Why does the American form of government work?

The Federalist Papers: No. 10 (http://avalon.law.yale.edu/18th_century/fed10.asp)
"From this view of the subject it may be concluded that a pure democracy, by which I mean a society consisting of a small number of citizens, who assemble and administer the government in person, can admit of no cure for the mischiefs of faction. A common passion or interest will, in almost every case, be felt by a majority of the whole; a communication and concert result from the form of government itself; and there is nothing to check the inducements to sacrifice the weaker party or an obnoxious individual."
One reason the American form of government works is because it is not a full democracy. As stated in this passage, the consequence of having a "pure democracy" is "the mischiefs of faction." This means groups of people with the same interest would be able to form a majority and not allow other groups to get a say in. The minority view would not be taken into account at all which could be the basis for an extremely unfair form of government. Like the passage states, the "weaker party" or "individual" would not be able to have any power in this form of government because they will always be outvoted. By not being a pure democracy, the American form of government prevents the majority belief from completely dominating the minority belief.

"The effect of the first difference is, on the one hand, to refine and enlarge the public views, by passing them through the medium of a chosen body of citizens, whose wisdom may best discern the true interest of their country, and whose patriotism and love of justice will be least likely to sacrifice it to temporary or partial considerations. Under such a regulation, it may well happen that the public voice, pronounced by the representatives of the people, will be more consonant to the public good than if pronounced by the people themselves, convened for the purpose."
The American government works because it allows the people to elect a group of representatives to make decisions rather than citizens directly making decisions. By electing representatives, citizens will be able to choose candidates with roughly the same views as them in order to make sure their opinion is heard. However these people should be more able to "discern the true interest of their country" meaning they will not blindly vote for their own interests but instead vote for what they think would be best for the country. These representatives are less likely to simply vote according to their own opinions and biases and so may actually "be more consonant to the public good than if pronounced by the people themselves," meaning they may actually benefit the people more than if the people directly made decisions.

The Federalist Papers: No. 51 (http://avalon.law.yale.edu/18th_century/fed51.asp)
"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."
Another strong point of the American government is the separation of power into the three different branches. Each of these branches has a "will of its own," meaning they behave separately, and they have "little agency," or little effect, on each other. The reasoning behind this is so that one branch doesn't get completely out of hand and can be counteracted by the other branches which are not strongly influenced by the first branch. This allows the different branches to check each others' power effectively. If one branch were dependent upon another, the power of one branch would be greater than that of the others, so they would not be able to balance each other out.

"There are but two methods of providing against this evil: [...] the other, by comprehending in the society so many separate descriptions of citizens as will render an unjust combination of a majority of the whole very improbable, if not impracticable[...] Whilst all authority in it will be derived from and dependent on the society, the society itself will be broken into so many parts, interests, and classes of citizens, that the rights of individuals, or of the minority, will be in little danger from interested combinations of the majority."
American government works because of the diversity of the citizens and the fact that the "society itself will be broken into so many parts." The different people will all have differing views, dependent on a variety of factors. This then makes it unlikely that a large faction would form consisting of a large majority all with the same exact view. This means it is almost never the case that a valid viewpoint is ignored because, due to the diversity of the citizens, there will never form a majority great enough to negate a minority viewpoint.