# Some problems about arrow's theorem and social choice [closed]

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?

• If you're right, you're the first person to notice an "obvious" mistake in a widely cited sixty-year-old theorem. Seems unlikely. – David Richerby Dec 18 '13 at 8:25
• Could you tell me why this is wrong? – Alex Dec 18 '13 at 10:11
• Sorry, no. I don't know about this area. – David Richerby Dec 18 '13 at 10:14
• david, do you mean the claim is more an unnoticed redundancy & not so much a "mistake"? if it were a mistake then is there some kind of contradiction? in any case it would be interesting to know of the proof that shows of all 3 features, none implies any others. – vzn Dec 18 '13 at 22:33
• @vzn - the proof crucially uses all 3 features. Indeed, the Borda-count does not satisfy one of them, and is not a dictatorship. And other examples can be constructed that violate each of the other conditions. – Shaull Dec 19 '13 at 4:16