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Multiagent Systems

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Prof. Dr. Jürgen Dix · Department of Informatics, TUC <strong>Multiagent</strong> <strong>Systems</strong>, WS 06/07 286/731<br />

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

Proof (of the lemma).<br />

Because |A| ≥ 3, the pair (a, b) is distinct from<br />

(α, β). We assume wlog that b≼ ≼ ∗ a. We are now<br />

constructing a different profile 〈≺ ′ 1, . . . , ≺ ′ |A| 〉<br />

obtained as follows (for all i):<br />

If a ≠ α, then we change ≺ i by moving α just<br />

above a.<br />

If b ≠ β, then we change ≺ i by moving β just<br />

below b.<br />

This can be done by maintaining the old<br />

preferences between α and β (as preferences<br />

between a and b are strict).

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