Why does the American form of government work?

No. 10:
"If a faction consists of less than a majority, relief is supplied by the republican principle, which enables the majority to defeat its sinister views by regular vote. . . . but it will be unable to execute and mask its violence under the forms of the Constitution. When a majority is included in a faction, the form of popular government, on the other hand, enables it to sacrifice to its ruling passion or interest both the public good and the rights of other citizens. To secure the public good and private rights against the danger of such a faction, and at the same time to preserve the spirit and the form of popular government, is then the great object to which our inquiries are directed."

In this quote, Madison describes how government reacts if a disruptive faction starts causing problems in society. He writes that as long as the majority of the people are not part of the bad faction, they can "defeat its sinister views by regular vote." He says that as long as the unruly faction is not comprised of the majority of the people, then the majority which will be comprised of the rest of the people can rise and pass legislation to stop that faction. Madison also brings up the downside of ruling with popular factions. They can become overly powerful and take power away from the minority factions. He says that point as to if the majority of the people are part of the unlawful faction. There, he says that it will be up to the rest of the people to sacrifice their passions in order to preserve the public good of the rest of the people. He says that to avoid that the people have to "preserve the spirit and the form of popular government", meaning that it will be up the the wholehearted goodness of the people to ensure a government will not fall into chaos.

No. 51:

"In a society under the forms of which the stronger faction can readily unite and oppress the weaker, anarchy may as truly be said to reign as in a state of nature, where the weaker individual is not secured against the violence of the stronger; and as, in the latter state, even the stronger individuals are prompted, by the uncertainty of their condition, to submit to a government which may protect the weak as well as themselves; so, in the former state, will the more powerful factions or parties be gradually induced, by a like motive, to wish for a government which will protect all parties, the weaker as well as the more powerful."

In this quote, Madison is saying that in order for a government to be successful and not overrun by corrupt people, there need to be "more powerful factions or parties be gradually introduced". What he is saying here is that with more factions vying for control, the flux of power will always be balanced between the various factions. As long as there is a good balance, no faction should be able to take overthrow the republic. This connects to Federalist Essays No. 10 because in both he discusses the issues of various factions. He talks about the need for the factions to be ruled by the popular government, and the fact that there needs to be multiple power factions in order to keep the balance not shifted in one way.