27. Multiple Criteria Decision Analysis and Sustainable Development

Emphasis added to the original.

Here I refer to the idea of orchestration of sciences as a combination of multi/inter-disciplinarity. Multi-disciplinarity: each expert takes her/his part. Inter-disciplinarity: methodological choices are discussed across the disciplines.

Composite indicators are indeed synthetic indexes, thus the two terms can be considered synonymous; here I use the term composite indicator since is the standard one in OECD/EC terminology [88].

One should note that this inconsistency is present in the majority of the environmental impact assessment studies too. In fact it is a common practice to aggregate environmental impact indicators by means of a linear rule and to attach weights to them according to the relative importance idea. Moreover, the use of a linear aggregation procedure implies that among the different ecosystem aspects there are not phenomena of synergy or conflict. This appears to be quite an unrealistic assumption for environmental impact assessment studies [39]. For example, “laboratory experiments made clear that the combined impact of the acidifying substances SO ₂ , NO _X , NH ₃ and O ₃ on plant growth is substantially more severe that the (linear) addition of the impacts of each of these substances alone would be.” [31].

Often this search for clear properties characterizing an algorithm is indicated as the axiomatic approach. However, one should note that properties or assumptions are NOT axioms. As perfectly synthesized by Saari [[110], p. 110] “Many, if not most, results in this area are merely properties that happen to uniquely identify a particular procedure. But unless these properties can be used to construct, or be identified with all properties of the procedure (such as in the development of utility functions in the individual choice literature), they are not building blocks and they most surely are not axioms: they are properties that just happen to identify but not characterize, a procedure. As an example, the two properties (1) Finnish-American heritage (2) a particular DNA structure, uniquely identify me, but they most surely do not characterize me”.

Arrow and Raynaud [[6], pp. 77–78] arrive at the conclusion that a Condorcet aggregation algorithm has always to be preferred in a multi-criterion framework. On the complete opposite side one can find Saari [108‐110]. His main criticism against Condorcet based approaches are based on two arguments: (1) if one wants to preserve relationships among pairs (e.g., to impose a side constraint to protect some relationship-balanced gender for candidates in a public concourse) then it is impossible to use pair-wise voting rules, a Borda count should be used necessarily. However, it is important to note that, although desirable in some cases, to preserve a relationship among pairs implies the loss of neutrality; this is not desirable on general grounds. (2) The individual rationality property (i.e. transitivity) has necessarily to be weakened if one wishes to adopt a Condorcet based voting rule. The underlying assumption of this definition is the identification of human rationality with consistency, and this can be criticized from many points of view. Simon [118] notes that humans have at their disposal neither the facts nor the consistent structure of values nor the reasoning power needed to apply the principles of utility theory. In microeconomics, where the assumption that an economic agent is always a utility maximize is a fundamental one, it is generally admitted that this behavioural assumption has a predictive meaning and not a descriptive one (see Friedman [37] for the most forceful defence of this non-descriptive meaning of the axioms of ordinal utility theory). As firstly noted by Luce [68], a down-to-earth preference modelling should imply the use of indifference and preference thresholds; this implies exactly the loss of the transitivity property of at least the indifference relation. A corroboration of this criticism in the framework of social choice can be found in Kelsey (1986), where it is stated that because of social choice problems, an individual with multiple objectives may find it impossible to construct a transitive ordering. Recent analyses of the concept of rational agent can also be found in Bykvist [19] and Sugden [124].

Anyway a Condorcet consistent rule always presents smaller probabilities of the occurrence of a rank reversal in comparison with any Borda consistent rule. This is again a strong argument in favour of a Condorcet’s approach in this framework.

In our case, this axiom is needed since the intensity of preference of individual indicators is not considered to be useful preference information given that compensability has to be avoided and weights have to be symmetrical importance coefficients. Moreover, thanks to this axiom, a normalisation step is not needed. This reduces the sources of uncertainty and imprecise assessment.

In social choice terms then the anonymity property (i.e. equal treatment of all individual indicators) is broken. Indeed, given that full decisiveness yields to dictatorship, Arrow’s impossibility theorem forces us to make a trade-off between decisiveness (an alternative has to be chosen or a ranking has to be made) and anonymity. In our case the loss of anonymity in favour of decisiveness is even a positive property. In general, it is essential that no individual indicator weight is more than 50 % of the total weight; otherwise the aggregation procedure would become lexicographic in nature, and the indicator would become a dictator in Arrow’s term.

One should note that indeed cost-benefit analysis can be easily criticised both from the distributive and environmental points of view (see e.g., [77, 120]). However I prefer not to deal with this issue here.

On the issue of legitimacy see also Roy and Damart [107].

On this point I disagree with Kleijnen [66], who claims that “modellers should try to develop robust models”, in the sense that models should not be very sensitive to modellers’ assumptions. Some ethical positions might be very different and thus lead to different rankings of the policy options. What is essential in a social framework is then transparency on these assumptions.