ASSESSMENT OF MULTIATTRIBUTED MEASURABLE VALUE AND UTILITY FUNCTIONS VIA MATHEMATICAL PROGRAMMING*

A major restriction on the use of decision analysis in practice is the frequent difficulty of determining a decision maker's multiattribute utility function. The assessment process can be complex and tedious and generally involves: (1) identifying relevant independence conditions, (2) assessing conditional utility functions, (3) assessing scaling constants, and (4) checking for consistency. Some of the assessment and modeling complexities encountered include an assessor's inability to respond in a quantitatively meaningful and consistent way to hypothetical gambles and an analyst's problem in selecting an appropriate functional form that accurately characterizes the conditional utility assessments. A simplified procedure that mitigates these difficulties is proposed. This procedure facilitates the determination of scaling constants by obtaining (via mathematical programming) a multiattributed measurable value function which is converted to a multiattributed utility function. The methodology can be developed advantageously to produce an interactive software package for use as an assessment aid.     

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.     

Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models

This paper proposes a new nested algorithm (NPL) for the estimation of a class of discrete Markov decision models and studies its statistical and computational properties. Our method is based on a representation of the solution of the dynamic programming problem in the space of conditional choice probabilities. When the NPL algorithm is initialized with consistent nonparametric estimates of conditional choice probabilities, successive iterations return a sequence of estimators of the structural parameters which we call K–stage policy iteration estimators. We show that the sequence includes as extreme cases a Hotz–Miller estimator (for K=1) and Rust's nested fixed point estimator (in the limit when K→∞). Furthermore, the asymptotic distribution of all the estimators in the sequence is the same and equal to that of the maximum likelihood estimator. We illustrate the performance of our method with several examples based on Rust's bus replacement model. Monte Carlo experiments reveal a trade–off between finite sample precision and computational cost in the sequence of policy iteration estimators.     

基于后悔理论和DEMATEL的语言型多属性决策方法

针对目前语言型多属性决策方法大多基于期望效用理论且不考虑指标间影响关系的不足，提出了一种将后悔理论和决策试验与评价试验法相结合的语言型多属性决策方法。首先，依据后悔理论的思想，定义了语言后悔-欣喜函数，给出了方案感知效用值的计算公式；然后，利用决策试验与评价试验法分析指标间的影响关系，给出了基于语言DEMATEL的指标权重确定方法，再通过指标总容量最大优化模型给出了基于注水原理的指标权重确定方法，并在此基础上求解方案的综合感知效用值，据此对方案进行排序择优；最后，通过两个应用实例来验证所提方法的可行性和有效性。实例结果表明，由于该方法同时考虑了决策者的心理行为和指标间的影响关系，因此可使决策结果更加贴近现实且更为可靠。     

METHODS FOR QUANTIFYING SUBJECTIVE PROBABILITIES AND MULTI-ATTRIBUTE UTILITIES*†

In many situations where normative decision-aiding techniques could be usefully applied, historical data are inadequate for estimating the required outcome probabilities, and economic methodologies are inadequate for estimating the aggregate utility derived from the several outcome attributes. In such cases it is often useful to obtain the required estimates in the form of expert judgments, i.e. to obtain subjective probabilities and multi-attribute utilities. Similarly, in many situations where behavioral decision processes are to be studied, it is necessary to scale the expectations and perceived values of the decision makers. This article describes the methods for eliciting subjective probabilities and multi-attribute utilities whose usefulness has been empirically studied and reported in the research literature. It also contains summary guidelines concerning the elicitation and use of such 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.     

Conditional Choice Probability Estimation of Dynamic Discrete Choice Models With Unobserved Heterogeneity

We adapt the expectation–maximization algorithm to incorporate unobserved heterogeneity into conditional choice probability (CCP) estimators of dynamic discrete choice problems. The unobserved heterogeneity can be time‐invariant or follow a Markov chain. By developing a class of problems where the difference in future value terms depends on a few conditional choice probabilities, we extend the class of dynamic optimization problems where CCP estimators provide a computationally cheap alternative to full solution methods. Monte Carlo results confirm that our algorithms perform quite well, both in terms of computational time and in the precision of the parameter estimates.     

How Probabilistic Risk Assessment Can Mislead Terrorism Risk Analysts

Traditional probabilistic risk assessment (PRA), of the type originally developed for engineered systems, is still proposed for terrorism risk analysis. We show that such PRA applications are unjustified in general. The capacity of terrorists to seek and use information and to actively research different attack options before deciding what to do raises unique features of terrorism risk assessment that are not adequately addressed by conventional PRA for natural and engineered systems—in part because decisions based on such PRA estimates do not adequately hedge against the different probabilities that attackers may eventually act upon. These probabilities may differ from the defender's (even if the defender's experts are thoroughly trained, well calibrated, unbiased probability assessors) because they may be conditioned on different information. We illustrate the fundamental differences between PRA and terrorism risk analysis, and suggest use of robust decision analysis for risk management when attackers may know more about some attack options than we do.     

