An Ordinal Banzhaf Index for Social Ranking

Hossein Khani (1) , Stefano Moretti (1) , Meltem Ozturk (1)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

We introduce a new method to rank single elements given an order over their sets. For this purpose, we extend the game theoretic notion of marginal contribution and of Banzhaf index to our ordinal framework. Furthermore, we characterize the resulting ordinal Banzhaf solution by means of a set of properties inspired from those used to axiomatically characterize another solution from the literature: the ceteris paribus majority. Finally, we show that the computational procedure for these two social ranking solutions boils down to a weighted combination of comparisons over the same subsets of elements.

Mots clés: Voting; Social Choice; Cooperative Games; Agent-based and Multi-agent Systems

Domaines: Système multi-agents [cs.MA]; Intelligence artificielle [cs.AI]

Hossein Khani, Stefano Moretti, Meltem Ozturk. An Ordinal Banzhaf Index for Social Ranking. 28th International Joint Conference on Artificial Intelligence (IJCAI 2019), Aug 2019, Macao, China. pp.378-384, ⟨10.24963/ijcai.2019/54⟩. ⟨hal-02302304⟩