The common issue that Madison discusses in Federalist Papers #10 and #51 are the proliferation of political factions in society. He notes that man is a violent animal who likes conflict, and suggests in both essays that the only way to solve these factions is to allow for a society where many of them form such that they limit each other's powers. Madison's thoughts on separation of government and the formation of a large republic were ahead of his time. Many thinkers of his era believed that the perfect society was a small republic where people were in contact with their government. A large republic looked extremely hard to govern. For Madison, the problem of governing could be solved by having many smaller states as the governing political units.
In Essay #10, Madison tackles the question of how to deal with factions whose interests or goals may be in contention with the people's rights. As he would later acknowledge in Essay #51, Madison believed that forming one big and powerful republic was the ultimate answer to providing all these rights. Smaller republics would quickly have to tackle factions, and they would go extremely powerful faster than the states could respond. Madison takes over the discussion from Hamilton's #9 on how factions can break up the republic. Madison, on the other hand, discusses how the law-abiding citizens can avoid the negative effects of the rebel groups. Part of this is to acknowledge that factions emerge from a diversity of opinion that divides the people on core issues such as religion. As he would later discuss in #51, Madison discusses the demerits of a direct democracy and makes a case for a representative democracy. He believes that this form of democracy is the most effective in protecting the individual from the majority, and to stemming the thorny class issue. Madison says that there are two ways to solve the problem of factions, either to break them or solve their causes.