An Experiment on the Numerical Modelling of Verbal Ratio Statements

Verbal statements are intuitively attractive for preference elicitation. In the analytic hierarchy process (AHP) the verbal responses to pairwise comparisons of relative importance are converted into real numbers according to the nine-point integer scale. Several alternative scales have been proposed for the conversion, but sufficient empirical evidence has not been produced to support the choice among these scales. We performed a comparative study in which subjects were requested to quantify verbal ratio statements by adjusting the heights of visually displayed bars. Subjects were also asked to employ verbal expressions in pairwise comparisons of areas of figures with different shapes. The principal result of the experiment was that the perceived meaning of the verbal expressions varies from one subject to the next and also depends on the set of elements involved in the comparison. Our results indicate that there are alternative numerical scales which yield more accurate estimates than the usual 1-to-9 scale and reduce the inconsistency of the comparison matrices. Alternative ways of using verbal preference statements are suggested to overcome the difficulties that arise from the context dependence of verbal pairwise comparisons. © 1997 John Wiley & Sons, Ltd.     

On the measurement of preferences in the analytic hierarchy process

In this paper we apply multiattribute value theory as a framework for examining the use of pairwise comparisons in the analytic hierarchy process (AHP). On one hand our analysis indicates that pairwise comparisons should be understood in terms of preference differences between pairs of alternatives. On the other hand it points out undesirable effects caused by the upper bound and the discretization of any given ratio scale. Both these observations apply equally well to the SMART procedure which also uses estimates of weight ratios. Furthermore, we demonstrate that the AHP can be modified so as to produce results similar to those of multiattribute value measurement; we also propose new balanced scales to improve the sensitivity of the AHP ratio scales. Finally we show that the so-called supermatrix technique does not eliminate the rank reversal phenomenon which can be attributed to the normalizations in the AHP. © 1997 John Wiley & Sons, Ltd.     

Variation of Preference Inconsistency When Applying Ratio and Interval Scale Pairwise Comparisons

Several studies on numerical rating in discrete choice problems address the tendency of inconsistencies in decision makers' measured preferences. This is partly due to true inconsistencies in preferences or the decision makers' uncertainty on what he or she really wants. This uncertainty may be reflected in the elicited preferences in different ways depending on the questions asked and methods used in deriving the preferences for alternatives. Some part of the inconsistency is due to only having a discrete set of possible judgments. This study examined the variation of preference inconsistency when applying different pairwise preference elicitation techniques in a five‐item discrete choice problem. The study data comprised preferences of five career alternatives elicited applying interval scale and numerically and verbally anchored ratio scale pairwise comparisons. Statistical regression technique was used to analyse the differences of inconsistencies between the tested methods. The resulting relative residual variances showed that the interval ratio scale comparison technique provided the greatest variation of inconsistencies between respondents, thus being the most sensitive to inconsistency in preferences. The numeric ratio scale comparison gave the most uniform preferences between the respondents. The verbal ratio scale comparison performed between the latter two when relative residual variances were considered. However, the verbal ratio scale comparison had weaker ability to differentiate the alternatives. The results indicated that the decision recommendation may not be sensitive to the selection between these preference elicitation methods in this kind of five‐item discrete choice problem. The numeric ratio scale comparison technique seemed to be the most suitable method to reveal the decision makers' true preferences. However, to confirm this result, more studying will be needed, with an attention paid to users' comprehension and learning in the course of the experiment. Copyright © 2013 John Wiley & Sons, Ltd.     

用文字概率衡量不确定性：特征和问题

文字概率是衡量不确定性的方式之一, 即人们使用诸如“也许”、“未必”的词汇来描述特定事件发生的可能性。文字概率不同于数字概率, 主要体现在文字概率的模糊性、非概率运算性和语义特性上。这使得相对于数字概率, 用文字概率衡量不确定性既有优势也有问题, 进而对人们的不确定信息沟通和风险决策造成影响。虽然文字概率与数字概率存在特征上的差异并且人们在日常交流中偏爱文字概率, 但是大部分风险领域的研究却仅局限于数字概率, 今后有必要研究使用文字概率测量的风险决策。在已有文字概率特征研究的基础上, 还可以进一步探究其不同于数字概率的其它特征(文字/数字概率与双系统模型的联系、文字概率的跨文化差异等)及其对风险决策的影响。     

Effects of probability mode on preference reversal.

Six analysts estimated verbally and numerically the chances that specific events will occur. Sixty decision makers used each type of estimate to make binary-choice decisions and to bid for lotteries based on the events. The usual reversal of preference between choice and bidding procedures was found in the numerical condition, but the frequency of preference reversals was significantly reduced in the verbal condition. This reduction occurred because risk aversion was reduced in choice when verbal estimates were given, whereas bidding was unaffected by presentation mode. The pattern of results was predicted by and supports the hypothesis that the relative importance given to the dimensions of a prospect depends on the form in which the information is displayed.     

