Rousseau opens Book III with an explanation of government and the executive power that it wields. The actions of a state, just like those of a person, can be analyzed into will and strength. To walk around the block, I must decide to walk around the block (will), and I must have the power in my legs to do it (strength). The will of the body politic is expressed in the laws, which are discussed at length in Book II. The strength that puts these laws into practice is found in the executive power of the government. Because the government deals with particular acts and applications of the law, it is distinct from the sovereign, which deals only with general matters. A great many dangers arise when government and sovereign are confused or mistaken for one another.
There is no kind of social contract between a government and the rest of the people, since the people do not surrender their power or will to the government in the way that they do to the sovereign. The government is an intermediary body that can be modified or disbanded according to the sovereign will (or general will).
In a large state, each individual will be only a small part of the sovereign, and so each individual will be less inclined to follow the general will and more inclined to follow his or her own particular will. In order to keep so many people in line, the government will need to be able to exercise a great deal of power. Thus, the larger the population, the greater force the government must have relative to each individual.
On the other hand, the more powerful the government is, the more tempted the magistrates in the government will be to abuse their power and take advantage of their position. Thus, just as a strong government is needed to control a large population, a strong sovereign is needed to control a strong government.
While there is obviously no precise mathematical relationship that can determine the proportionate power of government, Rousseau suggests the following ratio as a good formula. The ratio of the power of the government to the power of the people should be equal to the ratio of the power of the sovereign to the power of the government.
Rousseau proposes that the government, like the sovereign, can be considered a unified body, the main difference being that the sovereign acts according to its own interests, while the government acts according to the interests of the sovereign, or general, will. Nonetheless, the government still has a life and ego of its own, and has its own assemblies, councils, honors, and titles, as well as a supreme magistrate or chief that acts as its leader. The difficulty lies in arranging matters so that the government never acts solely on its own behalf, making the general will subordinate to its own will.