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New Tools for Decision Analysts


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IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS, VOL. 36, NO. 5, SEPTEMBER 2006

New Tools for Decision Analysts
Konstantinos V. Katsikopoulos, Member, IEEE, and Barbara Fasolo
Abstract—This paper presents psychological research that can help people make better decisions. Decision analysts typically: 1) elicit outcome probabilities; 2) assess attribute weights; and 3) suggest the option with the highest overall value. Decision analysis can be challenging because of environmental and psychological issues. Fast and frugal methods such as natural frequency formats, frugal multiattribute models, and fast and frugal decision trees can address these issues. Not only are the methods fast and frugal, but they can also produce results that are surprisingly close to or even better than those obtained by more extensive analysis. Apart from raising awareness of these ?ndings among engineers, the authors also call for further research on the application of fast and frugal methods to decision analysis. Index Terms—Adaptive decision making, decision analysis, fast and frugal heuristics, fast and frugal trees, natural frequency formats.

introduced to engineers.1 Not only are the methods fast and frugal, but they can also produce results that are surprisingly close to or even better than those obtained by more extensive analysis. In addition to raising awareness of these ?ndings among engineers, we call for further research on the application of fast and frugal methods to decision analysis. The rest of the paper is organized as follows. In Section II, we review the basics of decision analysis as it is typically practiced, the environmental and psychological issues it encounters, and past remedies. In Section III, we present three fast and frugal methods: 1) natural frequency formats; 2) frugal multiattribute models; and 3) fast and frugal decision trees, and discuss how they can be integrated with classical decision analysis. Conclusions are presented in Section IV. II. D ECISION A NALYSIS : I SSUES AND R EMEDIES A. Decision Analysis In decision analysis, the quality of a decision is determined by the process by which the decision was made and not by the outcome, which in an uncertain world could be due to chance factors. Brie?y (for a complete treatment, see [3] and [4]), this process can be expressed mathematically with three equations, namely: 1) Bayes’s rule for assessing probabilities of events E in the light of data D; 2) a multiattribute value model for computing the value of a nonrisky option X described by a set of attributes ak of varying importance weights wk ; and 3) a subjective expected value function for combining probabilities that events occur—as computed in (1)—with values given that events occur—as computed in (2)—and for determining the option’s overall value. We acknowledge a simpli?cation of this formulation in that the multiattribute model is assumed to be the same in (2) and (3). If the models are in fact different, the procedure for determining the value functions vk would differ in (2) and (3) (see also [5]). P (E|D) = MAV(X) =
k

I. I NTRODUCTION HEN HELPING people make decisions, analysts “create and analyze a model that represents the decision situation” [1] by performing three steps, namely: 1) they help the decision maker assess the probabilities of all possible outcomes for each available option; 2) they help assess the weights of all attributes for each option; and 3) they help combine these judgments and then suggest the option with the highest overall value. Even if, as we assume here, all relevant options, outcomes, and attributes have been identi?ed, the three steps can be considerably challenging for decision analysts and decision makers alike in face of environmental and psychological issues. The environmental issue is that real-world problems can exhibit statistical dependencies, in which case even fast computers are unable to compute expected values exactly. The psychological issues are that laypersons as well as expert decision makers can ?nd it challenging to provide the required judgments, to understand the underlying methods, and to accept the option suggested by the analysis as being the best for them. This holds especially true in decision analysis without any consultancy about the process. The goal of this paper is to present some new methods, i.e.,: 1) natural frequency formats; 2) frugal multiattribute models; and 3) fast and frugal decision trees, which address these issues but which, to the best of our knowledge, have not been

W

P (D|E)P (E) P (D) [wk vk (X)] [P (E|D)MAV(X)] .
E

(1) (2) (3)

SEV(X) =

Manuscript received December 4, 2003; revised October 9, 2004 and April 15, 2005. This paper was recommended by Associate Editor L. Fang. K. V. Katsikopoulos is with the Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development, Berlin 14195, Germany (e-mail: katsikop@mpib-berlin.mpg.de). B. Fasolo is with the Department of Operational Research, London School of Economics, London WC2A 2AE, U.K. (e-mail: b.fasolo@lse.ac.uk). Digital Object Identi?er 10.1109/TSMCA.2006.871798

