Two Stories, One Power Index

This paper demonstrates that the mathematical properties of the member bargaining power measure (MBP) are identical with those of the public good index (PGI). However, the underlying theoretical concepts of the two measures are different. The MBP refers to bargaining over shares of the coalition value, and thus has a private good perspective, whereas the PGI considers power with respect to providing a public good as coalition value. The identity of the mathematical properties is used to study the properties of the two measures. For weighted voting games, both measures violate monotonicity with respect to voting weights, and the paradox of weighted voting applies.