Preference‐based Learning of Ideal Solutions in TOPSIS‐like Decision Models

Combining established modelling techniques from multiple‐criteria decision aiding with recent algorithmic advances in the emerging field of preference learning, we propose a new method that can be seen as an adaptive version of TOPSIS, the technique for order preference by similarity to ideal solution decision model (or at least a simplified variant of this model). On the basis of exemplary preference information in the form of pairwise comparisons between alternatives, our method seeks to induce an ‘ideal solution’ that, in conjunction with a weight factor for each criterion, represents the preferences of the decision maker. To this end, we resort to probabilistic models of discrete choice and make use of maximum likelihood inference. First experimental results on suitable preference data suggest that our approach is not only intuitively appealing and interesting from an interpretation point of view but also competitive to state‐of‐the‐art preference learning methods in terms of prediction accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiple Framing: Verbal,Facial, and Vocal Cues in Risky Choice

Verbal framing effects have been widely studied, but little is known about how people react to multiple framing cues in risk communication, where verbal messages are often accompanied by facial and vocal cues. We examined joint and differential effects of verbal, facial, and vocal framing on risk preference in hypothetical monetary and life–death situations. In the multiple framing condition with the factorial design (2 verbal frames × 2 vocal tones × 4 basic facial expressions × 2 task domains), each scenario was presented auditorily with a written message on a photo of the messenger's face. Compared with verbal framing effects resulting in preference reversal, multiple frames made risky choice more consistent and shifted risk preference without reversal. Moreover, a positive tone of voice increased risk‐seeking preference in women. When the valence of facial and vocal cues was incongruent with verbal frame, verbal framing effects were significant. In contrast, when the affect cues were congruent with verbal frame, framing effects disappeared. These results suggest that verbal framing is given higher priority when other affect cues are incongruent. Further analysis revealed that participants were more risk‐averse when positive affect cues (positive tone or facial expressions) were congruently paired with a positive verbal frame whereas participants were more risk‐seeking when positive affect cues were incongruent with the verbal frame. In contrast, for negative affect cues, congruency promoted risk‐seeking tendency whereas incongruency increased risk‐aversion. Overall, the results show that facial and vocal cues interact with verbal framing and significantly affect risk communication. Copyright © 2016 John Wiley & Sons, Ltd.     

The effect of order of presentation of verbal probability expressions on numerical estimates in a medical context

Many medical decisions are made on a probability estimate. Models of risk benefit calculations in health behaviour rarely articulate how people perceive and appraise such probability. Cognitive processes may mediate the processing of probability expressions and may be important to understand the meaning or the range of meanings that probability statements portray to patients. Past studies have indicated that verbal expressions of probability are vague and subject to individual interpretation. On the theoretical level when subjects are asked to translate a set of verbal probability expressions, ranging from high to low, into their equivalent numerical expressions subjects usually produce a continuum of numerical equivalents also ranging from high to low. In practice clinicians frequently communicate information about uncertainty to the patients by verbal probability estimates. This study explored the effect of the order of presentation of the verbal expressions on the numerical probabilities produced by a group of medical students (n?=?87) in relation to medical probabilities. The results showed that the order of presentation (descending vs. random) of the verbal probability expressions was found to have a significant effect on three of the seven numerical probabilities produced by the subjects. The order effect is discussed to together with implications for clinical practice.     

Measurement scales and scale independence in the analytic hierarchy process

One approach to evaluate the relative performance of decision alternatives with respect to multiple criteria is provided by the analytic hierarchy process. The method is based on pairwise comparisons between attributes, and several numerical measurement scales for the ratio statements have been proposed. The choice of measurement scale is re‐examined, and new arguments supporting the measurement scale of geometric progression are derived. Separately from the measurement scale considerations, the effects of the scale parameter in geometric measurement scale are also studied. By using a regression model for pairwise comparisons data, it is shown that the statistical inference does not depend on the value of the scale parameter in the case of a single pairwise comparison matrix. It is also shown when the scale independence of statistical inference can be achieved in a decision hierarchy. This requires the use of the geometric‐mean aggregation rule instead of the traditional arithmetic‐mean aggregation. The results of the case study demonstrate that the measurement scale and the aggregation rule have potentially large impacts on decision support. Copyright © 2000 John Wiley & Sons, Ltd.     