1 One of the tools we will review—natural frequency formats—is taught at business schools, and thus, some engineers might have been introduced to it. Overall, it seems dif?cult for engineers to access this research. When we searched the Web of Science for citations in engineering journals, we discovered only one citation, and the article appeared in a journal not targeted to decision analysts [2]. Additionally, we could not ?nd references to the tools we will present in the descriptions of decision analysis courses taught in leading industrial and electrical engineering departments.

1083-4427/$20.00 ? 2006 IEEE

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Decision analysis has been applied to a wide range of problems, from buying ?owers for one’s spouse on the presumed day of one’s wedding anniversary [6] to managing the coastline of a trendy Los Angeles suburb [7] and building the new international airport of Mexico City [8]. There are also numerous applications in engineering, a good selection of which are discussed in the November/December 1992 issue of the journal Interfaces, where examples include strategic planning at Dupont Corporation, evaluation of preventive maintenance programs in Southern Electric Utility Company, and more than 40 major decision analysis projects at General Motors, as well as in a more recent book by Dennis Buede on engineering the design of systems [9]. B. Issues Equations (1)–(3) assume that decision makers can make reliable assessments of probabilities, attribute weights, and values. Phillips [10] argues that decision makers have this capability when the decision analyst uses a requisite decision model, i.e., a representation of the decision situation that is just suf?cient in form and content to generate a commitment on the part of the decision maker to improve the ?nal decision. However, without this model, the judgmental components of decision analysis have been claimed to be “usually fallible and often biased” by the heuristics and biases program of Tversky, Kahneman, and their colleagues [11], [12]. Biases—53 according to the latest count [13]—can be categorized in different ways. A useful classi?cation for the purpose of this paper is according to where the biases occur in the decision process [14]. Two classes are relevant here, namely: 1) biases in evaluating preferences or values of outcomes and 2) biases in judging the probability of events. Biases that belong to the ?rst class hinder the speci?cation of options, outcomes, attributes, and weights. Examples of the ?rst class of biases include the tendency to stick to the status quo or reference point of a decision problem [15]. Another example is the framing effect, i.e., the tendency to change preference depending on how the options or attributes are framed—e.g., in terms of survival or mortality rate, as in the famous Asian disease problem [16]. Other examples include humans’ susceptibility to the range of attribute levels when assessing the weights of attributes [17] and an undue attention to irrelevant attributes [18]. Biases that belong to the second class hinder the formulation of the probabilities that are inputs to both Bayes’s rule and the subjective expected value function. Examples of the second class of biases include the anchoring bias, i.e., the tendency to estimate quantities by anchoring on salient numbers and adjusting the estimate upward or downward but insuf?ciently so [19]. Another example is the primary bias, whereby frequencies of occurrence are overestimated for rare events and underestimated for frequent events [20]. Whereas the heuristics and biases literature challenged the assumption that humans can provide sound judgmental input to (1)–(3), scholars studying decision making in real-world stressful situations [21], [22] raised another psychological issue. When a decision needs to be made quickly under considerable pressure, decision makers are sometimes unable to provide the

