Final answer:
Belief in a democratic-style republic logically extends to the desire for a large nation as Madison posited that it reduces the likelihood of single factions overpowering and allows for a greater variety of interests, which protect minority views and prevent a common motive to invade the rights of others.
Step-by-step explanation:
If one believes in a democratic-style republic, according to Madison, it is logical to desire a physically large nation because it would prevent local interests from rising to dominance, thus safeguarding against tyranny. Madison argued that in a large republic, the variety of interests and opinions would make it less likely for a single faction to gain majority power and oppress others. He believed that having a variety of parties and interests would offer greater protection to minority views and would make it harder for factions to unite and execute plans that could potentially threaten the rights of others.
Factions were seen as a primary threat to the stability and fairness of a republic. In Federalist No. 10, Madison acknowledged the concerns about factions and specifically addressed that the size of the republic would actually serve as a defense against the dominion of a single interest group. A larger republic would include a greater variety of parties and interests, preventing any single group from becoming too powerful.
Madison favored a large republic over a small one and a republic over pure democracy because he believed a republic was better equipped to manage the negative effects of factions.