A method to compare influence of coalitions on group decision other than desirability relation

This paper proposes a method to compare influence of coalitions on group decision, called blockability relation. This relation is defined both on the set of all coalitions and on the set of all feasible coalitions. Examples show that this relation is definitely different from the desirability relation, which have been dealt with in the literature. In particular, an example shows that the desirability relation is not always transitive, and a proposition verifies that the blockability relation is always transitive. In order to clarify the simple games on which these relations are defined and to investigate interrelationships among these simple games, three types of operators, called L-intersection, L-restriction and extension, respectively, on simple games are defined, where L is a family of all feasible coalitions. It is verified that the extension of the L-intersection of a simple game coincides with the restriction of the simple game.