Check out the Federalist papers, in particular No. 10. Factions are like political parties or large groups together for a cause.
Madison's solution for controlling the effects of factions was the establishment of a republican government. He argued that the powers wielded by the factions be constitutionally limited.
Special interest groups and factions means the same thing but James Madison preferred to call it factions.
As many say, James Madison was a tyrannical soldier. His idea of factions meant that the slaves would be allowed to be free. He did this because he feared that slavery would never be abolished.
Madison defines factions as a number of citizens (representing either the minority or majority of the whole) who are united by common passions and interests. Examples of factions today are political parties and unions.
Create a large enough republic to ensure that majority factions will
James Madison warned against the dangers of what he called factions they produced "instability, injustice, and confusion."
James Madison believed that a democratic form of government, would tame the factions and cause them to work together as much as possible. Madison, in the The Federalist, argued that the federal system helps prevent factions from gaining too much control and causing tyranny of the majority
James Madison wrote about his concern regarding factions in his famous essay, "The Federalist No. 10." He believed that factions, or groups of individuals united by a common interest or opinion, were a natural and inevitable part of human nature. Madison argued that the danger of factions lied in their potential to oppress the rights of others or undermine the public good, but that a large and diverse republic with multiple factions could help control their effects through a system of checks and balances.
Federalist 10
James Madison.
Yes
Madison argued that in an extensive Republic interest groups (factions as he called them) will be so numerous and varied that no one faction or group of factions will be able to control government and impose their will on the minority.