How do you guys run early brainstorming?

[Grim Tuesday]

Our team is looking at how to improve our design process, and we were wondering how other teams do it.

We are a very large (45+) team, and want to keep everyone involved in the early design process. In years past, we have had teams of 5-6 design whole robots, and present them to the whole team for a vote. We use subsystems from each design. This system takes a long time, and I feel is noneffective. Especially now, with so many people on our team, 4 hour build sessions are not enough time to present ideas with comment, questions, and concerns and most importantly, discussion.

So, how do other teams do it?