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Multiagent Systems

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of. Dr. Jürgen Dix · Department of Informatics, TUC <strong>Multiagent</strong> <strong>Systems</strong>, WS 06/07 287/731<br />

4. Decision Making (2) 1. Voting<br />

≺ ′∗<br />

By unanimity, we have a≺ ≺ ′∗ α (for α ≠ a) and<br />

β≺ ≺ ′∗ b (for β ≠ b). Using transitivity, we get<br />

β ≺ ′∗ α. By IIA, we also get β ≺ ∗ α (because<br />

α≺ ≺ ′ iβ iff α≺ i β).<br />

By independence of irrelevant alternatives, we<br />

can change the roles of (a, b) with (α, β) and get<br />

b≺ ≺ ∗ a (note that there is no equality sign ≼ ∗ ).

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