Philosophy
Rousseau asks how people can remain free while living under laws backed by collective political authority.
The ability to force people to obey creates no duty to obey. You yield to a robber's gun out of prudence, not obligation, so when the stronger force changes hands, so does the 'right.' Only authority that rests on something other than strength can bind anyone.
War is a relation over possessions, not a quarrel between individuals. Private war between one person and another cannot exist where there is no lasting property, as in a state of nature, or where the law governs everything, as in civil society. Lasting conflict needs durable claims to things.
The core political puzzle, as Rousseau states it, is to find a way of uniting with others that protects each person with everyone's combined strength, while each still obeys only himself and stays as free as before. His answer is that people remain free under law when they are also the ones who make it.
The right to freedom cannot be transferred, so a people cannot validly promise to obey someone other than themselves. Handing lawmaking to a master turns natural equality into subjection. On this argument, slavery and rule by a monarch claiming his own right to legislate are both illegitimate.
Supreme power stays with the people themselves, not with representatives who speak for them. Having every citizen take part in making law is the check against abuse of power. When those who govern overstep the limits the people set, the people may abolish that government and begin again.
No one has a natural right to rule others. Even a father's authority lasts only while the child needs care, and once that need ends, any continued bond is voluntary. So all lasting political authority has to be founded on agreements people make, not on birth or nature.
In the founding pact, each person hands over himself and all his powers to the community's common will, on identical terms. Because everyone gives the same, no one has an interest in making the terms burdensome for others, and each receives the same protection back as an indivisible part of the whole.
Each person has a private will aimed at his own advantage and a share in a general will aimed at the common good. Legitimate law expresses only the general will, so it must apply equally to everyone. The sovereign people's authority covers only matters of public concern, but within that domain Rousseau makes it absolute.
The terms of the social pact are never written down yet are tacitly understood everywhere, because altering any of them would void the whole. Once the pact is violated, each person takes back the natural liberty he gave up and loses the civil liberty he received in exchange.
Extreme gaps in wealth undermine freedom, because people who depend on others cannot remain their own masters. Rousseau therefore holds that laws should work to preserve equality among citizens. In his account, society itself breeds inequality and self-interest through the pursuit of power and property.