judgments required by (1)–(3). These situations differ from those in which the decision maker can take the time to consult an analyst (for which procedures have been developed to make reliable subjective judgments [23]). For example, Klein and Calderwood [24] found that urban ?reground commanders reported being unable to come up with the relevant probabilities and utilities. To date, three volumes [25]–[27] have been assembled that contain similar ?ndings from a variety of domains. Finally, the environment in which decision making takes place introduces an issue with (1) and by extension (3); despite considerable advances in Bayesian networks, applying Bayes’s rule is computationally intractable when events are not independent [28]. C. Remedies These issues can make the application of decision analysis challenging. A common remedy has been to introduce debiasing methods for correcting the probabilities, weights, and utilities elicited. For a comprehensive review of debiasing, we refer to Larrick [29]. In a historical review of the major sources of biases and the methods that can be used to eliminate them, Fischhoff and colleagues [30], [31] found that the most successful debiasing methods did not involve retraining the decision maker, but rather restructuring the task, so that there is a match or ?t between the decision maker’s processes and the task; see also Arkes’ work [32]. This view is consistent with the thesis that human decision making is adapted to the environment—a view that dates back to Simon [33] and Brunswik [34]—and that good decisions follow when the decision process ?ts the environment. Payne et al. [35] were among the ?rst to show that people use different cognitive processes depending on a host of factors, such as available time, number, and correlation between attributes, and to discuss the meaning of these ?ndings for decision analysis. Since this work, a large amount of evidence has accumulated for the claim that people make decisions adaptively. A novel outlook on adaptive behavior and cognition (ABC) has recently emerged from a group researching fast and frugal heuristics [36]. Their ?ndings have important implications for decision analysis, but they seem to be little known to engineers; note that the fast-and-frugal-heuristics program is distinct from the heuristics-and-biases program, which is often discussed in the engineering literature. In the next section, we present some of this research and discuss conditions under which its application to decision analysis appears fruitful. III. N EW T OOLS FOR D ECISION A NALYSTS We present three methods that address the psychological and environmental issues in the application of decision analysis. 1) Formats that use natural frequencies instead of singleevent probabilities can, under some conditions, be used to make the task of probabilistic elicitation underlying (1) ?t better with the way humans make judgments. 2) Frugal multiattribute models that integrate a portion of all attributes can, under some conditions, approximate very

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IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS, VOL. 36, NO. 5, SEPTEMBER 2006

closely the full multiattribute value function of (2), but with less effort. 3) Fast and frugal decision trees that allow for quick, transparent, and accurate decisions can be used instead of the subjective expected value function of (3) when its computation is intractable or the required inputs cannot be obtained. A. Natural Frequency Formats The most frequent interpretation of probability among engineers is that of “a long-run frequency associated with a set of events that have been or could be repeated many times, e.g., ?ipping coins and removing production samples from a production line” [9, p. 374]. Yet when the data available are scarce, as in one-time decisions, and there is a great deal of uncertainty, as in early systems design decisions, the only feasible interpretation of probability becomes subjective, in terms of degrees of belief [37]. In Buede’s words [9, p. 374], “it is often not possible to contemplate repeating experiments to develop long-run frequencies within a reasonable amount of time and money.” We acknowledge the coexistence of both relative frequency and subjective views of probabilities in engineering, but we concentrate here on cases where data are available; see [23] for cases where probability estimation is subjective. Data may exist when the decision is, for example, about whether to make a test; in engineering, there is often a reliability record for tests of machines. In these cases, representation of probabilities in terms of natural frequencies helps to overcome some welldocumented problems of probability assessment for both experts and nonexperts [38]. Dif?culties in assessing probabilities correctly appear in important expert domains such as the use of DNA evidence in court [39] or the prediction of a prisoner’s future violent acts [40]. Gigerenzer [41] pointed out that these problems often have as a common source the dif?culty of reasoning about single events. Consider, for example, the cataract problem of Hammond et al. [42, p. 136]. A patient, Rob, has lost the vision in his left eye due to a cataract, and the vision in his right eye has deteriorated. To recommend surgery or not, the decision analyst needs to ask an expert for an assessment of the probability that Rob will have successful surgery. In classical decision analysis, the doctor is asked: “What is the probability that Rob will have successful cataract surgery?” The required probability is one that refers to the single event “Rob has successful surgery.” The problem with single events is that they leave the reference class, i.e., the set of objects—here patients—to which the probability refers unspeci?ed [43]. The concept of reference classes has been mentioned by decision analysts [44, pp. 108 and 143], but we could not ?nd clear instructions on how to specify a reference class. The importance of specifying the reference class in Rob’s example is exempli?ed by the results of an Internet search: One medical clinic Web site expresses the probability of successful cataract surgery in the following terms: “A signi?cant improvement in sight can be achieved with over 90% of all patients” (http://www.augentagesklinik.com/en/informationen/

