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.