An investigation of the role of scale values in the DS/AHP method of multi‐criteria decision making

DS/AHP is a method of multi‐criteria decision making based on the Dempster–Shafer theory of evidence and the analytic hierarchy process. Central to the utilization of DS/AHP is the composing of preference judgements on identified groups of decision alternatives (DA) across a number of criteria against all the DA present in the problem in question. This paper exposits a series of results whose objectives are to aid in the development of an effective set of preference scale values for use within DS/AHP. These results relate directly to the concomitant level of ignorance (uncertainty) with the judgements made on a single criterion. Two particular directions of investigation are undertaken, firstly in determining the necessary number of scale values available and secondly finding the necessary differences between scale values, dependent on whether an arithmetic or geometric progression is the basis for the scale values. Through an example, the implications and utilization of these results within DS/AHP are illustrated. Copyright © 2003 John Wiley & Sons, Ltd.     

认知闭合需要、框架效应与决策偏好

在带有模糊性的决策情境中,决策者个人的认知特征会对其判断决策产生重要影响。通过实验的方法,考察了认知闭合需要和特征框架效应对个体决策偏好的影响。93名工商管理硕士（MBA）参与了实验,研究的结果支持了本研究的3个假设,即认知闭合需要与特征框架效应不仅对被试的决策偏好存在显著的影响,而且二者还存在显著的交互作用。具体来说,研究发现,在模糊情境中：高认知闭合需要的被试偏好于立刻做出决策,而低认知闭合需要的被试偏好于暂缓做出决策;接收到正向框架信息的被试偏好于立刻做出决策,而接收到负向框架信息的被试偏好于暂缓做出决策;认知闭合需要与特征框架对被试的决策偏好还存在显著的交互作用。研究结论为根据个体认知闭合需要的水平来选拔决策者、利用框架效应来影响个体的信息加工方式进而提高决策质量提供了理论依据     

An Alternate Method of Deriving Priorities and Related Inferences for Group Decision Making in Analytic Hierarchy Process

Some work has been carried out in the past on statistically deriving priorities in Analytic Hierarchy Process (AHP). In AHP, the aggregated worths of the alternatives, when compared with respect to several criteria, are estimated in a hierarchical comparisons model introduced by Saaty. In this setup, statistical models are used for Saaty's method of scaling in paired comparisons experiments in any level of the hierarchy. At the end, the final priority weights of the alternatives and related inferences are developed with appropriate statistical methods. Existing statistical methods in the literature assume independence of the entries of the paired comparison matrix. However, these entries are highly dependent among themselves. In this article, we propose a statistical method that allows for the dependence among the entries of the pairwise comparisons matrix. The proposed method is then illustrated with a numerical example. Copyright © 2011 John Wiley & Sons, Ltd.     

Timed magnitude comparisons of numerical and nonnumerical expressions of uncertainty

Two experiments involving paired comparisons of numerical and nonnumerical expressions of uncertainty are reported. Subjects were timed under two opposing sets of instructions ("choose higher probability" vs. "choose lower probability"). Numerical comparisons were consistently faster and easier than their nonnumerical counterparts. Consistent distance and congruity effects were obtained, illustrating that both numerical and nonnumerical expressions of uncertainty contain subjective magnitude information, and suggesting that similar processes are employed in manipulating and comparing numerical and verbal terms. To account for the general pattern of results obtained, Holyoak's reference point model (1978) was generalized by explicitly including the vagueness of the nonnumerical expressions. This generalized model is based on the notion that probability expressions can be represented by membership functions (Wallsten, Budescu, Rapoport, Zwick, & Forsyth, 1986) from which measures of location for each word, and measures of overlap for each pair can be derived. A good level of fit was obtained for this model at the individual level.     

A Social Values Analysis of Self–Other Differences in Decision Making Involving Risk

Three experiments tested our social values analysis of self–other differences in decision making under risk. In Experiment 1, we showed that people make riskier decisions for others in domains where risk taking is valued but not in those where risk is not valued. Experiment 2 documented that it is considered more inappropriate to make a risk-averse decision for another person than for oneself in situations where risk is valued. Experiment 3 showed that self–other differences in decision making occur even when there are no self–other differences in prediction and for decisions made for a typical student as well as for a friend. We use these results to argue that decision making for others is based predominantly on the perceived value placed on risk, leading to a norm for how to decide for others in situations where such a social value exists.     

