Ordering: reflexive, transitive, complete. L(A) is the set of orderings on A.

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).

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).

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

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.

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.

We add the concept of forcing. Implications: IIA corresponds to collusion-resistance. Games where you are not in control cannot harm you.

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

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.