This part is particularly obvious, but I'll add it anyway. If you want a large number of people playing, a simple Facebook app is going to be a must. Signing up for an idea then becomes part of someone's stream and the viral magic kicks in. It's also a good way to drive Facebook traffic to websites associated with the good ideas. Then, of course, you have access to Facebook's toybox of viral techniques to grow participants and direct traffic.
"Peace on Facebook", a section which show how many friendships are occurring across lines of conflict, offers a glimpse on what the social networking site could provide towards world peace. http://ow.ly/EjfW