Avoiding MCDA Evaluation Pitfalls

One is not required to be a mechanical engineer to drive a car and, considering the advanced state of mechanical engineering, most people limit their interest in what lies “under the hood” to finding a competent mechanic. Users of evaluation, risk, and decision analysis tools that are based on classical decision theory should be aware that, as is demonstrated below, classical MCDA (multi-criteria decision analysis) has not reached the advanced state of mechanical engineering. Since evaluation and decision tools that are based on flawed mathematical foundations produce meaningless numbers, the purpose of this paper is to give a sample of typical errors and direct the reader to (i) practical tools that are based on sound mathematical foundations and (ii) to these mathematical foundations. Typically, even the simplest multi-criteria evaluation techniques involve numbers and operations such as addition and multiplication. Also typically, it is not recognized that the numbers on which the operations of addition and multiplication are performed represent preference scales and that these are mathematical operations albeit elementary ones. Although the construction of preference scales and the applicability of mathematical operations to preference scale values are of great theoretical and practical importance, the problem of applicability of these operations has been ignored in the literature following the publication of von Neumann and Morgenstern’s Theory of Games and Economic Behavior [21] and the conditions under which these operations are applicable have not been identified until recently (see Barzilai [5, 6 and 7]).