Abstract: The evidential reasoning rule effectively deals with the importance of evidence and reliability. In this study, we investigate the influence of weight normalization on evidence combinations and discuss whether evidence weights should be normalized in different cases. We survey the relation between the evidential reasoning rule and evidence discounting approach and prove that the beliefs of the former are proportional to those of the latter. Finally, we propose a modified approach that satisfies four synthesis axioms, following an analysis of the evidential reasoning rule problem in modeling the importance of evidence and reliability.