Given a set of utility functions defined on a decision space for a group of individuals, we introduce the concept of utopia point for the group as well as the group regret of a feasible decision. The group regret of a decision varies with a class of distance functions. The class of solutions under study are those which minimize the group regret according to the class of distance functions. We investigate its properties from!he viewpoint of decision rationale. The bounds and monotonicity of the solutions together with their computation are also explored.