I've been on a few, of personal and professional interest, and I've never even heard of a democratically governed board. If someone can correct me, I'd appreciate it.
Several months ago I found a forum called The Admin Zone, a "self-help" site for admins.
They have a whole forum dedicated to "how to keep your members in line". There were a few questions by owners of democratically run boards (so they exist
) - that is, the owners wanted the board to be democratic, and put decisions to the vote etc.
The questions usually ran something like: the members of my board are impossible to please, whatever I do, someone complains.
The answers from the other admins usually ran something like: you must be stark-raving mad to want your board to be a democracy - put your foot down and tell your members who's the boss!
Scared the hell out of me, I can tell you.
Let's show them it can work!