Of all the Federalist Papers written by John Jay, James Madison, and Alexander Hamilton, perhaps the most famous and the one most quoted is Federalist No. 10, by Madison. Many people had argued against the new Constitution claiming that the US would be too large to govern as a democracy (republic) and had too many groups, or "factions," as political parties were then called. While Madison acknowledged that there were many differing factions, he also indicated that a democratic form of government, using the ideal of majority rule, would tame the factions and cause them to work together as much as possible. He claimed that the republican form of government created by the new Constitution would allow all the factions the room and venues to express themselves and to influence the workings of government by getting their members elected and/or appointed to offices. Minority groups would be protected because the factions would have to negotiate their differences. In this way, the republic would create a system of government in which the majority would rule but the ideas of the minority would have to be taken into consideration. Numerous factions would also mean that no one group would be able to take complete control of the government and this would give rise to what Madison called "politics," namely, the art of governing.
The Federalist Papers are a series of essays written by Alexander Hamilton, James Madison, and John Jay. These essays were published in the New York newspapers, and their purpose was to persuade New Yorkers to ratify the Constitution. New York at the time was mostly anti-federalist.
One of the most famous essay is the Federalist No. 10 written by Madison. It constructs the problem of "factions" and how a large republic framed by the Constitution, can better give a cure for these.
Madison, with "factions" means a group of people who are united by the same beliefs, interests, and passions. To pursue these common goals they disregard the rights of other citizens, especially minorities. He affirms that factions, particularly when assembled together in a majority, have been a problem to popular government. By popular government he indicates those supported by the people.
Madison illustrates two methods for dealing with the violence of faction: to remove its causes, or to control its effects. There are two ways again of removing its causes, one is by taking away liberty, the other is by giving the same interests to every citizens. The first would work because "liberty is to faction what air is to fire" but it is impossible to perform because liberty is essential to political life and is what Americans have fought for during the revolutionary war. The second option is impracticable because common people's opinions are always influenced by their emotions and their self-interest. They don't always think clearly, they don't approach situations in the same way. The diverseness of people's ability which make them succeed more or less and in which inequality of property derive is a right that the government should protect.
Madison states "The latent causes of faction are thus sown in the nature of man" so the cure is to control factions' effects. He makes an argument on how this is not possible in a pure democracy but possible in a republic. With pure democracy he means a system in which every citizen vote directly for laws. And with republic he intends a society in which citizen’s vote for elected representatives who then vote for laws. He indicates that the voice of the people pronounced by a body of representatives is more conformable to the interest of the community because again, common people's decisions are affected by their self-interest.
Then he makes an argument in favor of a large republic against a small republic for the choice of "fit characters" to represent the public's voice. In a large republic where the number of voters and candidates is greater, the probability to elect competent representatives is broader. The voters have a wider option. In a small republic it would also be easier for the candidates to fool the voters, while in a large one, harder.
The last argument Madison makes in favor of a large republic is, in a small republic there will be a lower variety of interests and parties, so more frequently a majority will be found. The number of participants of that majority will be lower, and considering they live in a more limited territory, it would be easier for them to agree and work together for the accomplishment of their ideas. While in a large republic the variety of interests will be greater so to make it harder to find a majority. Even if there is a majority it would be harder for them to work together because of the large number of people and the fact they are spread out in a wider territory.