I have never experienced voting on the outcomes of a brainstorm session and that makes no sense at all to me. It's about generating ideas and it will, hopefully, include ideas that sound nice initially, but are bad when given some more thought. There should be a round to separate the wheat from the chaff.
In my experience (again), we do have two rounds to separate them. But both of them are voting-based rounds. One vote to narrow down the 30+ ideas to like 5 or so, and a second one to reduce it to one or two :) The outcome was very minimal compared to the overall time wasted on the process (5-6 people in a room, for one hour, ending up with a not-so-interesting idea... there are better ways to spend a team's time).
