Combining weights into scores: A linear transform approach

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