The Effectiveness of Partial Information about Attribute Weights for Ranking Alternatives in Multiattribute Decision Making

Weighted additive evaluation functions are widely used to rank alternatives in decision making under certainty with multiple evaluation attributes. Some researchers have suggested that approximate attribute weights may be adequate to accurately rank alternatives. Use of approximate weights would simplify decision analysis since detailed elicitation of weights can be time consuming and controversial. This article investigates the degree to which partial information about the relative magnitudes of attribute weights is sufficient to rank alternatives as a function of the number of decision alternatives, the number of attributes, and the number of allowed levels for each attribute. A simulation analysis, as well as a reanalysis of an actual application, shows that partial information about weights is often not sufficient to determine the most preferred alternative for realistic decision problems. Hence, approximation procedures for specifying weights may lead to errors. However, our work also shows that a simple analysis procedure can be used to accurately determine whether partial information about weights is adequate to correctly specify the most preferred alternative. This procedure can be useful for identifying situations in which detailed elicitation of weights is not needed.     

Using Ordinal Data to Estimate Cardinal Values

We investigate methods developed in multiple criteria decision‐making that use ordinal information to estimate numerical values. Such methods can be used to estimate attribute weights, attribute values, or event probabilities given ranks or partial ranks. We first review related studies and then develop a generalized rank‐sum (GRS) approach in which we provide a derivation of the rank‐sum approach that had been previously proposed. The GRS approach allows for incorporating the concept of degree of importance (or, difference in likelihood with respect to probabilities and difference in value for attribute values), information that most other rank‐based formulas do not utilize. We then present simulation results comparing the GRS method with other rank‐based formulas such as the rank order centroid method and comparing the GRS methods using as many as three levels of importance (i.e., GRS‐3) with Simos' procedure (which can also incorporate degree of importance). To our surprise, our results show that the incorporation of additional information (i.e., the degree of the importance), both GRS‐3 and Simos' procedure, did not result in better performance than rank order centroid or GRS. Further research is needed to investigate the modelling of such extra information. We also explore the scenario when a decision‐maker has indifference judgments and cannot provide a complete rank order. Copyright © 2014 John Wiley & Sons, Ltd.     

Do Ranks Suffice? A Comparison of Alternative Weighting Approaches in Value Elicitation

We compared both attribute weights and overall evaluations for students′ preferences among apartments described to them in terms of nine independent attributes. Methods used for eliciting attribute weights were (a) 7-point scales; (b) value hierarchy; (c) swing weights; and two methods using importance rankings only: (d) rank order centroid and (e) rank sum weights. Multiple linear regression was also used to infer attribute weights. Test–retest reliability of overall evaluations was found to be modest. Evaluation models based on all five weight elicitation methods were superior to an equal weights model, with rank order centroid weights modestly superior to other methods.     

When is a weight not illusory?

Weight illusions occur whenever some aspect of an object--such as its size, material or colour--arouses the expectation that its weight will be heavier or lighter than it actually is. The direction of the illusion normally contrasts with the expected weight. When objects are hidden from sight and lifted by strings they can provide no misleading cues, and a correct weight-expectation should be achieved after one or two trials. When a visible object has the same physical and apparent weight as a hidden object, it can be defined as non-illusory. Weighted tins and polystyrene blocks of various sizes were compared with hidden weights. Tins were found to be non-illusory when their density was about 1.7, and polystyrene blocks when their density was about 0.14.

Weight illusions may be due to a central scaling process which enables a wide range of weights to be estimated, different ranges being selected according to the expected value of the weight. If the selected range is inappropriate an illusion occurs. Changes in expected value could also allow for the operation of “weight-constancy” during changes in proprioceptive stimulation.     

A parameter analysis method for the weight‐set to satisfy preference orders of alternatives in additive multi‐criteria value models

In the context of the additive multi‐criteria value model, this paper investigates how the set of criteria weights (weight‐set hereafter) can be determined according to the preference orders of alternatives given by the decision maker. A construction method is proposed for the weight‐set for different intervals of β, where β is a differential amount of value between the preference information on two alternatives. The results of this paper are important for sensitivity analysis in multi‐criteria decision making (MCDM) problems and multi‐criteria group decision analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

