Final answer:
James Madison recommended a republican government as the cure for the problem of factions, arguing that a large republic would prevent the tyranny of the majority and protect individual rights.
Step-by-step explanation:
James Madison discussed the problem of factions in Federalist No. 10 and stated that the best solution to this problem is a republican form of government. He elaborated that a republic, with a representative framework, is superior to a pure democracy since it can effectively control the negative impacts of factions, and prevent the tyranny of the majority. In a republic, diverse interests can coexist, and elected representatives would serve as a buffer against the interests of a biased majority.
Madison argued that democracies are prone to turbulence due to the common passions of the majority and that there is no system in place within such governments to protect the minority or individual rights effectively. Contrary to this, the large republic envisioned by Madison would allow for a variety of interests and opinions, which would make it difficult for factions to unite and infringe on the rights of others. Therefore, Madison was an advocate for a large republic as the best defense against factions.