A DECISION THEORY EXAMPLE IN FOOTBALL

In the 1967 Harvard-Cornell football game, Harvard was ahead 14–0 late in the game when Cornell scored two touchdowns. On both occasions, Cornell tried and failed on the two-point conversion attempt and lost the game 14–12. Postgame arguments were divided on the merits of Cornell's strategy. For this frequently occurring scenario in college football, we derive a maximum expected utility decision rule for the decision of kicking versus running/passing based on the relative utility of a win, a tie, or a loss and the probabilities of success with a kick as opposed to a run/pass.     

排污权价格随机情境下基于CVaR 准则的企业生产决策

面向排污权市场价格随机情境,通过提取理性企业在产品生产、污染削减、排污权交易等方面决策行为与排污权市场价格之间的关联性,推导了排污权市场价格随机情境下的企业随机利润函数;基于条件风险价值(CVaR)风险度量准则,推导了任意置信水平下随机利润的风险价值(VaR)解析表达式,建立了不同排污权预期价格和置信水平下的CVaR测度模型;基于此,深入论证了给定置信水平下实现随机利润CVaR最大化的企业最优决策及其特征,并系统分析了外部情景要素变动对最优决策及其优化结果的影响。主要结论表明：在企业分别作为排污权出售者与购买者两种情况下,随机利润CVaR的具体测度因利润下行风险存在的排污权市场价格区间不同而存在差异;基于CVaR准则,考虑决策风险的最优决策受到决策主体置信水平、排污权初始配额、排污权市场价格均值及标准差等多因素的复杂影响,进而系统性地偏离风险中性最优决策,并表现出风险规避特征;通过算例分析对所得结论进行全面验证,进一步说明该模型能较好地刻画与反映排污权交易企业决策风险及其现实决策行为。     

DEA决策单元的广义价值效率测度模型

为了克服DEA模型存在权重取值过于灵活的缺陷,在DEA建模原理的基础上,通过引入价值偏好估计对经典DEA模型予以了科学推广,并依据该模型推广建立了能够适用于决策者价值函数为非线性函数情况的DEA权重置信域构造方法与相应的决策单元价值效率分析方法即DEA广义价值效率测度实用模型。该模型的主要优点在于:权重置信域的构造具有科学严密性和价值信息引入的可操作性,从而可以保证分析结论的可靠性。数值验证结果表明,该模型可以得出可靠、可信且具有较强分辨能力的价值效率评价结论。     

The Quantitative Estimation of IT‐Related Risk Probabilities

How well can people estimate IT‐related risk? Although estimating risk is a fundamental activity in software management and risk is the basis for many decisions, little is known about how well IT‐related risk can be estimated at all. Therefore, we executed a risk estimation experiment with 36 participants. They estimated the probabilities of IT‐related risks and we investigated the effect of the following factors on the quality of the risk estimation: the estimator's age, work experience in computing, (self‐reported) safety awareness and previous experience with this risk, the absolute value of the risk's probability, and the effect of knowing the estimates of the other participants (see: Delphi method). Our main findings are: risk probabilities are difficult to estimate. Younger and inexperienced estimators were not significantly worse than older and more experienced estimators, but the older and more experienced subjects better used the knowledge gained by knowing the other estimators' results. Persons with higher safety awareness tend to overestimate risk probabilities, but can better estimate ordinal ranks of risk probabilities. Previous own experience with a risk leads to an overestimation of its probability (unlike in other fields like medicine or disasters, where experience with a disease leads to more realistic probability estimates and nonexperience to an underestimation).     

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.     

