Why does the American form of government work?

"...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."

"The influence of factious leaders may kindle a flame within their particular States, but will be unable to spread a general conflagration through the other States." 

-Federalist Papers No.10

In this paper Madison brought up the point that while the causes of "faction", or division of people, is inevitable, its effects can be controlled. He claims that the negative effect of having factions is lessened in a republic versus a democracy. This is because in a democracy, anyone can hold power or influence, even those who are unqualified in doing so, whereas in a republic, power is concentrated into a number of chosen citizens. In such a regulation, the public's voice can be pronounced more effectively, thus "public good" can be better achieved. The second quote focuses on the presence of multiple factions in a republican system. Madison explains that this will not affect the nation as a whole, as the voice of one faction is unable to spread to other states, just due to the number and variety of groups and factions.

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"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." 

"In the extended republic of the United States, and among the great variety of interests, parties, and sects which which it embraces, a coalition of a majority of the whole society could seldom take place on any other principles than those of justice and the general good; whilst there being thus less danger to a minor from the will of a major party, there must be less pretext, also, to provide for the security of the former, by introducing into the government a will not dependent on the latter, or, in other words, a will independent of the society itself."

-Federalist Papers No.51

The first quote points out that in an ideal republican society, the minority will be safe and protected. This is because a great number of minorities prevents an "unjust majority" from forming. Thus, the society as a whole is made up of "combinations" of different groups and ideas. The second quote reinforces this idea by stating that if there is "a coalition of a majority" in the society, justice and the general good of people will be lost. Therefore, the government should prevent a major party from forming by isolating itself from the majority and protecting the minority. The policies it issues should also not be based on the different groups and factions in society.