Multiagent Systems

of. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 280/731
4. Decision Making (2) 1. Voting
What are desirable properties for f ∗ ?
Pareto-Efficiency: for all o, o ′ ∈ O: (∀i ∈ A : o≺ i o ′ )
implies o≺ ≺ ∗ o ′ .
Independence of Irrelevant Alternatives: for all
o, o ′ ∈ O:
(∀i ∈ A : o ≺ i o ′ iff o≺ ≺ ′ i o ′ ) ⇒ (o≺ ≺ ∗ o ′ iff o≺ ′ ∗
≺ ′∗ o ′ ) .
Note that this implies in particular
(∀i ∈ A : ≺ i | v = ≺ ′ i| v )
⇒
∀o, o ′ ∈ v, ∀v ′ ∈ V s.t. v ⊆ v ′ : (o≺ ≺ ∗ | v ′ o ′ iff o≺ ′ ∗
≺ ′∗ | v ′ o ′ )
Majority Vote
The simple majority vote protocol does not satisfy the
Independence of irrelevant alternatives.