Rousseau's Social Contract

1) Rousseau talks about the ideal community under a social contract like it was a human body, where each member is equally powerful and each act to nourish each other and, in effect, the whole. However, ordinary citizens aren't always out to benefit the body; sometimes because of a crisis or shortsightedness, a nation can be gridlocked in too many clashing opinions. Votes are rarely unanimous and the outcome isn't always fair to everyone or even morally right. So in an instance of national tension (basically everything that isn't a utopia), how is it possible for his sovereign/government system to function without everyone eventually leaving to lead their own Robinson Caruso kingship?

2) In Hegel's The Encyclopedia Logic truths about ideas and objects are composed of their innate state and how people subjectively view them. This works for gauging validity against natural occurrences like animals and behavior (for example: a dog we can imagine being any number of colors but if we see a purple dog we would assume that it isn't a "true" dog). These same "truths", however, don't apply to human ideas and institutions.  The issue here is that Hegel's thesis requires something definitively existing so we can conclude with a solid classification. Things that don't exist are immune to being classified because one can argue "that only exists because someone attributed it with an arbitrary value, so really it can be whatever I want". Art is a great example, because everyone perceives art differently and relies on people agreeing that it even has meaning; this means art is inherently subjective and there is no true interpretation of it. Because true art and true dogs are two different concepts how should they be classified, or should ideas even be classified as true?

*Concerning my second question: I only thought of this when Hegel brought up religion and it made me think that because different cultures believe in different things there isn't a rational way to prove or disprove anyone's truth -- not a problem for things that exist in a corporeal sense.