异性交友决策任务上为不同心理距离他人决策的风险偏好

使用中国文化背景下修订的Beisswanger等人的异性交友决策问卷, 采用2种方法操纵自我-他人心理距离, 考察了男女大学生在后果严重性不同的异性交友决策任务上为不同心理距离他人决策风险偏好的差异。实验1发现, 被试为具体和笼统他人决策时的风险偏好无显著差异, 在后果不严重任务上比后果严重任务上更冒险, 男性比女性更冒险。心理距离与决策者性别的交互作用显著：男性为具体他人决策更冒险, 而女性为笼统他人决策更冒险。实验2发现, 被试为不相似他人比为相似他人决策更冒险, 在后果不严重任务上比在后果严重任务上更冒险, 男性比女性更冒险。后果严重性与决策者性别交互作用显著：男性在后果严重和不严重任务上的风险偏好无显著差异, 而女性在后果不严重任务上比后果严重任务上更冒险。综合两个实验的结果, 可以得出以下结论：相对于具体和笼统他人的区分而言, 相似和不相似他人的区分是一种更加稳定和有效的区分自我-他人心理距离的方法。结合相关研究及理论对结果进行了讨论。     

Experiments comparing qualitative approaches to rank ordering of multiattribute alternatives

ZAPROS, a method to support rank ordering tasks using ordinal input from decision makers, is discussed and compared with a preference cone technique and the analytic hierarchy process (AHP). It provides a means to identify inconsistencies in ordinal decision tasks, yielding verification and explanation of results for partial ordering of a large set of alternatives. The results indicate that ZAPROS provides no less accuracy in task solution, while having some advantages from a behavioural point of view. Comparative analysis of the effectiveness of the methods under consideration in accordance with differences in task characteristics is carried out.     

Predicting similarity judgments in intertemporal choice with machine learning

Similarity models of intertemporal choice are heuristics that choose based on similarity judgments of the reward amounts and time delays. Yet, we do not know how these judgments are made. Here, we use machine-learning algorithms to assess what factors predict similarity judgments and whether decision trees capture the judgment outcomes and process. We find that combining small and large values into numerical differences and ratios and arranging them in tree-like structures can predict both similarity judgments and response times. Our results suggest that we can use machine learning to not only model decision outcomes but also model how decisions are made. Revealing how people make these important judgments may be useful in developing interventions to help them make better decisions.     

Reduction of pairwise comparisons in decision making via a duality approach

Although pairwise comparisons have been seen by many as an effective and intuitive way for eliciting qualitative data for multi‐criteria decision making problems, a major drawback is that the number of the required comparisons increases quadratically with the number of the entities to be compared. Thus, often even data for medium size decision problems may be impractical to be elicited via pairwise comparisons. The more the comparisons are, the higher is the likelihood that the decision maker will introduce erroneous data. This paper introduces a dual formulation to a given multi‐criteria decision making problem, which can significantly alleviate the previous problems. Some theoretical results establish that this is possible when the number of alternatives is greater than the number of decision criteria plus one. Copyright © 1999 John Wiley & Sons, Ltd.     

Diagnostic causal reasoning with verbal information

In diagnostic causal reasoning, the goal is to infer the probability of causes from one or multiple observed effects. Typically, studies investigating such tasks provide subjects with precise quantitative information regarding the strength of the relations between causes and effects or sample data from which the relevant quantities can be learned. By contrast, we sought to examine people’s inferences when causal information is communicated through qualitative, rather vague verbal expressions (e.g., “X occasionally causes A”). We conducted three experiments using a sequential diagnostic inference task, where multiple pieces of evidence were obtained one after the other. Quantitative predictions of different probabilistic models were derived using the numerical equivalents of the verbal terms, taken from an unrelated study with different subjects. We present a novel Bayesian model that allows for incorporating the temporal weighting of information in sequential diagnostic reasoning, which can be used to model both primacy and recency effects. On the basis of 19,848 judgments from 292 subjects, we found a remarkably close correspondence between the diagnostic inferences made by subjects who received only verbal information and those of a matched control group to whom information was presented numerically. Whether information was conveyed through verbal terms or numerical estimates, diagnostic judgments closely resembled the posterior probabilities entailed by the causes’ prior probabilities and the effects’ likelihoods. We observed interindividual differences regarding the temporal weighting of evidence in sequential diagnostic reasoning. Our work provides pathways for investigating judgment and decision making with verbal information within a computational modeling framework.     

成人与幼儿面部表情注意偏好的眼动研究

本研究选取45名3-5岁幼儿和39名大学本科生作为被试。实验材料为恐惧、愤怒、悲伤、惊讶和高兴五种面部表情图片。用Tobbi眼动仪记录被试观察表情图片时的眼动轨迹。结果发现：（1）成人偏好高兴表情,并在高兴表情上的注视时间和次数显著大于幼儿;（2）成人偏好注视眼部,幼儿偏好注视嘴部。结果表明,面部表情注意偏好的发展具有社会依存性,趋向于偏好积极情绪,这种发展变化与面部表情部位的注意偏好相关。