Multi-Criteria Decision Making

Almost all human choices are multicriteria, which means that they require the comparison of alternatives under more than one single criterion. A criterion corresponds to getting positive (valuable) outcomes according to an objective-function: for instance, we choose a car between competing products, based on the criterion of price, safety, size, comforts, speed, etc. The hardest question arises from the fact that, with special exceptions, two conditions generally occur:

1. the criteria are conflicting each others, i.e. they do not order our preferences in the same way;

2. criteria are genuinely independent, i.e. they are not transformable into one another through some coefficient.

What people usually do to cope with these situations is just assigning weights to each criterion and then multiplying each weight per the corresponding score. This method means building an aggregate function and then implicitly assuming that the criteria can be transformed into one another by applying the implicit coefficients. But when criteria are genuinely independent, this method cannot be applied. Standard operations research suggests some other expedient, which indeed do not overcome the problem.

The problem is that multicriteria choices cannot be optimized. Analogously, if the behavior of a system is multicriteria or the characteristics of a phenomenon are multicriteria, the evaluation cannot be optimized. The main reason is that multicriteriality implies that the choice, the behavior or the phenomenon cannot be expressed by means of a single function, whatever its eventual complexity. It can be expressed by means of a set of functions, which, mathematically speaking, is not a function, and thus, a fortiori it cannot be optimized.

However, the impossibility to maximize does not mean that we lack any rational method to choose. The French school of operations research has developed a family of algorithms able to solve multicriteria problems in a way that is fully consistent with satisfying (non-optimizing) approaches to decision making or evaluation. They call outranking methods, and can be easily applied through some dedicated software. 

In the following papers can be found a theoretical discussion of the characteristics of multicriteria problems and phenomena, some applications to economics, management, and innovation policy, and a discussion of the basic concepts of the French school of operations research (with the main references)

- L. Biggiero, 2009. A short presentation of three (relatively new) methodologies: multicriteria decision making; social network analysis, and agent-based simulation modelling. New methods MCDM SNA ABSM [slides]
- L. Biggiero and D. Laise 2007. On Choosing Governance Structures: Theoretical and methodological issues. Human Systems Management. 26: 69-84.
- L. Biggiero, G. Iazzolino and D. Laise 2005. On Multicriteria Business Performance Measurement. The Journal of Financial Decision Making. 1 (2): 37-56.
- L. Biggiero and D. Laise 2004a. La valutazione multicriteriale delle strategie aziendali (The Multicriteria Evaluation of Business Strategy). Sinergie. 63: 199-219.
- L. Biggiero and D. Laise 2004b. Comportamento organizzativo e aiuto alle decisioni multicriteriali (Organizational Behavior and Multicriteria Decision Aid). Sistemi intelligenti. 3: 435-456.
- L. Biggiero and D. Laise 2003a. Choosing and Comparing Organizational Structures: A Multicriteria Methodology. Human Systems Management. 30(1): 13-23.
- L. Biggiero and D. Laise 2003b. Outranking Methods. Choosing and Evaluating Technology Policy: A Multicriteria Approach. Science & Public Policy. 30(1): 13-23.
- Laise, D. 2004. Benchmarking and learning organization: ranking methods to identify ‘Best in class. Benchmarking: An International Journal. 11(6): 621-629.