Multi-Attribute Decision Making Research Paper

1. Prescriptive Decision Theory

The most broadly accepted prescriptive decision theory is Multi-attribute Utility Theory (MUT). It builds on utility theory from economics, statistics, and operations research. Differences between observed decision making and the prescriptions of MUT suggest specific opportunities to make better decisions. The arguments that MUT requires too much information and is too difficult to understand emphasize the need to derive operational methods from theory to reduce information requirements and ease application.

1.1 Multi-Attribute Utility Theory

A multi-attribute problem can be described as a matrix in which rows are alternatives, columns are attributes, and each cell is a measure of the effect of an alternative with respect to an attribute. To illustrate, the decision might be to choose among three sites (A, B, and C) for a landfill by considering four attributes: costs to the local government in dollars, number of persons displaced, index of groundwater contamination, and capacity of site in cubic meters. Each of the three sites is described in terms of these measures. The problem is then to choose the best alternative, based on the attributes. Hill (1968) and Litchfield et al. (1975) are classic descriptions of such matrices for use in planning. Attributes should be chosen so as to be independent of each other in value terms, meaning that the value of a level on one attribute does not depend on the level of another attribute. Carefully designed questions can, however, elicit valid value judgments under certain types of attribute interdependence (Keeney and Raiffa 1976).

Choosing an alternative requires two types of judgments from the decision maker: transformations of effects into value measures, and transformations of value measures for each attribute into a common value measure across all attributes. The theory behind such judgments is most thoroughly developed in Keeney and Raiffa (1976).

The value-scale transformation recognizes that measures of effects are not the same as measures of value. The unit of value can be set arbitrarily, often by setting the difference between the lowest level of an effect and the highest level of that effect equal to a value of 1.0 unit. This unit of value is valid for the entire range of the effect only if the value transformation is linear (a constant rate of change in value with change in effect). For example, a decision maker might judge that an increase in the groundwater contamination index yields a constant decrease in value regardless of the level of contamination. More likely, a decision maker would decide that when the index gets very high, there is little further change in value because the groundwater is already so contaminated that it makes little difference. In this latter case the transformation is nonlinear, and the decision maker must estimate a function that describes the rate of change in value with respect to the rate of change in the index for each level of the index. In practice, such functions are estimated from a sample of levels of the index and extrapolated for other levels. Other methods for such judgments are described below.

To choose the best alternative, considering all attributes, the units of value for each attribute must be transformed to a common unit of value. Although a decision maker might try to judge each attribute directly in the same unit of value, this is extremely difficult to do and is confounded by the usual case in which the value transformation is nonlinear. Instead, decision makers are asked to assess weights that transform the units of value judged for each attribute into a common unit.

Multi-attribute utility theory is consistent with utility theory incorporating uncertainty. Thus value transformations can be used in conjunction with subjective expected utilities to consider uncertain outcomes with respect to alternatives. For a textbook treatment of decision analysis in these terms see Kirkwood (1997). Value scales can be estimated so as to take into account variation among decision makers in relative aversion to taking risks on outcomes.

1.2 Prescriptive Theory And Behavioral Theory

Over the past 20 years, research in psychology, most prominently by Kahneman and Tversky (e.g., Kahneman et al. 1982), has identified several biases in the way people make decisions. Biases are distortions from what a decision maker would want to have chosen after fully reflecting on the character of the bias in a particular situation, but the biases persist even for people who are well aware of them as general behaviors. These biases are very predictable in form and direction of error, though not in precise quantity. Recognizing these biases allows decision makers to follow routines that are likely to counter them (von Winterfeldt and Edwards 1986). For example, estimates expressed numerically tend toward previously considered numbers (called ‘anchoring and adjustment’). A counter to this bias would be to have the decision maker estimate value tradeoffs more than once and ask the tradeoff questions in different sequences each time.

