Multiagent Systems

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.