holds only for the tenth man.
The Tzitz Eliezer‎{&&}‎8 relies on the opinion that holds that one person who is davening counts along with eight who have finished the amida (plus the chazan) in order to start the repetition. However, he says that it is better, when practical, to wait.