Simple games and weighted voting¶

A simple game typically has \(v(S) \in \{0,1\}\) for every coalition \(S\).

Weighted voting games are a common subclass:

• Given weights \(w_i\) and a quota \(q\), coalition \(S\) is winning if \(\sum_{i \in S} w_i \ge q\).

Power indices:

• Shapley-Shubik index
• (Normalized) Banzhaf index

In the code, we validate the "simple game" assumption before computing these indices.

Definition (simple game)¶