Risk-Adjusted Mission Value: Trading Off Mission Risk for Mission Value

This article develops a decision-theoretic methodology for the risk-adjusted mission value (RAMV) for selecting between alternative missions in the presence of uncertainty in the outcomes of the missions. This methodology permits trading off mission risk for mission value, something that probabilistic risk analysis cannot do unless it explicitly incorporates both mission value and risk aversion of the project management. The methodology, in its complete implementation, is consistent with the decision theory known as expected utility theory, although it differs from conventional decision theory in that the probabilities and all but one of the utilities are not those of the decision maker. The article also introduces a new interpretation of risk aversion. The methodology is consistent with the elementary management concept concerning division of labor. An example is presented for selecting between discrete alternatives-four landing sites on Mars. A second example is presented for selecting among a set of continuous alternatives-a comet flyby distance. The methodology is developed within the context of scientific missions, but the methodology is equally applicable to any situation requiring outcome value judgments, probability judgments, and risk aversion judgments by different constituencies.     

Dynamic Preference for Flexibility

We consider a decision maker who faces dynamic decision situations that involve intertemporal trade‐offs, as in consumption–savings problems, and who experiences taste shocks that are transient contingent on the state of the world. We axiomatize a recursive representation of choice over state contingent infinite horizon consumption problems, where uncertainty about consumption utilities depends on the observable state and the state follows a subjective Markov process. The parameters of the representation are the subjective process that governs the evolution of beliefs over consumption utilities and the discount factor; they are uniquely identified from behavior. We characterize a natural notion of greater preference for flexibility in terms of a dilation of beliefs. An important special case of our representation is a recursive version of the Anscombe–Aumann model with parameters that include a subjective Markov process over states and state‐dependent utilities, all of which are uniquely identified.     

基于VIKOR和诱导广义直觉梯形模糊Choquet积分算子的多属性群决策方法

针对属性值为直觉梯形模糊数,决策者间和属性间存在相互关联的多属性群决策问题,引入模糊测度和Choquet积分的概念,在直觉梯形模糊数的运算法则基础上构建了诱导型广义直觉梯形模糊choquet积分平均(IG-ITFCA)算子和诱导型广义直觉梯形模糊choquet积分几何(IG-ITFCG)算子,探讨上述算子的若干性质及一些特例,进而提出了基于诱导型广义直觉梯形模糊Choquet积分算子和多准则妥协优化解(VIKOR)的直觉梯形模糊多属性群决策方法。实例分析验证该方法的有效性和合理性。     

Representation,Propagation, and Decision Issues in Risk Analysis Under Incomplete Probabilistic Information

This article tries to clarify the potential role to be played by uncertainty theories such as imprecise probabilities, random sets, and possibility theory in the risk analysis process. Instead of opposing an objective bounding analysis, where only statistically founded probability distributions are taken into account, to the full‐fledged probabilistic approach, exploiting expert subjective judgment, we advocate the idea that both analyses are useful and should be articulated with one another. Moreover, the idea that risk analysis under incomplete information is purely objective is misconceived. The use of uncertainty theories cannot be reduced to a choice between probability distributions and intervals. Indeed, they offer representation tools that are more expressive than each of the latter approaches and can capture expert judgments while being faithful to their limited precision. Consequences of this thesis are examined for uncertainty elicitation, propagation, and at the decision‐making step.     

Evaluating the Simplified Conjoint Expected Risk Model: Comparing the Use of Objective and Subjective Information

The simplified Conjoint Expected Risk (CER) model by Holtgrave and Weber posits that perceived risk is a linear combination of the subjective judgments of the probabilities of harm, benefit, and status quo, and the expected harm and benefit of an activity. It modifies Luce and Weber's original CER model—that uses objective information to evaluate financial gambles—to accommodate activities such as health/technology activities where values of the model variables are subjective. If the simplified model is a valid modification of the original model, its performance should not be sensitive to the use of subjective information. However, because people may evaluate information differently when objective information is provided to them than when they generate information on their own, the performance of the simplified CER model may not be robust to the source of model-variable information. We compared the use of objective and subjective information, and results indicate that the estimates of the simplified CER model parameters and the proportion of variance in risk judgments accounted for by the model are similar under these two conditions. Thus, the simplified CER model is viable with activities for which harm and benefit information is subjective.     

