In a small group where your opinions about something have enough weight to change things, if you profess your true opinions, the balance of the group will probably not agree with you exactly. So perhaps you should profess slightly more extreme opinions to counteract that. That may not be enough, especially if everyone else has the same idea. Why not go ahead and go as extreme as you can, just to move the balance even a little bit? If you do that, either you will not be taken seriously or everyone in the group is already completely extreme.
Where is the equilibrium? And how come groups get along anyway?
Facebook comment by Vanja Huoltén: This is a classic question in game theory. The cool fairly general result is that despite talk being cheap (or free), some meaningful information can still be transmitted in equilibrium. The classic paper that everybody references is Crawford and Sobel (1982): Strategic Information Transmission.
sam