1.3 Contending Approaches

Other approaches to multi-attribute decision making are based on fundamentally different theories (Lai and Hopkins 1989). The most salient current contender is the Analytic Hierarchy Process (AHP). The Analytic Hierarchy Process (AHP), developed by Saaty (1980), uses pairwise comparison questions to elicit a matrix of judgments of the relative preference between each pair of alternatives with respect to each attribute, and a matrix of judgments of the relative importance of each pair of attributes. For each matrix, the eigenvector associated with the maximum eigenvalue is the set of value scores for alternatives or the set of weights for the attributes. These two types of matrices correspond to the transformation of effects into value scales and to the transformation of value scales to a common unit. Saaty’s explanation of an underlying theory of judgment for AHP is rejected by those working in the MUT tradition (Dyer 1990) and defended by advocates of AHP (Harker and Vargas 1990). The debate centers on the meaning of weights in AHP and some implications of these meanings: the possibility of rank reversals among previously included alternatives in AHP when additional alternatives are considered, and the problem of assessing weights based on vague notions of importance without regard to units of measure of effects or units of value.

Applications of AHP continue to appear in the planning literature. One of the attractions of AHP is that the judgments required seem to be easier to make, but this occurs, at least in part, because the difficulties of nonlinear value transformations, interdependent attributes, and careful consistency among measurement units are submerged and ignored. One of the major dilemmas in multi-attribute decision making is finding techniques that people will use but that do not submerge the actuality of hard tradeoff questions.

2. Methods In Use

Fully developed applications of MUT that justify value functions and weights and include uncertainty and sensitivity analysis seldom occur in urban planning. Kirkwood (1997) gives examples of applications in related fields. Most applications in planning make the simplifying assumptions of linear value functions and independent attributes, but without justifying them. Making these assumptions results in ‘rating and weighting,’ in which a unit of value for each attribute and weights for each attribute are sufficient to arrive at aggregate values measured in a common unit.

Complete estimation of value functions and weights for MUT or AHP is a daunting task. In most decision situations, however, good choices can be made without estimating the value functions and weights. Instead estimates can be made of only those aspects of these functions necessary to distinguish among available alternatives. ‘Computation of Equivalent Alternatives’ (CEA) (Stokey and Zeckhauser 1978), which is also called ‘even swaps’ (Hammond et al. 1999) takes advantage of this idea.

Starting from a multi-attribute matrix of alternatives, CEA focuses on making a small number of tradeoff judgments just sufficient to discover an alternative that dominates all others. The approach has the distinct advantages of requiring significantly fewer hard tradeoff judgments, while at the same time keeping the concrete performance measures salient and allowing for valid value transformations, even when attributes are nonlinear with respect to value and attributes are interdependent. The CEA procedure is a sequence of judgments that creates hypothetical alternatives that are equivalent in value to available real alternatives but have different combinations of levels on attributes.

For example, consider an instance in which alternative A is preferred to alternative B on the cost attribute but not preferred on the groundwater contamination attribute. Ask the decision maker to imagine a hypothetical alternative that is equivalent in value to alternative A, but has a cost equal to the cost of alternative B. For the hypothetical alternative to be equivalent in value to alternative A while increasing the cost, the contamination index of alternative A must be improved by an amount judged by the decision maker. If this improvement in the contamination index is less than the difference in contamination index between alternatives A and B, then B is preferred to the hypothetical alternative because they have equal costs, and B is preferred on ground water contamination. And, because the hypothetical alternative was created as equivalent in value to A, B is also preferred to A. This procedure can be repeated to discover preferred alternatives among many alternatives with many attributes, but without specifying complete value transformation functions or weights. The judgments are always made for specific combinations of levels of attributes so they do not assume linear value transformations or independence of attributes. Lee and Hopkins (1995) suggest tools to reduce the number of judgments necessary in applying CEA.

3. Problems And Future Work

The dilemma for multi-attribute decision making is how to devise methods that are easy enough to use to achieve common use in practice without creating methods that hide the choices rather than help decision makers face choices. Future research will focus on efficient techniques for framing such judgments for decision makers so as to ensure validity, require as small a number of judgments as possible, counter persistent biases, and give decision makers confidence that they understand what they are doing as they use the techniques.

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