Prove Arrow's Theorem is not true when there are two candidates I'm trying to prove the Arrow's Theorem is not true when there are two candidates, however I'm having trouble trying to prove that there is no dictator. I have suggested that in a majority rules voting system, unanimity and IIA are satisfied but I have no idea how to prove that it isn't a dictatorship.

A dictator has his way whenever he expresses strict preferences.

Suppose that in the majority rule, there is a dictator $d$ and suppose that $x\succ_d y$ for some choices $x$ and $y$. If everybody else has the reverse preference: $y\succ_i x$ for all $i\
eq d$, what does the majority rule say about the social choice? Does $d$ get his way in this situation?

The majority rule is the correct candidate for your situation. It fails transitivity in general but when there are only 2 candidates, transitivity is vacuously satisfied