信息非对称程度与企业家效用、资本结构、企业市场价值

本文分析了市场信息非对称程度对企业家投资效用、企业债务水平及企业市场价值的影响。分析表明,若企业项目是高质量的,信息非对称程度的降低可使企业项目市场价值和债务水平提高;反之,若企业项目是低质量的,信息非对称程度的降低可使企业项目市场价值和债务水平减少;外部知情投资者比例的变化与企业家效用的变化之间的关系与企业质量有关。     

IT服务外包项目工期与费用控制的 多属性英氏逆拍卖机制

工期和费用是影响IT服务外包项目成败的两个重要因素,且两者之间呈负相关的关系。在IT服务外包项目执行前,发包方与接包方需要就项目的工期和费用达成一致。通常,发包方并不完全了解外包项目的市场行情,在这种情况下,就需要一种有效的方式使发包方和接包方之间就工期和费用达成一致。本文设计了改进的英氏逆拍卖机制,针对一对多的情况设计了新的拍卖协议;针对工期和费用的多属性情况,引入多属性效用理论解决,设计了相应的效用增加函数。最后通过一个算例来演示所设计的拍卖机制对解决此类决策问题的作用。得出一些结论:所设计机制能够以拍卖方式描述费用和工期管理流程;找到了发包方和接包方的最佳增量效用,并且建议的拍卖协议是发包方和接包方获得双赢结果的机制;从不同大小的案例中可以得到完全一致的结果,这表明设计的拍卖机制的有效性和效用增加函数对协商结果的有效性。     

RISK AVERSION AND EXPECTED UTILITY THEORY: AN EXPERIMENT WITH LARGE AND SMALL STAKES

We employ a novel data set to estimate a structural econometric model of the decisions under risk of players in a game show where lotteries present payoffs in excess of half a million dollars. The decisions under risk of players in the presence of large payoffs allow us to estimate the parameters of the curvature of the von Neumann–Morgenstern utility function—not only locally, as in previous studies in the literature, but also globally. Our estimates of relative risk aversion indicate that a constant relative risk aversion parameter of about 1 captures the average of the sample population. We also find that individuals are practically risk neutral at small stakes and risk averse at large stakes—a necessary condition, according to Rabin’s calibration theorem, for expected utility to provide a unified account of individuals’ attitudes toward risk. Finally, we show that for lotteries characterized by substantial stakes, nonexpected utility theories fit the data equally as well as expected utility theory.     

战略联盟、价值网络中关系形成的效用组合分析

过于关注价值占有阻碍了人们对联盟及价值网络中关系的本质,即价值创造的理解。我们认为,价值创造关系是建立在联盟及价值网络中各经济主体的效用体系上的,这是一种彼此的效用相互得到满足的状态。当每个经济主体的效用空间不只是包含价值占有时,那么,为建立这样的效用体系,经济主体就可能在价值占有问题上做出让步。本文通过所建立的模型支持了这样的论点,而且,在一定的条件下,由价值占有引起的冲突也可在这样的效用体系下自动得到解决。     

Estimation of Downside Risks in Project Portfolio Selection

In project portfolio selection, the aim is to choose projects which are expected to offer most value and satisfy relevant risk and other constraints. In this study, we show that uncertainties about how much value the projects will offer, combined with the fact that only a subset of the proposed projects will be selected, lead to inaccurate risk estimates about the aggregate value provided by the selected project portfolio. In particular, when downside risks are measured in terms of lower percentiles of the distribution of portfolio value, these risk estimates will exhibit a systematic bias. For deriving unbiased risk estimates, we present a calibration framework in which the required calibration can be presented in closed‐form in some cases or, more generally, derived by using Monte Carlo simulation to study a large number of project selection decisions. We also show that when the decision must comply with risk constraints, the introduction of tighter (more demanding) risk constraints can counterintuitively aggravate the underestimation of risks. Finally, we present how the calibrated risk estimates can be employed to align the portfolio with the decision maker's risk preferences while eliminating systematic biases in risk estimates.     

Selecting a Portfolio of Technologies: An Application of Decision Analysis

The Department of Energy is faced with the critical and complex decision of selecting technologies for waste site remediation. This research focuses on developing a decision support tool which assists the decision maker to find an optimal portfolio. A portfolio consists of selecting the appropriate processes for a remediation site and, subsequently, selecting a technology for each process so that the decision maker's objectives are achieved. The measures supporting the objectives are risk, life-cycle cost, and time required for remediation. The model uses exponential attribute utility functions with an additive objective function. The model provides the decision maker with estimates of the cost and time distributions, and their associated utility. Cumulative frequency distributions illustrate the dominance of technology choices and the variance in the results. The model permits sensitivity analysis in the form of rainbow and tornado diagrams to display the effects of changes in the values of the input variables. Overall, the model provides a generic technology selection tool that can be used to make better informed decisions and may be easily manipulated to reflect changes in the remediation process.     

消费者效用测度与产业需求函数

把概率解释为Ramsey的信念度,商品效用便可赋予von Neumann-Morgenstern效用性质从而得到测度;按二元价值结构的消费偏好特性建立新的需求模型,可导出在严格意义上用于产业分析的非线性需求函数,为解释现代产业组织及竞争行为提供科学依据。