The Cylons use some form of democracy via the mass-production Numbers. We know this because there's a episode where there's a contentious vote and Boomer (a Number Eight model) votes against her fellow Eights, thus breaking what would have been a stalemate.
Cavil insists the Raiders should undergo a procedure to remove or at least reduce their sentience, and he enlists Boomer's aid when the Cylons become deadlocked over the matter. While her fellow Eights vote as a group against the procedure, Boomer decides to vote yes in order to make the Raiders effective fighters once again. In so doing, she becomes the first Cylon to ever vote against her own model (meaning that in a six-vote bloc, she casts an unheard-of seventh vote).
It's also clear than not everyone is on board with Cavill and his quest to exterminate humanity.
When the Resurrection Hub is destroyed, Cavil and Boomer demand Ellen help them redevelop the technology. Cavil threatens to cut open Ellen's brain in order to access her knowledge, but Boomer spirits her away in a Raptor, telling Ellen she is forgiving her.
It appeared that things became considerably less democratic after the Resurrection Hub was destroyed. Of course, by this time, we learn that Cavill has commited other crimes against Cylons, most notably he destroyed the Daniel line out of jealousy
One of the plot points was that the human cylons wrestled with the morality of their decisions (most notably Boomer regrets kidnapping Hera and dies after rescuing her). Given the Cylon civil war, it's also clear that Cavill was losing his hold as leader, and this eventually pushes Cavill over the edge, repulsing the other models.