基于头脑风暴原则的主观证据融合决策方法

为了解决证据源是主观的或者客观证据源因无法获取有效信息而不得不寻求主观经验、知识、直觉帮助的决策问题,采用基于互补判断的相对估计方式构建了能够提取决策专家主观推断信息的柔性知识矩阵,给出了由柔性知识矩阵向BPA函数转化的主观证据提取模型,在此基础上将头脑风暴方法中的延迟评判、独立思考、以量求质、结合改善四项原则引入到主观证据的提取过程之中,构建了可以从识别框架中辨识出可能为最优方案的融合决策方法,最后分别应用数值对比分析和案例模拟分析验证了提出方法的科学有效性和应用可行性。     

HERESY IN DECISION ANALYSIS: MODELING SUBSEQUENT ACTS WITHOUT ROLLBACK *

When making a current decision, like choosing an experiment, a subject will often take into account “subsequent acts” which he does not yet commit to. Common practice requires modeling through preposterior analysis, which treats one act as certain, conditional on the intervening information modeled. This is not logically necessary since the same expected utilities could be obtained by properly conditioning utility on any selection of events (including subsequent acts). The subject could assess utility marginal on subsequent acts or conditional on subsequent acts treated as uncertain events. The preposterior model is a special case of the latter where conditioning information is sufficiently modeled to imply subsequent act probabilities of zero or one. This paper argues that attempts at preposterior modeling are often unsuccessful and have critically flawed much current practice in decision analysis. Simpler approaches such as the “acts-as-events” model are intrinsically less dependent on restrictive assumptions and have been successfully applied to many real-world decisions.     

REORDER-POINT MODELS WITH DISCRETE PROBABILITY DISTRIBUTIONS

This paper is concerned with the determination of reorder points and safety-stock levels for situations where both the demand and lead-time distributions are discrete and independent. Formulas are developed for computing exact probabilities for the lead-time demand distribution on the basis of empirical distributions. Practitioners can use the model to obtain exact probabilities for situations where the computational burden is justified, while academicians can use the model to evaluate heuristic approaches to the reorder-point problem.     

群决策中基于二元语义的主客观权重集成方法

针对一类属性值和属性权重信息均以语言评价信息形式给出的多属性群决策问题,提出了一种基于二元语义信息处理的主客观属性权重集成方法.首先运用二元语义集成算子计算属性的主观权重,然后给出一种基于最小偏差的属性客观权重计算方法,该方法根据决策者给出的语言决策矩阵计算决策群体对属性判断的偏差,偏差越大,表明决策者对该属性评价意见的分歧越大,则应赋给该属性越小的权重值,以提高群体意见的一致性.在此基础上,对属性的主、客观权重信息进行集成,得到属性综合权重.最后通过算例说明了该方法的有效性和实用性.     

Preference for Flexibility and Random Choice

We study a two‐stage model where the agent has preferences over menus as in Dekel, Lipman, and Rustichini (2001) in the first period and then makes random choices from menus as in Gul and Pesendorfer (2006) in the second period. Both preference for flexibility in the first period and strictly random choices in the second period can be, respectively, rationalized by subjective state spaces. Our main result characterizes the representation where the two state spaces align, so the agent correctly anticipates her future choices. The joint representation uniquely identifies probabilities over subjective states and magnitudes of utilities across states. We also characterize when the agent completely overlooks some subjective states that realize at the point of choice.     

Using Uncertainty Analysis to Improve Consistency in Regulatory Assessments of Criteria Pollutant Standards

Regulatory impact analyses (RIAs), required for new major federal regulations, are often criticized for not incorporating epistemic uncertainties into their quantitative estimates of benefits and costs. “Integrated uncertainty analysis,” which relies on subjective judgments about epistemic uncertainty to quantitatively combine epistemic and statistical uncertainties, is often prescribed. This article identifies an additional source for subjective judgment regarding a key epistemic uncertainty in RIAs for National Ambient Air Quality Standards (NAAQS)—the regulator's degree of confidence in continuation of the relationship between pollutant concentration and health effects at varying concentration levels. An illustrative example is provided based on the 2013 decision on the NAAQS for fine particulate matter (PM_2.5). It shows how the regulator's justification for setting that NAAQS was structured around the regulator's subjective confidence in the continuation of health risks at different concentration levels, and it illustrates how such expressions of uncertainty might be directly incorporated into the risk reduction calculations used in the rule's RIA. The resulting confidence-weighted quantitative risk estimates are found to be substantially different from those in the RIA for that rule. This approach for accounting for an important source of subjective uncertainty also offers the advantage of establishing consistency between the scientific assumptions underlying RIA risk and benefit estimates and the science-based judgments developed when deciding on the relevant standards for important air pollutants such as PM_2.5.     

