Based on: Axiomatic Foundations for Ranking Systems
by Alon Altman (Stanford) and
Moshe Tennenholtz (technion)
published 2008

Generalize agents rank each other.
Our multi-agent system: the agents rank each other based on 
the side-choosing game results.
We are looking for a social ranking rules and their properties.
We show general properties of social ranking rules 
for side-choosing games.
Aggregate information provided by the semantic games
into a social ranking.

Natural application: ranking of agents who debate claims.

Normative perspective.

Ahmed's collusion-resistance 
for side-choosing games 
corresponds to Arrows' IIA property
(independence of irrelevant alternatives)
for social choice settings.

IIA axioms mean that a participants rank must only depend
on a property of its immediate predecessors.

Adapt IIA to the context of side-choosing games.

<P>
Ordering: reflexive, transitive, complete.
L(A) is the set of orderings on A.
<P>
Ranking system:
A ranking system F is a functional that for any finite vertex set V
maps graphs in G(V) to an ordering <= (F,G) in L(V).

<P>
Our generalization:
A ranking system F is a functional that for any finite vertex set V
maps labeled graphs in G[SCG](V) to an ordering <= (F,G) in L(V).

<P>
Definition of G[SCG]:
Table with columns W,L,Forced etc.

<P>
In the side-choosing game case we use game results
to produce a ranking. The game results are a table
with several columns, including a winner and loser
column. Each row in the table can be viewed as
a labeled edge in a graph. The labels are about
who was forced, it can be either of the two nodes
incident with the edge 
or none.

<P>
According to [], we can view the above concept of 
a ranking system as a variation/extension 
of the classical theory of social choice
as modeled by Arrow.

<P>
We add the concept of forcing. Implications:

IIA corresponds to collusion-resistance.
Games where you are not in control cannot harm you.

<P>
Social choice theory  is a theoretical framework 
for analysis of combining individual opinions
to reach a collective decision.


<P>
Ahmed takes the normative perspective:
Devise a set of requirements that a social aggregation
rule should satisfy, and try to find whether there
is a social aggregation rule that satisfies these requirements.