In the literature of cooperative games, the notion of power index has been widely used to evaluate the inuence" of individual players (e.g., voters, political parties, nations, etc.) involved in a collective decision process, i.e. their ability to force a decision in situations like an electoral system, parliament, a governing council, a management board, etc. In practical situations, however, the information concerning the strength of coalitions and their e ective possibilities of cooperation is not easily accessible due to heterogeneous and hardly quanti able factors about the performance of groups, their bargaining abilities, moral and ethical codes and other psychological" attributes (e.g., the power obtained by threatening not to cooperate with other players). So, any attempt to numerically represent the inuence of groups and individuals conicts with the complex and multi-attribute qualitative nature of the problem. Previous applications of cooperative games show that this type of qualitative information is central for the evaluation of the individual inuence in voting systems and in social networks, the degree of acceptability of arguments in a debate, or the importance of criteria in a multi-criteria decision-making process, etc.
université Paris DauphineFanny PASCUAL