What relation does Madison draw between the size of society and its ability to self govern

In Federalist No. 10, Madison discusses the advantages and disadvantages that different sized republics would have when it comes to the quality of their democracy. He believes that a small society would have a worse chance to successfully exercise self-government because such a society would more easily succumb to "factions." Factions are groups that pursue their own goals as opposed to the common good. In a small society, undesirable ideas can very quickly spread to a lot of people. Therefore, he favors the creation of large republics.

Madison believes that a large country with many different groups bolsters self-government. It can be too large for self-government to prosper but modifications such as the United States adjusting the federal principle can still support self-government. Madison further explains that a powerful government with a "community will" (that is larger and independent of the simple majority) can avoid the evils of the majority threatening minorities.