Voting Paradoxes and the Human Intuition

Brams (2003) presents three paradoxes for power indices: some rather counter-intuitive behaviour that is exhibited by both the Shapley-Shubik and the Banzhaf indices. We show that the proportional index is free from such paradoxical behaviour. This result suggests that our intuition may be based on the proportional index and as such its use in evaluating power measures is limited.