The correct answer to this open question is the following.
You do not include any reference to what argument, text, or paper written by James Madison, because he wrote many as part of the authors of the Federalists papers.
However, probably you are referring to "Federalist N.-10." If this is the case, then the correct answer is the following.
Madison used the comparison to bolster his argument in that he compares two forms of government: Republic and Pure Democracy. In that comparison, James Madison says that the wrongdoings and failures of Pure Democracy represent the benefits of a Republic. So he tries to promote the idea of a Republic as the new form of government for the new nation.