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Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 308/731 4. Decision Making (2) 2. Tactical Voting Definition 4.19 (Strategy-proof social correspondence) A social correspondence W ∗ : Ord par → 2 O ; 〈≺ 1 , . . . , ≺ |A| 〉 ↦→ v ′ is called strategy-proof, if the following two conditions hold for every agent i, for any two profiles p = 〈≺ 1 , . . . , ≺ i , . . . , ≺ |A| 〉 and p ′ = 〈≺ 1 , . . . , ≺ ′ i, . . . , ≺ |A| 〉 that only differ in agent i’s preference: 1 ∀a ∈ W ∗ (p) \ W ∗ (p ′ ), ∀b ∈ W ∗ (p ′ ): if a ⊲⊳ ≺i b then a ⊲⊳ ≺ ′ i b or a≺′ ib, and if a≺ ib then a≺ ′ ib. 2 ∀a ∈ W ∗ (p) \ W ∗ (p ′ ), ∃b ∈ W ∗ (p ′ ) such that: if b≺ ia then a ⊲⊳ ≺ ′ i b or a≺′ ib, and if a ⊲⊳ ≺i b then a≺ ′ ib.
Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 309/731 4. Decision Making (2) 2. Tactical Voting Here are two examples for social correspondences. 1 Let W ∗ 1 : Ord par → 2 O ; |A| ⋃ W ∗ 1 (〈≺ 1 , . . . , ≺ |A| 〉) := top(≺ i ) i=1 2 Let W ∗ 2 : Ord par → 2 O ; W ∗ 2 (〈≺ 1 , . . . , ≺ |A| 〉) := top(≺ pareto ) where a≺ pareto b iff a≺ i b for all 1 ≤ i ≤ |A|, otherwise a, b are incomparable. Exercise Are these correspondences strategy-proof? Prove or give counterexamples.
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9. Agents based on FOL 7. Reference
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