Multiagent Systems

Prof. Dr. Jürgen Dix · Department of Informatics, TUC Multiagent Systems, WS 06/07 289/731
4. Decision Making (2) 1. Voting
There must be one step, let’s call it n ∗ , where
a≺ ≺ n∗ − 1 b but b≺ ≺ n∗ a (because of unanimity and
strict neutrality). (Here we denote by ≺ n∗ − 1 the
ordering obtained from 〈≺ n∗ − 1
1 , . . . , ≺ n∗ − 1
|A|
〉 and,
similarly, for ≺ n∗ ).
Note again that this reasoning is true not just for
one profile 〈≺ i 1, . . . , ≺ i |A|
〉, but for all such
profiles with the same relative ranking of a and
b.
We claim that n ∗ is a dictator.
n ∗