# Comparing Actions and Modeling Consequences

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

## Summary

Constructing any of the systems of preference relations on A requires a model of the information that affects the formation, justification, and evolution of an actor’s preferences. This information is rarely available in a well-structured, quantified, or organized form, and what the analyst can use is often subject to imprecision, uncertainty, and inaccurate determination. In this chapter, we propose a methodology for approaching this phase of the modeling effort.

In Section 8.1.1, we define the term “consequence of an action” (Def. 8.1.1) to denote the various elements (effects, attributes, aspects,…) that can interact with the objectives or value system of an actor and affect how she builds, justifies, or transforms her preferences. Our methodology is designed to analyze and distinguish the various consequences according to their quantitative and qualitative influences on the comparison of actions. Before the modeling effort begins, these consequences are ill-defined and possess fuzzy boundaries. They stem from complex and highly interwoven entities. At this stage, we refer to the consequence cloud.

In Section 8.1.2, we show the breadth and general nature of the approach used to isolate and define what we call elementary consequences (Def. 8.1.2) and offer concrete examples and practical illustr ations. An elementary consequence usually points out the existence of an underlying dimension that reflects a preference shared among the different actors. This leads to the two basic concepts of Section 8.1.3: a preference scale (Def. 8.1.3) and a preference dimension (Def. 8.1.4). We present various examples and illustrations of these definitions in Section 8.1.3.2.

For a dimension to be operational, one must be able to map the impacts of a potential action on this dimension into a state or group of states with the help of some procedure. The procedure could be an empirical rule, a mathematical formula, a survey technique, or an experiment. This idea is the subject of Section 8.1.4 and leads to the concept of a state indicator (Def. 8.1.5) and the distinction between point and nonpoint state indicators. We end Section 8.1.4 with a discussion of the set of dimensions, which we call the consequence spectrum (Def. 8.1.6), that is used to describe the consequence cloud. Section 8.1.5 illustrates this first aspect of the methodology concerned with evaluating actions in the continuation of Examples 3, 5, and 6.

In Section 8.2.1, we discuss the deficiencies of using only point state indicators. These deficiencies are related to a lack of knowledge about the consequences of actions. The concept of a dispersion index is introduced to help model complementary information that can help portray the imprecision, uncertainty, and inaccurate determination associated with the consequences.

We introduce and illustrate the concept of dispersion thresholds in Section 8.2.2. We explain the difference between a nonpoint state indicator and a point state indicator with a threshold and define positive and negative dispersion thresholds associated with a point state indicator. We finish Section 8.2.2 by discussing the important difference between intrinsic and nonintrinsic dispersion thresholds.

The dispersion indicator that represents thresholds is in fact a special case of a category of dispersion indicators that we call modulation indicators. In Section 8.2.3, we illustrate four types of modulation indicators and provide a general definition (Def. 8.2.1).

Section 8.2.4 is devoted to a more general form of dispersion indicator: the referenced dispersion indicator.

We end the chapter with Section 8.2.5, where we summarize the importance of the different components of the evaluation model Г(A). We also summarize the principles that should guide determination of such a model for any problem.

## Keywords

State Indicator Elementary Consequence Preference Scale Point Indicator Consequence Cloud
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