graustar.html). Another Web site reports that “the patient has a .98 probability that (he or she) will attain 20/40 legal driving vision or better if there are no other preexisting conditions such as hardening of the arteries of the retina, macular degeneration, old stroke to the eye, glaucoma damage, corneal dystrophy, etc.” (http://www.informedconsent.org/cataract.html). Behind the two different probability assessments lurk different reference classes—all patients versus patients with no preexisting conditions. The reference class is often not given. An example is weather forecasting where the public is often informed that, say, “There is a probability of 30% of rain tomorrow.” It was recently found [45] that people do not have a coherent understanding of this statement. Perhaps more worryingly, only one-third of lay people in the streets of ?ve major cities in Europe and the U.S. found the interpretation “It will rain in 30 out of 100 days like tomorrow” as the most appropriate, when this statement is the one the U.S. weather forecasting agency intends to communicate. An alternative way of representing the probability of successful cataract surgery is by means of a natural frequency format: “90 out of 100 men like Rob have successful cataract surgery.” Here, a class of events is introduced instead of a single event, namely, the class of men like Rob—men with the same values as Rob on characteristics like age, overall health, and so on—who have successful surgery. Thus, the reference class is speci?ed. We propose that the decision analyst ask the doctor: “Out of 100 men like Rob, how many have successful cataract surgery?” and, of course, also clarify what is meant by the phrase “like Rob.” It is important to note the difference between natural frequencies and relative frequencies. In natural frequencies, information is acquired sequentially by updating event frequencies, but without arti?cially ?xing the marginal frequencies (for example, of successful and unsuccessful surgeries); on the other hand, relative frequencies are normalized. For more details, see [46], [47], and the references therein. It has been found that natural frequencies greatly improve the accuracy of Bayesian reasoning, more so than relative frequencies and probabilities [47]. These results have been observed in a variety of domains, including medicine and law. It has also been argued that natural frequencies are perceived as being clearer than single-event probabilities [48]. The main intuition for the facilitating effect of natural frequencies is that different ways of representing information are mathematically equivalent but not necessarily psychologically equivalent. The natural frequency format appears to correspond better with how decision makers process information, possibly because frequencies abound in nature and minds have adapted to them or because of computational simpli?cation [41], [49]. Natural frequency formats have been found to improve the understanding of lay people as well [47], [50]–[52]. Contrary to the grim results of the heuristics and biases literature [12] showing that experts and lay people alike are hopelessly confused by Bayes’s rule in a probabilistic form as in (1), natural frequencies have been shown to improve Bayesian reasoning. In sum, when there are plentiful data available on the event for which probability is to be assessed, natural frequency

