During the meetings I manage, a few people tend to dominate the conversation. How do I change this dynamic and get more people involved?
Unfortunately, asking your mouthy staffers to take a vow of silence probably isn't a realistic option. So I suggest trying these steps to encourage everyone on your staff to have a say.
Prior to your next meeting, inform your staff, via emails and personal reminders, that everyone should participate and that they should be sure to share the floor with others. This creates an expectation that you want to hear from all the parties present, not just a vocal minority.
Next, develop an agenda estimating how much time you need to devote to each item. Appoint a timekeeper from your staff to help the group stay on track during the meeting. If you start to spend too much time on item A because someone is droning on, the timekeeper can alert you that it's time to move to item B.
Finally, during meetings, when dominant talkers start their spiels, stop them at some point to summarize what they're saying, and then call on the others for their take on the topic. This will assuage the long-winded, who may have a hidden need to be demonstrably listened to, as well as encourage the laconic, who might have a more obvious need to be coaxed to share their opinions.
Using these steps, you should be able to get some people to pipe down, and others to speak up.