Wealth redistribution in a society is related to the social planner’s beliefs about social justice. In this paper, the social planner’s preferences are described by a Choquet integral, which is a convex combination of a weighted utilitarian social welfare function and an egalitarian social welfare function. By spending resources on lobbying, interest groups can change the social planner’s preferences, by shifting the weights of the utilitarian part, or by shifting more or less weight to the egalitarian part. We use a model of a two-player lobbying game and obtain the conditions for a pure strategy Nash equilibrium of the game.