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formats have considerable advantages in representing uncertainty. Although the effects of natural frequency formats are very dramatic and have even been claimed to be stronger than those of traditional debiasing methods [52], [53] we do not suggest that probabilistic information should always be represented in frequency formats. Such a suggestion would be exactly contrary to the central premise of our thesis. We view the decision analyst as having available a wide range of tools for improving the decision process and choosing the tool that best ?ts the particular task and the decision maker with whom the analyst is working. For example, we acknowledge that probabilistic information in some decision tasks is tied to a single event. Howard [54] mentions the ?rst launching of a missile. In the eye disease example previously discussed, the disease might be rare and there might be too few people “like Rob.” In all these cases, it may not be possible to use natural frequency formats, and traditional decision analytic techniques, like spinner wheels and reference wagers [24, p. 19], may be more appropriate. B. Frugal Multiattribute Models Classical decision analysis requires that all attributes are scored and weighted for all options. In complex real-world problems, exhaustive scoring and weighting can be exhausting for decision makers and analysts and more so as the number of options and attributes increases. If speed is important, as when mission-critical systems such as airline reservation systems fail, a more “frugal” multiattribute model might be valuable. Here, we review conditions under which the overall value of an option can be assessed on the basis of less than full information without greatly sacri?cing accuracy. Results from computer simulations [55] indicated that the number of attributes that need to be weighted and aggregated to choose an option that has at least 90% of the highest overall multiattribute value decreases to one or two when one of the following two conditions holds: 1) the scores of the attributes are positively related; or 2) the decision maker assigns unequal weights to all attributes. The second condition might be common in engineering. Buede [9, p. 366] notes that “no application of the authors (out of over a hundred) has generated a set of objectives that were nearly equal in importance.” Thus, while frugal multiattribute models have not yet been applied in a real decision situation, this work suggests that there are alternatives to time-consuming weight elicitation techniques. In the simulations, rank ordered centroid (ROC) attribute weights were used [9, p. 368], [56]. The ROC weighting procedure has been suggested as a more effort-saving procedure for eliciting weights than the traditional SMART swing weighting procedure [57]. As in SMART, weights for the attributes are based on comparisons of differences in attribute values. The question asked is how the swing from worst to best on one attribute scale compares to the same swing on another attribute scale. The difference with SMART is that, to generate ROC weights, the swings are ranked instead of rated. Ranking makes the ROC procedure psychologically plausible. Previous

research indicates that ROC weights produce the same preferences over options as a full multiattribute model in nearly 85% of cases and that, when the ROC procedure does not produce the same choice, the average loss is fairly small [57]. ROC weights also predict choices that are highly correlated with actual choices made [58]. ROC weights are derived from the ranks by a simple formula. Given n attributes with ranks from 1 (most important) to n (least important), the ROC weights w1 , . . . , wn are provided by the following: (1) i ,

wk =

i≥k

n

k = 1, . . . , n.

(4)

For example, the ROC weights for n = 2 are w1 = 0.75 for the most important attribute and w2 = 0.25 for the least important attribute. For three attributes, w1 = 0.61, w2 = 0.28, and w3 = 0.11. Note that w1 > w2 + w3 ; i.e., in a sense, the most important attribute is more important than the two other attributes combined. Calculating the weights for n = 4 yields w1 > w2 + w3 + w4 and w2 > w3 + w4 . That is, when the decision maker is interested in less than ?ve attributes, the ROC weight of any given attribute is larger than the sum of the ROC weights of the less important attributes. In psychological jargon, ROC weights are noncompensatory for less than ?ve attributes; the weight of the ?rst attribute cannot be compensated for by any combination of weights of the remaining attributes. Noncompensatory weights are important because they imply that the full multiattribute value model of (2) can be substituted by a much simpler lexicographic model when attributes are binary.2 The lexicographic model considers attributes sequentially in decreasing order of importance weight and, thus, bases its decision on only one attribute. If there are just two options, the model identi?es the ?rst attribute that has unequal values on the two options and then chooses the option with the value of unity in this attribute. For more than two options, the model is generalized as follows: Consider attributes in order of decreasing importance. Ignore any attributes on which all options have the same value. If there is only one option with a value of unity on the most important attribute, choose it. If there is more than one option with a value of unity on the most important attribute, eliminate all options that have a value of zero on that attribute. Consider the second most important attribute. As before, choose the option that has the value of unity on that attribute if all other options have a value of zero. Otherwise, eliminate the options with a value of zero and proceed to the next attribute. Stop when there is only one option left and choose that option. If more than one option is left, choose one option randomly.
2 Although the assumption of binary attributes might appear as an oversimpli?cation, decision makers often dichotomize information: When choosing an apartment, one might be solely interested in whether it is located in the downtown area or not. Furthermore, attributes are naturally binary in some decision problems, too: a patient either will or will not survive an operation. When we present fast and frugal trees, we discuss other binary attributes in a real-world medical example.

