What is the second thing that Madison argued tirelessly for?

large republic

Explanation:

James Madison's arguments were well documented in Federalist 10. He first argued about the issue of factions. He explored this well when he concluded that, more factions and diversity will prevent the tyranny of the majority over the minority.

On the other hand, his second argument was in support of the Large Republic. James Madison believed that a Large Republic will make the country to have a wider pool of candidates and voters to pick the best available candidates. He also argued that the Larger Republic will lead to more varying interests and parties, which will make it difficult to have the majority over the minority.