<p><a href="https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem" rel="nofollow noreferrer">Arrow's Impossibility Theorem</a> merely states that (with a ranked voting method) we cannot simultaneously satisfy IIA, Pareto Efficiency, Non-dictatorship and unrestricted domain.  You <em>can</em> satisfy any subset of those conditions, though.  So Non-dictatorship with IIA is fine &mdash; so long as you're willing to drop Pareto Efficiency.  Similarly, Non-dictatorship and Pareto Efficiency can be satisfied &mdash; if you drop IIA.</p>

<p>You can also use a system that is <em>not</em> ranked, such as <a href="https://en.wikipedia.org/wiki/Cardinal_voting" rel="nofollow noreferrer">Cardinal Voting</a> although there is some debate as to  how to adapt the IIA criterion in such cases, and some such systems nonetheless fail <em>different</em> <a href="https://en.wikipedia.org/wiki/Category:Electoral_system_criteria" rel="nofollow noreferrer">criteria</a> not addressed by Arrow, such as the <a href="https://en.wikipedia.org/wiki/Majority_criterion" rel="nofollow noreferrer">Majority Criterion</a>.</p>

<p>(Unrestricted domain has more to do with how to decide which candidates are eligible to appear on the ballot, and which voters are allowed to vote in general, and so isn't usually considered as one of the criteria that can be relaxed... it's more a formality in Arrow's theorem, than the other criteria.)</p>

CC BY-SA 4.0
2019-06-06T16:00:25.010Z
2019-06-06T16:40:31.357Z
2019-06-06T16:40:31.357Z
Bill Clark
<p>How does Arrow's Impossible Theorem show that the only aggregation rule that works is Dictatorship. Couldn't we have a Non-dictatorship with IIA or a Non-Dictatorship with Pareto Efficiency?</p>

CC BY-SA 4.0
2019-06-06T13:48:58.443Z
Why do you think this is what the Theorem shows? Please include a reference.
Giskard
<political-economy><social-choice>
Arrows Theorem: Dictatorship
Maths
# Arrows Theorem: Dictatorship

(Asked by: username_0 on 2019-06-06)

How does Arrow's Impossible Theorem show that the only aggregation rule that works is Dictatorship. Couldn't we have a Non-dictatorship with IIA or a Non-Dictatorship with Pareto Efficiency?

**Tags:** political-economy, social-choice

> **Comments:**
> **username_1**: Why do you think this is what the Theorem shows? Please include a reference.  

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## 1 answers

### Answer by username_2 on 2019-06-06. Score: 1

[Arrow's Impossibility Theorem](https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem) merely states that (with a ranked voting method) we cannot simultaneously satisfy IIA, Pareto Efficiency, Non-dictatorship and unrestricted domain. You *can* satisfy any subset of those conditions, though. So Non-dictatorship with IIA is fine — so long as you're willing to drop Pareto Efficiency. Similarly, Non-dictatorship and Pareto Efficiency can be satisfied — if you drop IIA.

You can also use a system that is *not* ranked, such as [Cardinal Voting](https://en.wikipedia.org/wiki/Cardinal_voting) although there is some debate as to how to adapt the IIA criterion in such cases, and some such systems nonetheless fail *different* [criteria](https://en.wikipedia.org/wiki/Category:Electoral_system_criteria) not addressed by Arrow, such as the [Majority Criterion](https://en.wikipedia.org/wiki/Majority_criterion).

(Unrestricted domain has more to do with how to decide which candidates are eligible to appear on the ballot, and which voters are allowed to vote in general, and so isn't usually considered as one of the criteria that can be relaxed... it's more a formality in Arrow's theorem, than the other criteria.)


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