Why does the American form of government work?

The Federalist Papers Number 10

"In the first place, it is to be remarked that, however small the republic may be, the representatives must be raised to a certain number, in order to guard against the cabals of a few; and that, however large it may be, they must be limited to a certain number, in order to guard against the confusion of a multitude."

With this quote, Madison is discussing the ideal American government. If there are too few people representing the people and controlling the government of the country, their objectives and opinions will take control of the government, so we have representatives and senators from each state, "in order to guard against the cabals of a few". However, we do limit our number of representatives, so that not every citizen can be in government, "in order to guard against the confusion of a multitude". In other words, he is saying our government works because we have a diversity set of people who represent most of the common viewpoints held by different groups across the country. However, we do not have so many people in our government that each different individual idea and objective makes it impossible to get anything done.

"In the next place, as each representative will be chosen by a greater number of citizens in the large than in the small republic, it will be more difficult for unworthy candidates to practice with success the vicious arts by which elections are too often carried; and the suffrages of the people being more free, will be more likely to centre in men who possess the most attractive merit and the most diffusive and established characters."

Madison goes on to discuss how we will keep our government uncorrupt and full of good individuals. What he says in this section is that by having a large group vote in the election of a single person, multiple viewpoints will go into determining the winner, and a big group of the general public with varied interests will be unlikely to elect a corrupt individual who will not serve them and the country well in government.

The Federalist Papers Number 51

"It is equally evident, that the members of each department should be as little dependent as possible on those of the others, for the emoluments annexed to their offices. Were the executive magistrate, or the judges, not independent of the legislature in this particular, their independence in every other would be merely nominal. 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."

With the three branches of government established in America, each branch remains both independent and codependent. Therefore there cannot be a "gradual concentration" of powers because each branch holds the power to stop another branch from "encroachments of the others". The heads of each branch of government constitutionally have the authority to do a certain portion of governing the American people. In this way, no branch may take all the power.

"In a single republic, all the power surrendered by the people is submitted to the administration of a single government; and the usurpations are guarded against by a division of the government into distinct and separate departments. In the compound republic of America, the power surrendered by the people is first divided between two distinct governments, and then the portion allotted to each subdivided among distinct and separate departments. Hence a double security arises to the rights of the people. "

Not only does the federal government contain the strength of the three branches of government, but each person is governed by both a federal and a state government ("divided between two distinct governments"). Therefore, the government cannot govern in favor of some states but not in others, because if that happens, the state can make opposing laws to protect their own interests. On the flipside, a state cannot govern themselves in a radically different way than the rest of the Union, because the federal government at all times maintains at least some control over the states. This balance causes a "double security" for citizens.