An Empirical Study of Equivalence Judgments vs. Ratio Judgments in Decision Analysis*

Two commonly used elicitation modes on strength of preference, equivalence and ratio judgments, were compared in an experiment. The result from the experiment showed that ratio judgments were less effective than equivalence judgments. Based on an iterative design for eliciting multiattribute preference structures, equivalence judgments outperformed ratio judgments in estimating single‐attribute measurable value functions, while being nearly more effective than ratio judgments in assessing multiattribute preference structures. The implications of the results from the experiment are that multiattribute decision‐making techniques should take advantage of the decision maker's inclination of making effective equivalence trade‐off judgments, and that useful techniques should be devised to incorporate different commonly used techniques, such as multiattribute utility theory and the Analytic Hierarchy Process, to elicit and consolidate equivalence trade‐off judgments.     

Establishing dominance between strategies with interval judgments of state probabilities

In decision-making under uncertainty, a decision-maker is required to specify, possibly with the help of decision analysts, point estimates of the probabilities of uncertain events. In this setting, it is often difficult to obtain very precise measurements of the decision-maker׳s probabilities on the states of nature particularly when little information is available to evaluate probabilities, available information is not specific enough, or we have to model the conflict case where several information sources are available.In this paper, imprecise probabilities are considered for representing the decision-maker׳s perception or past experience about the states of nature, to be specific, interval probabilities, which can be further categorized as (a) intervals of individual probabilities, (b) intervals of probability differences, and (c) intervals of ratio probabilities. We present a heuristic approach to modeling a wider range of types of probabilities as well as three types of interval probabilities. In particular, the intervals of ratio probabilities, which are widely used in the uncertain AHP context, are analyzed to find extreme points by the use of change of variables, not to mention the first two types of interval probabilities. Finally, we examine how these extreme points can be used to determine an ordering or partial ordering of the expected values of strategies.     

基于基元前景交叉判断的前景价值模型

针对现有概率权重非参数确定方法存在的两方面缺陷,即因假设概率权重仅与概率有关而没有考虑概率权重受概率与结果共同影响的问题和没有针对决策者主观判断不准确性予以判断偏差有效控制的问题,通过引入两两比较思维构建了反映概率和结果对概率权重复杂影响的基元前景两两比较交叉判断新模式,并在此基础上运用误差控制优化技术提出了基元前景价值确定模型和前景优劣排序模型.数值模拟分析结果表明,应用前景优劣排序模型得到的前景排序与假定能够事先知道、能够真实反映决策者在有限理性下实际选择行为的真实排序具有高度一致性,证实了其克服现有非参数法固有缺陷的有效性.     

MODEL UNCERTAINTY

We study decision problems in which consequences of the various alternative actions depend on states determined by a generative mechanism representing some natural or social phenomenon. Model uncertainty arises because decision makers may not know this mechanism. Two types of uncertainty result, a state uncertainty within models and a model uncertainty across them. We discuss some two‐stage static decision criteria proposed in the literature that address state uncertainty in the first stage and model uncertainty in the second (by considering subjective probabilities over models). We consider two approaches to the Ellsberg‐type phenomena characteristic of such decision problems: a Bayesian approach based on the distinction between subjective attitudes toward the two kinds of uncertainty; and a non‐Bayesian approach that permits multiple subjective probabilities. Several applications are used to illustrate concepts as they are introduced.     

How Should Autonomous Cars Drive? A Preference for Defaults in Moral Judgments Under Risk and Uncertainty

Autonomous vehicles (AVs) promise to make traffic safer, but their societal integration poses ethical challenges. What behavior of AVs is morally acceptable in critical traffic situations when consequences are only probabilistically known (a situation of risk) or even unknown (a situation of uncertainty)?  How do people retrospectively evaluate the behavior of an AV in situations in which a road user has been harmed? We addressed these questions in two empirical studies (N = 1,638) that approximated the real‐world conditions under which AVs operate by varying the degree of risk and uncertainty of the situation. In Experiment 1, subjects learned that an AV had to decide between staying in the lane or swerving. Each action could lead to a collision with another road user, with some known or unknown likelihood. Subjects’ decision preferences and moral judgments varied considerably with specified probabilities under risk, yet less so under uncertainty. The results suggest that staying in the lane and performing an emergency stop is considered a reasonable default, even when this action does not minimize expected loss. Experiment 2 demonstrated that if an AV collided with another road user, subjects’ retrospective evaluations of the default action were also more robust against unwanted outcome and hindsight effects than the alternative swerve maneuver. The findings highlight the importance of investigating moral judgments under risk and uncertainty in order to develop policies that are societally acceptable even under critical conditions.     

