Preference-based argumentation frameworks are instantiation of Dung's framework in which the defeat relation (in the sense of Dung) is computed from an attack relation and a preference relation over the set of arguments. Value-based argumentation framework is a preference-based argumentation framework where the preference relation over arguments is derived from a preference relation over values they promote. We extend value-based argumentation framework with collective defeats and arguments promoting values with various strengths. In the extended framework, we define a function which computes the strength of a collective defeat. We define desired properties for the proposed function. Surprisingly, we show that this function obeying the corresponding properties is Choquet integral, a well-known aggregation function at work in multiple criteria decision.