I realise I'm just plucking a small point out of a large comment here, but I'd like to drill down into this one a little.
My very limited experience is that teams can generally self-manage this sort of thing. You tell them what you're trying to optimise, under what constraints, and lay down some ground rules for equal and fair participation, and then the team can make their own tough decisions and tell each other when they're not acting in the best interest of the team.
What am I missing?