Why does the American form of government work?

The smaller the society, the fewer probably will be the distinct parties and interests composing it; the fewer the distinct parties and interests, the more frequently will a majority be found of the same party; and the smaller the number of individuals composing a majority, and the smaller the compass within which they are placed, the more easily will they concert and execute their plans of oppression. 

Extend the sphere, and you take in a greater variety of parties and interests; you make it less probable that a majority of the whole will have a common motive to invade the rights of other citizens; or if such a common motive exists, it will be more difficult for all who feel it to discover their own strength, and to act in unison with each other.

These quotes are an example of why the American form of government is effective in terms of representing all the people involved: the majority and the minority. Essentially, Madison is vying for a large representative based government as a way of controlling the effects of factionalism in the government. When he writes, "the smaller the compass within which they are placed, the more easily will they concert and execute their plans of oppression," he is saying that in groups of people that are too small, it is too easy for a majority to exist and to east for them to control policy. The larger percentage of the people can too easily dictate the goings on around them even if it is not in the best interest of everyone. When he describes a larger sphere, he says that the if there is a "greater variety of parties and interests; you make it less probable that a majority of the whole will have a common motive to invade the rights of other citizens." In other words, the vastness of different opinions will make it difficult for their to be one large majority party which have the same goals. This will prevent one party from dictating policy for their own best interest. He also says that even if common goals exist, in such a government "it will be more difficult for all who feel it to discover their own strength, and to act in unison with each other." In other words, the representative form of government with such a large population will make it difficult for a few groups to able to control policy and force others to oblige with them. The prevention of a domination of the many by the few or the few by the many is important in order to protect everyone's rights.

In order to lay a due foundation for that separate and distinct exercise of the different powers of government, which to a certain extent is admitted on all hands to be essential to the preservation of liberty, it is evident that each department should have a will of its own; and consequently should be so constituted that the members of each should have as little agency as possible in the appointment of the members of the others.

But the great security against a gradual concentration of the several powers in the same department, consists in giving to those who administer each department the necessary constitutional means and personal motives to resist encroachments of the others.

Through these passages, Madison is trying to explain one of the key characteristics of our government, the separation of powers. When Madison says, "it is evident that each department should have a will of its own," he means that the goals of each department should be separate and should be able to control itself so that no two departments can control another or so that no one department can find itself dictating the policy of another. Through the passage, "the members of each should have as little agency as possible in the appointment of the members of the others," he is trying to prevent a means of indirect control, which is that one branch could appoint members of another branch that have similar interests. This why Madison says it is necessary that each  is able to "resist encroachments of the others." They need to be able to stand alone. Without separation of powers, it would be impossible for one branch to fairly judge its own actions and act upon them. The bias of human beings would prevent them from judging their own actions fairly and without preference towards what would benefit them. Because of the separation of powers, "liberty" or the rights of the people, can be protected because no one right's can be easily overlooked.