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This model has also been recently studied by Hogarth and his colleagues [59], [60]. Note that the elimination component is critical; without it, the decision maker would need to guess much more often. This is because the attributes are binary. Note also that this model is similar to the elimination-by-aspects model, an alternative noncompensatory model proposed by Tversky [61]. Martignon and Hoffrage [62, Th. 3] formally showed that, for two options, the lexicographic model makes the same predictions as a linear model with noncompensatory weights. We show this for more than two options. Result: The general lexicographic model makes the same predictions as a linear model with noncompensatory weights. Proof: Let o1 , o2 , . . . , om be the options, a1 , a2 , . . . , an be the attributes in order of decreasing importance, and vik be the value of option oi on attribute ak . Let oi? be the option that the lexicographic model chooses. We assume that oi? is not chosen by guessing, in which case it will be obvious how the argument can be adapted. Consider also an arbitrary but ?xed option oi with i = i? . It suf?ces to show that if wk ≥ i≥k wi for all attributes ak , then k (wk vi? k ) ≥ k (wk vik ). Let the last attribute considered by the lexicographic model be ak? . There exists k(i) ≤ k ? such that option oi is eliminated when ak(i) is considered. This implies vi? k(i) = 1 and vik(i) = 0, and, for k < k(i), vi? k ≥ vik . Combining these two statements leads to [ k≤k(i) (wk vi? k )]?[ k≤k(i) (wk vik )] ≥ wk(i) . Also, [ k>k(i) (wk vi? k )]?[ k>k(i) (wk vik )]≤ ?( k>k(i) wk ). The result follows from wk(i) ≥ k≥k(i) wk . To summarize, multiattribute models need not be exhaustive. A decision can be made on the basis of two attributes when there are positive correlations, or when the decision maker does not care equally about all attributes but can still rank attributes in order of importance. Furthermore, when there are less than ?ve binary attributes and ROC weights are used, the decision can be made on the basis of the most important attribute only. The frugal model has a number of advantages over the traditional multiattribute model. First, having to elicit less information, it might plausibly enhance the quality of information elicited due to decreased fatigue and increased attention. Second, the frugal model might be more requisite. A decision model is requisite—rather than prescriptive or normative—when it allows to “compare, at any stage in the aggregation, the current results with the holistic intuitive judgments of the decision maker(s)” [10]. In other words, the goal of the model is not to prescribe what the decision maker should do but, after the decision analyst leaves the decision maker on their own, to generate intuitions about how the model would suggest different decisions if the situation changed. In the ?eld, a requisite approach to decision analysis has been found to enhance decision processes and to increase commitment to action. For applications of requisite models, see [63] and [64]. Some of the aforementioned results rely on the assumption of binary attributes. Future research needs to investigate when it is appropriate for a decision analyst to dichotomize attributes that are not naturally binary, as well as whether decision makers prefer to work with binary attributes. In data analysis, there is evidence that dichotomizing continuous variables by means of median splits, or any other split, can have negative

