Abstract
We introduce the axiom of composition independence for power indices and value maps. In the context of compound (two-tier) voting, the axiom requires the power attributed to a voter to be independent of the second-tier voting games played in all constituencies other than that of the voter. We show that the Banzhaf power index is uniquely characterized by the combination of composition independence, four semivalue axioms (transfer, positivity, symmetry, and dummy), and a mild efficiency-related requirement. A similar characterization is obtained as a corollary for the Banzhaf value on the space of all finite games (with transfer replaced by additivity).
| Original language | English |
|---|---|
| Pages (from-to) | 755-768 |
| Number of pages | 14 |
| Journal | International Journal of Game Theory |
| Volume | 48 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Sep 2019 |
Keywords
- Banzhaf power index
- Banzhaf value
- Composition property
- Compound games
- Dummy
- Positivity
- Semivalues
- Simple games
- Symmetry
- Transfer
ASJC Scopus subject areas
- Statistics and Probability
- Mathematics (miscellaneous)
- Social Sciences (miscellaneous)
- Economics and Econometrics
- Statistics, Probability and Uncertainty