I am not concerned about double booking and make it common practice. Why? Industry history tells us that 35% of our appointments will cancel or reschedule. So, how do I get away with this practice without any conflicts?
If a time slot is double booked, my assistant asks me one day prior to the appointment which appointment I would like to see first. She then calls the #1 person for each appointment the next day. If they cannot make it or have to reschedule, she reschedules them at that time and calls my #2 appointment in order to maintain a full calendar. If the #1 person confirms, my assistant calls the #2 person and reschedules that person for a later date.