Why Does the American Government Work?

In Federalist essay number 10, James Madison is essentially arguing how the American Government can combat the destructiveness of factions in government. In the essay he talks about how a large republic is better than a 'pure democracy' in combating factions.

"Extend the sphere, and you take in a greater variety of parties and interests; you make it less probable that a majority of the whole will have a common motive to invade the rights of other citizens; or if such a common motive exists, it will be more difficult for all who feel it to discover their own strength, and to act in unison with each other."

Madison is arguing that the larger the republic, the less likely factions will become corrupt and take over the government. For example let's say there was a government with 1000 people living in its country, and a government with 10 million people. The government with 1000 people is more likely to become unstable due to factions because of its smaller population. With a smaller population, there will be less parties/interests within its people, with less parties, the majority population could be found in the same party. The American Government is very efficient when it comes to controlling its factions, because of its large population, and diverse parties in government. If a radical faction were to spread its views on government, there is a low chance that everyone would join that party because of our diverse parties and population that can overrule those radical factions. 

In Federalist essay number 51, Madison is defending the system of checks and balances: where one branch of government can "check" the other branch so that no individual branch gains significant power and becomes corrupt. 

“It may be a reflection on human nature, that such devices [checks and balances] should be necessary to control the abuses of government. But what is government itself, but the greatest of all reflections on human nature? If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary. In framing a government which is to be administered by men over men, the great difficulty lies in this: you must first enable the government to control the governed; and in the next place oblige it to control itself. A dependence on the people is, no doubt, the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions.”

Madison is discussing two different things here: the system of checks and balances and the social contract. He argues that the primary purpose of government is to represent the people. Through the social contract he says that the government is to control the governed, but also control themselves so that it doesn't become corrupt. In order to control itself, the system of checks and balances is implemented. The American Government has been able to 1. not become corrupt and 2. represent its people because of this system of checks and balances and the social contract.