In this paper the method of synthesis using geometric mean of the judgments(CMJ)for making group decisions in AHP was discussed theoretically.The conclusion indicated that the consistency of GMJ was less than the mean of the consistencies of judgments.If the pertubation factors in judgments are stochastic,it was proved in this paper that the matrix of GMJ will converge in probability at a consistent positive reciprocal matrix whose vector of priorities is just the geometric mean of the vectors of priorities for each judgments.That should be and important coclusions when GMJ is used to sythesize judgments for making group decision in AHP.