Some problems about arrow's theorem and social choice I'm just started lecture myself about arrow's theorem. There are some problems which make me confused.

ARROW'S THEOREM: Any constitution that respects transitivity, independence of irrelevant alternatives, and unanimity is a dictatorship.

This is a kind of statement from john Geanakoplos' paper. 

I think unanimity+transitivity and independence of irrelevant alternatives are equivalent. For example:

voter A: a>b>c>d
voter B: a>c>b>d
voter C: a>d>c>b

So we can conclude that everybody prefers a to b just according to unanimity and transitivity. And I think this conclusion implies independence of irrelevant alternatives. So if I drop the constraint of independence of irrelevant alternatives, Is this still right?
Unanimity and transitivity do no imply IIA.

For example, consider the Borda-count voting mechanism. There is an example of the violation of IIA here.