Ranking has been widely used in many applications. A ranking scheme usually employs a "scoring rule" that assigns a final numerical value to each and every object to be ranked. A scoring rule normally involves the use of one or many scores, and it gives more weight to the scores that is more important. In this paper, we give a scheme that can combine weights into scores in a natural way. We compare our scheme to the formula given by Fagin. We give additional desirable properties that weighted "scoring rule" are desirable to possess. Some interesting issues on weighted scoring rule are also discussed.