Linking Disjoint Supermatrices and Criteria Clusters

An axiom of the Analytic Network Process (ANP) requires the elements being considered to be strongly connected in order to obtain a meaningful priority vector. A simple example demonstrates the issues that can arise when a decision contains disjoint clusters within the Supermatrix. From the example it can be observed that the necessary information to complete additional linking pin comparisons would have already been collected; and by performing linking pin comparisons a decision maker can convert a disjoint Supermatrix into a strongly connected Supermatrix. The linking process is summarized in five steps and provided in the general form. This linking comparison methodology exploits the fundamental advantages of pairwise comparisons and can also be used to weight the criteria clusters within a decision network. Linking pin comparisons performed at the level of a criterion of a single alternative with respect to another criterion of that same alternative can be used to obtain the criteria cluster weights. Linking pin comparisons at this level can reduce the decision maker's cognitive burden in comparison to totality comparisons. The ability to strongly connect an otherwise disjoint Supermatrix and reduce the decision maker's cognitive burden demonstrates the usefulness of linking pin comparisons in ANP decision models. Copyright © 2016 John Wiley & Sons, Ltd.     

A theory of perceived risk and attractiveness

People judged both the attractiveness and risk of lotteries to win or lose money. The lotteries were designed to test whether risk and attractiveness judgments show systematic deviations from the simple sum of probability-by-utility-products analogous to (S)EU theory. Our results led to an alternative combination rule for probability and outcome information, with a relative weight averaging component and a configural (i.e., sign- or rank-dependent) probability weighting component. Ratings of risk and attractiveness were negatively correlated, but the two tasks showed systematic differences in the rank order of judgments. Both judgments could be fit by the same configural relative weight averaging model, but with different parameters (especially the sign-dependent probability weighting functions). Risk judgments were more sensitive to the probability of losses and zero outcomes compared to attractiveness judgments, which were more sensitive to the probability of gains. There were individual differences on the extent of this difference in probability weights between risk and attractiveness judgments.     

Cognitions related to anxiety: a pilot study of treatment

In general, where anxiety appears to have a specific external focus, such as the situations which are avoided by phobic patients, treatment involving systematic exposure to those situations seems to be effective. This is less appropriate, or even impossible, where anxiety is not dependent on any external circumstance, but is described by the patient as occurring at any time or place, either chronically over long periods, or acutely in the form of ‘panic attacks’. These patients with ‘generalised’ anxiety often describe internal cues for anxiety either in the form of thoughts (e.g. worry over a current problem) or somatic (e.g. chest sensations interpreted as possible heart disease). Beck et al. (1974) has suggested that on interview, all patients diagnosed as suffering from diffuse or generalised anxiety can report specific ideas or other cognitive cues which are associated with anxiety. These usually concern possible traumatic events, such as illness and death, or social rejection. Clearly Beck has in mind the possibility that these cognitions have the effect of inducing anxiety, although even if the validity of the subjective reports were to be accepted, the problem remains of whether the relationship between mood state and cognitions is causal and if so, in which direction it operates. Obviously a causal relationship may also operate in both directions simultaneously, to form a ‘vicious circle’ in which each exacerbates the other. To establish whether there is a sense in which particular cognitions contribute causally to anxious mood, it would be necessary to find a method of manipulating the type or frequency of cognitions thought to be operating in this way.

One obvious possibility is that of ‘thought-stopping’: that is, patients could be taught to identify thoughts which are associated with anxiety and stop them in the usual way (Wolpe, 1973, p. 211) e.g. by' shouting stop, and substituting an alternative thought. The present study was planned as a pilot experiment to determine (i) if appropriate anxiety related cognitions could be elicited from a series of patients with generalised anxiety, (ii) if the reported frequency of such thoughts could be modified by a thought-stopping technique, and (iii) if any changes in thought frequency were associated with improvements in mood.

Clearly there are many ‘non-specific’ features involved in thought-stopping which could also have therapeutic effects on mood. For this reason it was necessary to include an alternative procedure, not directed at reducing thought frequency, but having the same degree of plausibility to patients, and preferably to therapists. The control procedure chosen for this purpose was modelled on desensitisation, in which patients were encouraged to allow the supposedly anxiety-provoking thoughts into their mind and tolerate them, rather than attempt to stop them. In summary, the study employed a relaxation training phase as a base-line, followed by a cross-over design in which the two treatment phases of thought-stopping and ‘cognitive desensitisation’ were given to each patient, in balanced order.     

More historical dimensions of commonsense knowledge: Spiritual consolation for the depressed

Ss were given 15 propositions derived from the neoclassical canon of advice on spiritual consolation for the depressed and were asked either to rate the extent of their personal agreement with each and to predict the average ratings for the group, or to say whether they regarded each proposition as ‘true’ or ‘not true’ and to predict the percentage of the group that would choose ‘true’ for each proposition. The observed and mean predicted rank orders were compared within and between methods; all correlations were high, positive, and significant. The results suggest that people's higher-order ideas about other people's ideas include notions about the intensity of beliefs as well as about the proportion of believers. Contemporary developments of those propositions which a clear majority of the present Ss endorsed are discussed.     

