<p>Unanimity and transitivity do no imply IIA.</p>

<p>For example, consider the Borda-count voting mechanism. There is an example of the violation of IIA <a href="http://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives#Borda_count">here</a>.</p>

CC BY-SA 3.0
2013-12-18T15:55:46.250Z
2013-12-18T15:55:46.250Z
Shaull
<p>I'm just started lecture myself about arrow's theorem. There are some problems which make me confused.</p>

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

<p>This is a kind of statement from john Geanakoplos' paper. </p>

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

<p>voter A: a>b>c>d
voter B: a>c>b>d
voter C: a>d>c>b</p>

<p>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?</p>

CC BY-SA 3.0
2013-12-18T08:25:50.137Z
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
CC BY-SA 3.0
2013-12-18T10:11:04.877Z
Could you tell me why this is wrong?
Alex
CC BY-SA 3.0
2013-12-18T10:14:04.747Z
Sorry, no. I don't know about this area.
David Richerby
CC BY-SA 3.0
2013-12-18T22:33:23.547Z
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
CC BY-SA 3.0
2013-12-19T04:16:42.680Z
@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
<gt.game-theory><social-sciences>
Some problems about arrow's theorem and social choice
Alex
# Some problems about arrow's theorem and social choice

(Asked by: username_0 on 2013-12-18)

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?

**Tags:** gt.game-theory, social-sciences

> **Comments:**
> **username_1**: If you're right, you're the first person to notice an "obvious" mistake in a widely cited sixty-year-old theorem. Seems unlikely.  
> **username_0**: Could you tell me why this is wrong?  
> **username_1**: Sorry, no. I don't know about this area.  
> **username_2**: 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.  
> **username_3**: @username_2 - 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.  

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## 1 answers

### Answer by username_3 on 2013-12-18. Score: 5

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](http://en.wikipedia.org/wiki/Independence_of_irrelevant_alternatives#Borda_count).


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