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This paper proposes a new method for assigning distribution system (DS) losses to consumers and distributed generations in the framework of a liberalized energy market. The architecture of the proposed method is based on a synthesis of electrical network analytical theory and cooperative game theory (CGT). Weighted shapely value (WSV) is a solution idea that is regarded to be efficient in CGT for n-player games with characteristic function form. By retaining the notion of electrical networks, the axioms of game theory will be preserved while employing the WSV in loss allocation theory. To allocate system losses, the proposed method estimates the average marginal contribution of each participant to all conceivable coalitions and also determines the weight of the marginal contribution of each participant based on its power rating. Rather than a sequential branch-oriented approach, the proposed methodology is node-oriented. Additionally, a majority rule game is used to constrain the population of a coalition without jeopardizing the efficacy of the solutions to achieve a fair allocation of losses. The results of the proposed method are presented and contrasted with those obtained using the conventional pro-rata method and the well-known Shapley value solution concept in CGT.