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.
Any magistrate in government will have to exercise three different kinds of will: his individual will that pursues his own interests, the corporate will that expresses the will of the government, and the general will that expresses the will of the people as a whole. The fewer magistrates there are, the more the corporate will shall resemble particular wills, and the stronger and more active relative to the people it will be. With a great many magistrates, the corporate will shall resemble the general will, but it will also be relatively weaker and less active. In a large state, where a strong government is needed, fewer magistrates are desirable.
The first two books of The Social Contract deal with the abstract level of political right. In those books, Rousseau explains the principles according to which a republic that upholds freedom and equality might exist. He concerns himself there with the sovereign and with laws, both of which apply generally to all people equally and at all times.
In Book III Rousseau makes the transition from abstract to practical and from legislative to executive, discussing how a republic should be governed rather than the principles on which it should be founded. Instead of discussing a sovereign or laws that are general and apply to all, he discusses a government that is made up of a select group of magistrates and that exercises power in particular cases.
Rousseau's distinction between will and strength is closely linked to the distinction between force and right. In the first two books, he deals with will and right: he discusses simply how things ought to be, how we should will them to be. Now he discusses strength and force: how we can make things be the way we want them to be, how we can put matters into effect. On the whole, Rousseau is very careful to distinguish between force and right. A failure to do so leads to a confusion between government and sovereign, and such confusions lead thinkers like Grotius or ##Hobbes## to assert that there is a social contract binding subjects to a government of one person, who is also the sovereign. A proper distinction between force and right is necessary to grasp the subtleties of legitimate government. The importance Rousseau normally places on this distinction further highlights his own confusion of this distinction when, in Book I, Chapter 7, he insists that people who do not obey the social contract must be "forced to be free."
The discussion of the relative strengths of sovereign, government, and people can be a bit confusing. Rousseau tries to explain himself in terms of mathematical analogies whose clarity can be helpful. But, as he himself acknowledges, we won't find the precision of mathematics in moral calculations, and such precise ratios can be misleading, especially since there is no precise numerical measure for political power.
Rousseau's calculations are based on the assumption that every citizen exercises more than one kind of will. I act first and foremost in my own interests, as a single individual, and exercise a particular will. However, as a member of the sovereign, I also think and act with the general will in mind. If I am a magistrate in government, I also think and act with a corporate will, in concert with my fellow magistrates.
In a state with just one hundred people, I will constitute 1 percent of the sovereign. In a state with ten thousand people, I will constitute only one one-hundredth of 1 percent of the sovereign. The larger the state becomes, the less I constitute the sovereign. Rousseau concludes that the larger the state becomes, the more my particular will shall take precedence over my participation in the general will. Thus, in a large state, each individual will care less about the well-being of the state, and will care more about himself. To prevent selfish anarchy, Rousseau argues that a large population needs a strong government to keep it in line.
A strong government does not mean a large government. On the contrary, Rousseau asserts that the smaller a government is the stronger it is. In a large state, each individual's particular will is so much stronger than his general will because his particular will concerns only himself, while his general will concerns a large group of which he is only a small part. Similarly, in a large government, the corporate will of each magistrate will be weak, and he will be more interested in his own particular will. In a small government, the corporate will of each magistrate will be stronger.
The larger the population, the smaller the government that controls them should be. The danger, then, is that the corporate will of a small government will be so much stronger than the general will that the general will shall be ignored. The danger, it seems, of large states, is that each individual will feel less committed to the general will, and so the general will might be neglected. Rousseau's ideas are deeply indebted to Greek political philosophers, especially Aristotle, and so he thinks of the ideal political unit as a small city-state, like Athens or Sparta, or the Geneva that he grew up in. A large country is ill suited to his recommendations.