Is your school forming committees or task forces to tackle a pressing issue? Whom does one select to serve on committee/task force x, y, or z? Is there a single criterion that stands out?
A recent article from McKinsey Quarterly suggests that it is this: "pick people who can answer the questions you're asking."
That seems a rather obvious response, yet too frequently it is not the norm when groups are brainstorming ideas. If you'd like to have a productive brainstorming session, you absolutely need to have people in the group who can answer the questions you're asking.
Whom should one not choose? The "idea crushers." That could mean subject-matter experts to whom everyone always defers because of some presupposed wisdom, but, more importantly, it usually means "big mouths," those who "take up air time, intimidate the less confident, and give everyone else the excuse to be lazy."
So, choose wisely.
But what if you don't have the luxury to choose wisely? Group leadership will have to be highly politic; there is no other way. If any substantive work is to be accomplished, a group leader must allocate a fairly significant portion of his/her time to cultivating and growing relationships with every single person in the group so that s/he knows the pressure points within the group. That leader must have the political skill to navigate many kinds of seas, guiding the ship toward its port.