Federalist 10 concerns the influence of factions, which James Madison, the author, defines in this way:
...[A] number of citizens, whether amounting to a majority or a minority of the whole, who are united and actuated by some common impulse of passion, or of interest, adversed to the rights of other citizens, or to the permanent and aggregate interests of the community.
While some might reach the conclusion that Madison was referring to political parties, his definition is closer to that of modern interest groups. He especially drew distinctions between people who owned property and those who did not. The point is that these groups would place their own particular interest ahead of that of the people and the nation as a whole. This was a concern of many eighteenth-century political theorists, one seen as fatal to republics. This led some to conclude that a republican form of government would not be able to rule a country as large in territory as the new United States. Given the size and the diversity of peoples and economies, many thought the nation would collapse into chaos, which might give way to a tyrant.
One of the key insights of this particular essay is that Madison views the existence of factions as inevitable given human nature. Therefore it is pointless to argue that people will submit to the common good out of patriotism or self-sacrifice. Moreover, in a republic, where people have the liberty to pursue their interest through political ends, this issue was inevitable. Only a tyrannical government would eliminate factions. "Liberty is to faction what air is to fire, an aliment without which it instantly expires," he writes in Federalist 10.
Madison expands on this very issue in Federalist 51, where he describes the system of checks and balances established by the Constitution. In Federalist 10, as in the essay published later in the collection, he explains how the Constitution will attempt to control the effects of faction. He argues that the criticism that the nation is too big for a republic is completely wrong. Rather, the size of the republic will actually keep one faction from being able to gain a majority, since there are so many interests in such a large expanse of land. "The influence of factious leaders may kindle a flame within their particular States," he writes, "but will be unable to spread a general conflagration through the other States" because the people in those states did not share their interest.
In short, Madison turns a criticism of the Constitution, and the government it would create, on its head, writing that a common critique of the government is actually a strength, one that enables it to address an intractable problem posed by human nature.