Children''s self-initiated approach to spiders

Seventeen school children were invited to stay in the presence of a harmless spider for 4 minutes under instructions which were designed mildly to encourage touching the spider but which left open a clear alternative of not touching. Subjects confronted the spider in dyads which differed in composition in terms of fear-level and sex of subjects. The main finding was that boys did not show any more approach when paired with girls, thus confirming previous negative findings in this regard. Other findings were that boys showed more approach than girls, level of fear interacted with sex of subject, and ‘fearless’ but not ‘fearful’ subjects showed more approach with repeated experience.     

The modified star graph and the petal diagram: two new visual aids for discrete alternative multicriteria decision making

Many studies have looked into the provisions of visual aids to multicriteria decision making. However, most of them have separated the display of alternative profiles and criteria weight information into two displays. This makes the analysis of the relationship between the criteria and alternatives and the effect of changing the criteria weights on the decision difficult. In this study, displays that can incorporate the display of both alternative profiles and criteria weight information for discrete alternative multicriteria decision-making problems are examined. The simple additive model is the multicriteria analysis method used. The result is two new visual aids for representing data of multicriteria decision-making problems, the modified star graph and the petal diagram. This paper discusses the two displays and compares their strengths and weaknesses. The results of a preliminary test conducted to evaluate the effectiveness of the displays are also included. © 1998 John Wiley & Sons, Ltd.     

Notes on the weighting biases in value trees

The variation in the structure of value trees can have undesirable effects on the attribute weights. Earlier experiments suggest that an attribute receives a higher weight if it is presented at an upper level in a value tree or if it is split into subattributes. Here we show that it is flawed to make conclusions about the biases at the individual level based on the averages of weights across large groups of subjects. Averages do not describe individual behavior. Furthermore, the averages of weights tend to approach even weights. By using the data from earlier experiments we illustrate how the averaging can produce different phenomena. We also show that the use of weights based on the rank order of attributes only can easily lead to biases when the structure of a value tree is changed. © 1998 John Wiley & Sons, Ltd.     

Weight approximations in multi‐attribute decision models

The use of surrogate weights based on rankings has been proposed as a method for avoiding difficulties associated with the elicitation of weights in multi‐attribute decision analysis. When the simple multiattribute rating technique using swings (SMARTS) method is being employed it has been suggested that rank order centroid (ROC) weights are the best surrogate weights to use. This study shows that ROC weights are appropriate to use as a substitute for original weights that are constrained to sum to a fixed total (usually 1 or 100) as used in the point allocation method. If, however, the original weights are determined without any initial restrictions, as in the direct rating method, and are then normalized, which is the common procedure in SMARTS analysis, then the ROC weights do not provide the best approximations to the original weights. This paper shows how to obtain rank order distribution (ROD) weights that provide a better approximation than the ROC approach to unrestricted original weights. The paper also shows that, as the number of attributes in a decision problem increases, the ROD weights approximate to the more easily calculated rank sum weights. Copyright © 2003 John Wiley & Sons, Ltd.     

Panic attacks without fear: An overview*

‘Non-fearful panic disorder’ (NFPD) is a condition that meets DSM III-R criteria for panic disorder but lacks a report of subjective fear or anxiety. Presenting the first comprehensive overview of this issue, the authors describe studies investigating a wide range of apparently overlapping phenomena including NFPD, ‘somatically expressed panic’, ‘non-cognitive panic’, ‘alexithymic panic’, ‘non-clinical panic’, and ‘masked anxiety’. The review shows that such conditions account for from 20 to 40% of the panic disorder found in various medical populations, and that this group resembles conventional panic disorder in cross-sectional comparisons. We emphasize that a ‘triple-response’ model of anxiety is consistent with our conclusion that NFPD should be conceptualized as a panic disorder subtype. Finally, we discuss unresolved issues regarding the construct and predictive diagnostic validity of NFPD.     

