Coherent Criterion Family and Decision Aiding in the Description Problematic

  • Bernard Roy
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 12)


The model Г(a) presented in Section 8.2.5 does not generally allow the comparison of two actions. Therefore, we use the techniques presented in Chapter 9 to synthesize Г(a) into a criterion family F. In Section 10.1 we show that for both theoretical and practical reasons there are no set rules for automatically deducing F from Г(A). However, the analyst must respect some logical requirements, which then lead to the definitions of exhaustiveness, cohesiveness, and nonredundancy that characterize the concept of a coherent criterion family.

In Section 10.2, we introduce the performance tableau which indicates the performance level for each criterion member gj of a coherent family F for each action a in a subset A′ of A. Indifference and preference thresholds associated with the criteria can also be included in the tableau. In a description problematic, the performance tableau usually represents the final product of the study. We highlight the types of fruitful discussions these tableaus can engender and caution against their common misuses.

In Section 10.3 we discuss several forms of dependence among criteria and place them in two main categories. We also discuss these types of dependence in the context of the two major approaches to preference modeling. Section 10.3.1 presents these descriptive and constructive approaches. The former is based on the existence of a rational decision maker with a coherent and stable SPR that is to be described as reliably as possible. The latter pays special attention to the conflicting and unstable nature of preference judgments and emphasizes the importance of significance axes for facilitating discussion of these preferences and constructing one or several SPR’s. In Section 10.3.2 we show how the components of the criterion supports — the state indicators, dispersion indicators, and factors used to define them — can cause dependence among criteria and emphasize the often contingent nature of the set A. Although in a descriptive approach this form of dependence will lead to a desire to reduce the number of criteria, it is not considered a weakness in a constructive approach. We turn our attention in Section 10.3.3 to dependence stemming from value systems. Such dependence can be characterized by the fact that one cannot reason on the basis “all other things considered equal.” One type of this dependence is related to the very notion of a criterion, which implies a certain ability to consider the criterion in isolation from others in the family F and gives meaning to the idea of preferences restricted to a significance axis of the criterion. Such a dependence, called utility dependence, is extremely troublesome in a descriptive approach. In a constructive approach, utility dependence is considered to be the sign of a missing criterion. We then introduce a second way of reasoning based on “all other things being equal” for a subfamily J of F. This “preference independence” of J in F allows the possibility of replacing the multiple criteria of J by a single criterion.

In Section 10.4, we contrast multicriteria and single criterion analysis. Multicriteria analysis is based on value systems that make explicit a family F of n (n > 1) unanimous, clear, and exhaustive criteria. Single criterion analysis avoids such explicitness by amalgamating, often prematurely, two types of information — information related to the consequences of actions and intercriteria information that is strongly influenced by the actors’ value systems. To finish, we discuss the notions of dominance, substitution rate, concordance, discordance, and veto in the context of interpreting performance tableaus in δ-problematics.


Constructive Approach Significance Axis Single Criterion Descriptive Approach Multicriteria Analysis 
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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Bernard Roy
    • 1
  1. 1.LAMSADEUniversité Paris-DauphineFrance

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