Why did james madison believe that a large, diverse republic would be best for the common good

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

Diverse interests could check one another

Explanation:

he believed that congress would be better not dealing with "lobbyists", or people who seek to influence (a politician or public official) on an issue, since historically, they had problems with these kinds of people. he thought lobbying produces benefits, but should be carefully monitored.