Why does the American form of government work?

10
"Complaints are everywhere heard from our most considerate and virtuous citizens, equally the friends of public and private faith, and of public and personal liberty, that our governments are too unstable, that the public good is disregarded in the conflicts of rival parties, and that measures are too often decided, not according to the rules of justice and the rights of the minor party, but by the superior force of an interested and overbearing majority."

In this section Madison explains that governments are too unstable to consider all the suggestions of the people especially if they oppose each other. However, he believes that these situations have too often been decided democratically where the majority gets what they want while the minority is completely ignored. I disagree and believe that these situations are best resolved by the direct vote of the population instead of by representatives. By deciding on what the majority wants, you are following the rules of justice because you are fully representing the population. In a republican system, only the representatives are able to fully express their beliefs which is unjust to the rest of the population. Overall, however, our republican system of settling conflicts and issues works generally well as opposed to that of other liberal governments which proves that our system is successful.

"The second expedient is as impracticable as the first would be unwise. As long as the reason of man continues fallible, and he is at liberty to exercise it, different opinions will be formed. As long as the connection subsists between his reason and his self-love, his opinions and his passions will have a reciprocal influence on each other; and the former will be objects to which the latter will attach themselves. The diversity in the faculties of men, from which the rights of property originate, is not less an insuperable obstacle to a uniformity of interests. The protection of these faculties is the first object of government. From the protection of different and unequal faculties of acquiring property, the possession of different degrees and kinds of property immediately results; and from the influence of these on the sentiments and views of the respective proprietors, ensues a division of the society into different interests and parties."

In this section, he is acknowledging the fact that everyone is entitled to he or she's own opinion. He uses property as an example and suggests that the government must represent all the diverse and opposing opinions on this issue. The government's job is to protect these rights and powers of the people to acquire property and the possession of property. This compares to Lockean idea of a social contract between the people and the sovereign where society will obey the sovereign if their natural rights(including property) are protected. 

51
“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.”
The reason that people need a government is to manage and limit the wrongdoings of mankind. Without a government, there would no visible fine line between what is socially acceptable and what is not. However, at a certain point, the people must learn to be self governed and to make their own judgement. This is the definition of democracy where the people run the show and make the decisions amongst themselves. If people are unable learn to control themselves, then this form of government is unattainable.

"But it is not possible to give to each department an equal power of self-defense. In republican government, the legislative authority necessarily predominates. The remedy for this inconveniency is to divide the legislature into different branches; and to render them, by different modes of election and different principles of action, as little connected with each other as the nature of their common functions and their common dependence on the society will admit."
Separation of powers is one of the fundamental principles upon which our government is based. The idea is for branches to check each others' power to ensure a balance in power among the branches. Another idea in this philosophy is to keep the tasks of each branch as distant from each other as possible so that no two branches are doing the same task and thus being inefficient. This idea was adopted by Montesquieu, a French philosopher during the Enlightenment who believed that a separation of powers could help stabilize the French government.