Government is a specific case of that general rule if and only if group decision making is isomorphic to individual decision making.
The idea behind government is that 1) it is occasionally necessary to impose some course of action on individuals or groups, 2) force or threat of force is a necessary component of said imposition, and 3) making the decision to use force is safer (under the assumption that there is in fact some 'correct' course of action) if you first discuss that decision with as many people as possible than if you decide by yourself.
Whether or not that all holds would appear to be up for debate.
Do you agree that "the idea behind government" exists entirely in heads of people? E.g. my idea of govt is different from yours. Does the fact that many people share the same idea make it right? If so, does god exist? Is Earth flat when most people think it is?
I'll agree that it's difficult to think about ideas with a rock :)
As for the rest, people believing something certainly does provide evidence for that thing the strength of which scales with the number of people believing, if not nearly linearly. It depends on which people too ;) Fortunately we have plenty of other sources of evidence to base our opinions on (and remember that sources of evidence aren't necessarily independent; one can screen off another). Whether or not those other sources are leveraged in group decision making is one of the things that would appear to be up for debate.
The idea behind government is that 1) it is occasionally necessary to impose some course of action on individuals or groups, 2) force or threat of force is a necessary component of said imposition, and 3) making the decision to use force is safer (under the assumption that there is in fact some 'correct' course of action) if you first discuss that decision with as many people as possible than if you decide by yourself.
Whether or not that all holds would appear to be up for debate.