Multiagent Systems

Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 279/731
4. Decision Making (2) 1. Voting
Definition 4.9 (Social welfare function)
A social welfare function is any function
≺ ∗
f ∗ : U → Ord par ; (≺ 1 , . . . , ≺ |A| ) ↦→ ≺ ∗
For each V ⊆ 2 O \ {∅} the function f ∗ w.r.t. U induces a
choice function C 〈≺1 ,...,≺ |A| 〉 as follows:
{ V −→ V
C 〈≺1 ,...,≺ |A| 〉 = def
v ↦→ C 〈≺1 ,...,≺ |A| 〉(v) = max ≺ ∗
max ≺ ∗ | V
to ≺ ∗ | V .
≺ ∗ | V
v is the set of all maximal elements in v according
Each tuple u = (≺ 1 , . . . , ≺ |A| ) determines the election for
all possible v ∈ V .
v