Testing the sensitivity of linear additive weighting to variations in a criterion weight

Linear additive weighting is a multicriterion decision-making technique used to find a preference ordering over a discrete set of options generated to satisfy multiple criteria/objectives. Given, for example, that option A is ranked ‘best’ and option B is ranked ‘second best’, then an important question is the extent to which the results of additive weighting are sensitive to variations in a particular criterion weight such that options A and B are equated in terms of aggregate value as ‘joint best’. This paper presents a simple formula to assess such possibilities. In addition, an approach to testing the sensitivity of the results of additive weighting to variations in all criterion weights is presented using the concepts of ‘directed divergence’ (‘discrimination information’) and ‘least squares’