Why did James Madison believe that a large republic would be best for the common goods?

Answer 1

James Madison believed that a large diverse republic would be the best for the common good because diverse interests could check one another.

Answer 2

Madison's point, which was later fleshed out in letters to Jefferson and George Washington, and finally in Federalist 10, was that in a larger republic there was much less likelihood of the tyranny of the majority that had wreaked such havoc under the old Articles. Why? First of all, in a large republic it would be harder for people of "common sentiment" to join together to impose their will. But equally important, in a large republic more people would - following the dictates of their pursuit of self-interest - constantly shift in and out of a larger number of different factions.