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Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 272/731 4. Decision Making (2) 1. Voting What are fair conditions for an election process? Note that our preferences are total. Definition 4.5 (Unanimity, Monotonicity) A social choice C ∗ function satisfies unanimity, if for any profile l = (≺ 1 , . . . , ≺ |A| ), v ∈ V and outcome o ∈ v: If for all 1 ≤ i ≤ |A| : o = max ≺ i then C ∗ (v, l) = o A social choice C ∗ function satisfies monotonicity, if for any profile l = (≺ 1 , . . . , ≺ |A| ), v ∈ V and outcome o = C ∗ (v, l) ∈ v: if l ′ == (≺ ≺ ′ 1, . . . ,≺ ≺ ′ |A|) is a different profile such that for all o ′ and i o ′ ≺ i o implies o ′ ≺ ′ io then C ∗ (v, l ′ ) = o.
Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 273/731 4. Decision Making (2) 1. Voting Finally we call C ∗ dictatorial, if there exists an agent i such that for all l = (≺ 1 , . . . , ≺ |A| ) : C ∗ (v, l) = max ≺ i v. Theorem 4.6 (May (1952)) If there are only two candidates, there is a social choice function which is not dictatorial but yet satisfies unanimity and monotonicity.
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9. Agents based on FOL 7. Reference
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