迫选规则体验法: 检验规范性和描述性风险决策理论的新尝试

为寻求检验规范性和描述性风险决策理论的通用标准, 本研究以期望价值理论和齐当别抉择模型为例, 探讨了“迫选规则体验法”的适用性。被试为120名大学生, 实验任务为要求被试分别完成自主决策(采用未知规则: 真规则)和规则迫选决策(遵循给定规则: 假规则)任务, 并对决策后的情感和认可程度进行评定。研究发现: (1) 被试在自主决策条件下比在规则迫选条件下体验到的正性情感程度更强, 负性情感的程度更弱; (2) 被试在自主决策与规则迫选决策两种条件下做出的相同决策越多, 该被试对迫选规则更加认可并体验到的正性情感程度越强, 负性情感的程度越弱; (3) 与期望价值理论相比, 齐当别抉择模型可能符合更多决策者的实际决策规则。这些结果表明, 作为检验规范性和描述性风险决策理论的新尝试, 迫选规则体验法可能更有助于回答“决策者实际采用的决策规则是什么”的问题。     

Rank disagreement: A comparison of multi-criteria methodologies

A number of multi-criteria decision support techniques have emerged in recent years that use varying computational approaches to arrive at the most desirable solution and thereby ‘recommend’ a course of action. Decision makers who use the results of this analytic work should be assured that the computational schemes used by their supporting analysts or decision support software produce the appropriate solutions. We conducted a series of simulation experiments that compared the top-ranked options resulting from the computational algorithms that support Multi-Attribute Value Theory (MAVT) and three methods that are reported in the literature that allow rank reversals, the change in rank order of two options when an unrelated option is added or deleted from the analysis: the Analytical Hierarchy Process (AHP), Percentaging and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). We also included a Fuzzy algorithm proposed by Yager to gauge its consistency with the other algorithms, even though it is not subject to rank reversals. These experiments demonstrated that the MAVT and AHP techniques, when provided with the same decision outcome data, very often identify the same alternative as ‘best’. The other techniques are noticeably less consistent with MAVT, the Fuzzy algorithm being the least consistent. The situations under which the most frequent and significant differences occurred were dependent upon the method. The results of our experiments indicate that other issues (e.g. the processes used for problem structuring and the elicitation of value weights) are likely to be of greater significance to problem outcome (based on our experience) than the choice between the computational algorithms of MAVT and AHP. The results cause us to be concerned about the use of the other methods.     

Emotion as a tradeable quantity

Three studies investigate how physiological emotional responses can be combined with symbolic information to predict preferences. The first study used a weighted proportional difference rule to combine explicitly quantified symbolic and emotional information. The proportion of emotion model was more predictive than a simple additive emotional (AE) combination in decisions about selecting dating partners. Study 2 showed that a simple proportion algorithm of emotionally derived weights and a simple AE model predicted preference equally well for decisions between equal expected value (EV) gambles. Study 3 provided additional evidence for decision mechanisms that combine physiological measures within symbolic trade‐off algorithms for choices between diamond rings. Self‐reported emotion measures proved to be better predictors than physiological measures. The results are discussed in the context of other major models of emotional influence on preference and provide a foundation for future research on emotional decision‐making mechanisms. Copyright © 2008 John Wiley & Sons, Ltd.     

A clinical trial of continuous, intermittent and overlearning ‘bell and pad’ treatments for nocturnal enuresis

Sixty-one enuretic children were allocated sequentially to ‘standard’, ‘intermittent’ or ‘overlearning’ bell and pad treatment. The results suggest that the ‘overlearning’ modification of standard treatment was successful in bringing about a reduction in the relapse rate. The present status and implications of research into nocturnal enuresis were discussed in the light of the results of the investigation.     

Causing harm and allowing harm: a study of beliefs in obsessional problems

This study investigates two factors hypothesised as relevant to obsessional problems because of the way in which they influence decisions whether or not to act to prevent harm. These are (i) the way in which intrusive thoughts increase the internal awareness of harm, and confront the person with the possibility of taking action to prevent such harm and (ii) the extent to which there is some obvious external factor which increases awareness of the possibility of preventing harm. Obsessional patients, anxious and non-clinical controls completed a scale which systematically measured these factors across a wide range of situations. Results across all situations evaluated confirmed previous findings that both obsessionals and nonobsessionals were more likely to report acting to prevent harm when awareness of it is prompted by an intrusion than when it is not. It was also found that participants in all groups acted more ‘obsessionally’ when a scenario is described in ways which suggest that harm may be by ‘commission’ than when it is described in terms of an ‘omission’. When scenarios about which each individual is most disturbed were analysed, anxious and non-clinical controls continued to differentially rate omission and commission situations; as predicted, this differential was not present for obsessional patients.

It is concluded that obsessionals are more sensitive to omission than are nonobsessionals when considering scenarios about which they are concerned, and that this sensitivity is one factor influencing the decision whether to act to prevent harm.