The impact of learning opportunities and decision authority on occupational health

In an investigation of 418 employees in the Norwegian Postal Service, employees with high learning opportunities and high decision authority were found to be better off on psychological functioning, health and organizational outcome variables than employees with low scores on these variables. Decision authority and learning opportunities had specific and independent impact on subjective health, psychological functioning, coping style and organizational outcome variables. There were, however, also interaction effects between demands, learning opportunities, and decision authority on subjective health. Learning opportunities and decision authority were operationalized with a questionnaire, supplemented with questions on the opportunities to learn skills beyond the present job situation. It is suggested that this is a particularly important dimension for coping with the present day rapid changes in working life, where the objective for many workers will be to broaden their repertoire and competence to increase their flexibility in the labour market.     

AN EMPIRICAL EXAMINATION OF SOCIAL POWER IN TERMS OF DECISION THEORY1

The paper presents an extension of decision theory to the analysis of social power. The power of a person, A, over another person, B, is viewed in terms of the effect A has on B's decision. The analysis is based on the idea that B's decision regarding the performance of alternative behaviors is a function of 1) B's utility for the consequences of the behaviors and 2) B's subjective probabilities that the behaviors will lead to these consequences. In these terms, A's power over B lies in A's ability to mediate various consequences for B, contingent upon B's compliance or noncompliance. Subjects were asked to consider eight situations in which hypothetical individuals had to make a choice between two courses of action. In each situation another person (A) was attempting to induce the hypothetical individual (B) to choose one of the alternatives, while various situational factors were influencing B to choose the other alternative. The subjects were asked to consider B's utilities and subjective probabilities in each situation and to indicate whether or not B should comply with A and to make ratings of A's power. The decision theory analysis did well in predicting whether or not subjects would indicate that B should comply with A. Also, subjects generally were able to correctly specify whether A or the situational factors had more influence over B's decision. Finally, the subjects' ratings of A's power in the eight situations were highly related to the decision theoretic measure of power.     

An Experimental Study of the Effectiveness of Three Debiasing Techniques*

Subjective probability distributions constitute an important part of the input to decision analysis and other decision aids. The long list of persistent biases associated with human judgments under uncertainy [16] suggests, however, that these biases can be translated into the elicited probabilities which, in turn, may be reflected in the output of the decision aids, potentially leading to biased decisions. This experiment studies the effectiveness of three debiasing techniques in elicitation of subjective probability distributions. It is hypothesized that the Socratic procedure [18] and the devil's advocate approach [6] [7] [31] [32] [33] [34] will increase subjective uncertainty and thus help assessors overcome a persistent bias called “overconfidence.” Mental encoding of the frequency of the observed instances into prespecified intervals, however, is expected to decrease subjective uncertainty and to help assessors better capture, mentally, the location and skewness of the observed distribution. The assessors' ratings of uncertainty confirm these hypotheses related to subjective uncertainty but three other measures based on the dispersion of the elicited subjective probability distributions do not. Possible explanations are discussed. An intriguing explanation is that debiasing may affect what some have called “second order” uncertainty. While uncertainty ratings may include this second component, the measures based on the elicited distributions relate only to “first order” uncertainty.     

Stochastic Judgments in the AHP: The Measurement of Rank Reversal Probabilities

This paper presents a methodology for analyzing Analytic Hierarchy Process (AHP) rankings if the pairwise preference judgments are uncertain (stochastic). If the relative preference statements are represented by judgment intervals, rather than single values, then the rankings resulting from a traditional (deterministic) AHP analysis based on single judgment values may be reversed, and therefore incorrect. In the presence of stochastic judgments, the traditional AHP rankings may be stable or unstable, depending on the nature of the uncertainty. We develop multivariate statistical techniques to obtain both point estimates and confidence intervals of the rank reversal probabilities, and show how simulation experiments can be used as an effective and accurate tool for analyzing the stability of the preference rankings under uncertainty. If the rank reversal probability is low, then the rankings are stable and the decision maker can be confident that the AHP ranking is correct. However, if the likelihood of rank reversal is high, then the decision maker should interpret the AHP rankings cautiously, as there is a subtantial probability that these rankings are incorrect. High rank reversal probabilities indicate a need for exploring alternative problem formulations and methods of analysis. The information about the extent to which the ranking of the alternatives is sensitive to the stochastic nature of the pairwise judgments should be valuable information into the decision-making process, much like variability and confidence intervals are crucial tools for statistical inference. We provide simulation experiments and numerical examples to evaluate our method. Our analysis of rank reversal due to stochastic judgments is not related to previous research on rank reversal that focuses on mathematical properties inherent to the AHP methodology, for instance, the occurrence of rank reversal if a new alternative is added or an existing one is deleted.