consequences because it reduces the variance of the predictors, thus reducing the effect size and statistical power of the analysis [65], [66]. Research, however, still needs to determine the effect of dichotomization when binary attributes are used in decision analysis. It is possible, although not yet formally explored, that too many attribute levels can lead to over?tting, a problem that dichotomization can avoid. It is also important to investigate when decision makers can tolerate losing 10% of the overall maximum value obtainable. Overall, the advantages are to be gauged against the disadvantages. C. Fast and Frugal Decision Trees Fast and frugal decision trees are the third relevant ?nding of the ABC group. This tool would be useful in those cases when the computations required by the subjective expected value function of (3) are intractable or the needed inputs (outcome probabilities, attribute weights) cannot be obtained. We introduce fast and frugal trees by way of example. Consider the following medical decision: Should antibiotic treatment involving macrolides be prescribed to a young child suffering from community-acquired pneumonia? What makes this decision crucial is that the pathogens underlying this illness are often resistant to macrolides [67]. Children are fragile creatures, and pediatricians have a lot of responsibility. Making the decision of prescribing strong antibiotic medication to children is far more delicate than prescribing the same to most adults. Only after classifying children’s pneumonia as a microstreptococal infection are doctors inclined to give macrolides. Additionally, whereas not as temporally critical as other medical decisions, the macrolide decision needs to be made quickly: Pneumonia spreads rapidly among children and can lead to more serious problems, even death. Classical decision analysis has been applied to the medical domain, and many practitioners are exposed to the basics of the approach. On the other hand, the doctors themselves have recently started to discuss the limitations of the approach [67]–[70]. The efforts of conscientious decision analysts notwithstanding, doctors still often feel at a loss when having to apply decision analysis on the spot, especially in situations with high stakes. Doctors prefer to use simple rules that are easy to communicate to the patients and easy to apply, rather than to consult tables or other computational aids. For these reasons, Fischer et al. [67] did not take a classical decision analysis approach attempting to identify and integrate variables like probability and costs of pathogen resistance. They simply assumed that two pieces of information, cues in psychological jargon, are known for each child. The ?rst cue is whether the child is older than 3 years or not, and the second cue is whether the child has had fever for more than 2 days or not.3 These cues were used because doctors are virtually guaranteed access to them and because they are very easy to process. Of course, one can imagine that pediatricians have easy access to other cues such as, for example, the occurrence of microstreptococal infection in the past. However, as we will
3 We are not aware of why these particular cutoffs to dichotomize the cues were used.

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Fig. 1. Fast and frugal tree of Fischer et al. [67] for macrolide prescription.

see below, the age and fever duration cues suf?ce for greatly alleviating the problem of macrolide overprescription. The next question is how to combine the cues. Recall that the primary goal is to guard against prescribing macrolides to healthy children. Thus, the cues can be combined, so that macrolides are prescribed only when both cues suggest that the child is sick. A simple heuristic rule that implements this idea is the following: Prescribe macrolides only if the child is older than three years and the child has had fever for more than two days. How successful is this fast and frugal tree? Its structure is transparent, and it does not suffer from lack of acceptance. In fact, because pediatricians know the variables included well, they can learn its structure and teach others quickly. Transparency, however, is not the only criterion of performance: Time, money, and accuracy also matter when resources are limited. Because the tree uses only two cues, it saves time and costs, but how accurate is it? When the tree was evaluated and double-checked on real data, it classi?ed 72% of those children who actually were at high risk as having a high risk of microstreptococal pneumonia infection, whereas a scoring system based on logistic regression identi?ed 75% of them [67]. In addition, the tree would curtail the prescription of macrolides by 68% and the scoring system by 75%. This tree does not require the evaluation and combination of all possible outcomes for the options of prescribing or not prescribing macrolides. It only uses readily available cues about each child. The cues can be inspected in a simple sequential fashion. First, it can be asked whether the child is more than three years old. If the answer is “no,” then it can be immediately concluded that macrolides should not be prescribed. If the answer is “yes,” whether the child has had fever for more than three days will determine whether macrolides should be prescribed or not. That is, the macrolide heuristic can be visually represented as a tree (Fig. 1). Note that a tree in which the cues were inspected in the reverse order would make exactly the same classi?cations. A reason for looking up the age cue ?rst is that it is quicker and easier to assess without error. This tree is called a fast and frugal decision tree. It is frugal because it uses only one or two cues, and it is also fast because it processes each cue by just asking and answering one question. Fast and frugal trees were introduced by Martignon et al. [71]; this paper also describes how one can construct fast and frugal

