Why does the American form of government work?

           According to federalist articles no. 10 and no. 51, both written by James Madison, factions are the biggest problem a government has to deal with and can be eliminated by destroying the faction or by destroying its effect. Factions are groups of people with a common interest such as the wealthy or the poor. Each will group up making every individual's idea amplified with strength and publicity. Madison believes that a direct democracy is not a good form of government because it allows the majority factions to treat the minority functions badly, focusing on their factions benefit only. On the other hand, he argues that a republic, only a large one, would be able to eliminated the problem the factions are causing. The reason for this is that not only does a republic limit the power of the people so the majority faction can't rule over the minority faction, but also by having a large amount of people, the effect of majority and minority is drastically reduced, for more people means more factions and more factions means less power for each faction. The American government fits the perfectly into Madison's description of a large Republic and works flawlessly for the reasons he stated.