Vladislav Podinovski – Professor, Department of Higher Mathematics, Faculty of Economics, National Research University Higher School of Economics.
Address: 20, Myasnitskaya str., Moscow, 101000, Russian Federation.
E-mail: podinovski@mail.ru

Mikhail Potapov – Leading Researcher, Institute of Automation and Design, Russian Academy of Sciences.
Address: 19/18, Brestskaya str., Moscow, 123056, Russian Federation.  
E-mail: potapov@icad.org.ru 

In most cases decision-making tasks turn to be multi-criteria: decision alternatives are evaluated in terms of a number of decision criteria. As each criterion determines its own best alternative, i.e. there are no alternative that is the best in terms of several criteria at the same time, then multi-criteria tasks are more complicated than single-criterion ones and require special methods and solutions for task performance. The best known, most popular and widely used method is a weighted sum method based on conversion of all criteria into a single generalized criterion representing a sum of criteria weighted by their relative importance coefficients (weights).

The weighted sum method (WSM) is an attractive heuristic method, however, with a number of irremediable fundamental drawbacks. The task of this article to provide a complex review of critical WSM analysis results mentioned in various scientific publications.

WSM drawbacks include but not limited to: use of non-physical values; use of constant criteria weights; no check for naturally independence of criteria; unjustified consideration of criteria rating scale as quantitative; unjustified acceptance of assumption of general criteria rating scale uniformity; unjustified non-consideration of some alternatives; unjustified consideration of importance coefficients as quantitative criteria importance evaluation; intellectual error resulting from independence of criteria normalization and weight assignment procedures; unjustified selection of functions to normalize criteria; violation of independence from irrelevant alternatives axiom.