trees. Informally, a fast and frugal tree is a classi?cation tree [72] where it is possible to make a decision after each question asked. Fast and frugal trees can also be thought of as representing the “recommended strategy” by classic decision trees [3]. Fast and frugal trees tend to be simpler than traditional decision trees [71], [73], but a number of fast and frugal tree structures are possible as the number of cues increases. In another medical application, Green and Mehr [69] proposed fast and frugal trees for deciding whether to admit patients suspected of ischemic heart disease to the emergency care unit or not. Using real data, this tree outperformed logistic regression; see [71] for a discussion of the statistical reasons for this. A complete theory of fast and frugal trees is not yet available, but their formal properties have been studied to some extent [73]. Overall, there are good mathematical reasons why those trees are, under some conditions, accurate, robust, and stable. For example, they are robust and stable because they do not attempt to model in detail the interdependencies between cues. Because they are frugal, they might—like frugal multiattribute models—plausibly enhance the quality of information elicited through decreased fatigue and increased attention, and they might be more requisite. Additionally, there is preliminary empirical evidence that people are able to apply, memorize, and reapply fast and frugal trees [74]. Future research needs to discover the boundary conditions under which fast and frugal trees lead to accurate decisions and how easily fast and frugal trees are learned and applied in different tasks. D. Fast and Frugal Tools and Decision Analysis: Synergy, Not Competition Fast and frugal tools are not meant to replace the classic approach to decision analysis. The three kinds of tools we presented are rather interventions to be used within the approach when psychological and environmental reasons call for their application: 1) natural frequency formats can remove the ambiguity of reference classes in single-event probabilities and improve the accuracy of Bayesian reasoning; 2) frugal multiattribute models can be used to decrease the burden of weight and value elicitation without much loss of value; and 3) fast and frugal trees can be used when the computation of subjective expected value is impossible or obscure to the decision makers, again with not much loss—or even with an increase—of accuracy. Natural frequency formats are not needed when probabilities can be assessed reliably and are not appropriate when there are not enough data to create a meaningful reference class. In addition, when fatigue is not an issue, it is not advisable to settle for possibly losing some value by using frugal multiattribute models. Finally, there is no reason to use fast and frugal trees when subjective expected values can be calculated and decision makers understand them. The theory of fast and frugal heuristics has grown from an adaptive approach to human psychology. We cannot overemphasize that when fast and frugal heuristics are viewed as engineering tools, their application should also be adapted to the problem at hand.

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IV. C ONCLUSION The goal of this work was to make engineers aware of a novel and promising area of psychological research. We presented three fast and frugal methods, namely: 1) natural frequency formats; 2) frugal multiattribute models; and 3) fast and frugal decision trees, which have the potential to address some of the psychological and environmental issues that make classical decision analysis challenging. These methods can be added to the toolbox of engineering analysts. While we attempted to sketch the boundaries within which the tools can be applied, more research is needed to re?ne these boundaries for decision analysis as applied to engineering. This paper suggests some lines of future research and hopes to encourage academics and practitioners to join this enterprise. ACKNOWLEDGMENT The authors thank G. Gigerenzer, Y. Hanoch, G. McClelland, A. Morton, L. Phillips, D. Weiss, an anonymous reviewer, and several members of the ABC group for helpful comments and suggestions. R EFERENCES
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Konstantinos V. Katsikopoulos (M’00) was born in Athens, Greece, in 1970. He received the B.Sc. degree in mathematics and the M.Phil. degree in operations research and informatics from the University of Athens, in 1992 and 1994, respectively, and the Ph.D. degree in industrial engineering from the University of Massachusetts, Amherst, in 1999. He was a Visiting Assistant Professor at the Naval Postgraduate School, Monterey, CA. He is currently a Research Scientist at the Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development, Berlin, Germany. His research interests include descriptive models of human performance, especially decision making, and their relation to normative models. Dr. Katsikopoulos is an Associate Editor of the IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS.

Barbara Fasolo was born in Varese, Italy, in 1971. She received the B.Sc. degree in economics from Bocconi University, Milan, Italy, in 1995, the M.Sc. degree in decision sciences from the London School of Economics, London, U.K., in 1997, and the Ph.D. degree in psychology from the University of Colorado, Boulder, in 2002. After receiving her B.Sc. degree, she joined the Center for Research on Internationalization Processes, Bocconi University, where she became interested in the psychological aspects of decision making. She spent two years as a Postdoctoral Researcher at the Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development, Berlin. She is currently a Lecturer in decision sciences at the Department of Operational Research, London School of Economics. Her research interests are at the intersection of behavioral and prescriptive decision making.


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