Stochastic Dominance: An Approach to Decision Making Under Risk

This paper introduces stochastic dominance as a technique to reduce the set of possible actions that a decision maker must consider in a decision problem under risk. The procedure usually does not choose an optimal action, but instead eliminates certain actions as unacceptable. Very little need be known about the decision maker's utility function. Two possible applications are presented: upgrading buildings to better withstand an earthquake; and choosing a site for a LNG facility.     

Multiattribute Risk Analysis in Nuclear Emergency Management

Radiation protection authorities have seen a potential for applying multiattribute risk analysis in nuclear emergency management and planning to deal with conflicting objectives, different parties involved, and uncertainties. This type of approach is expected to help in the following areas: to ensure that all relevant attributes are considered in decision making; to enhance communication between the concerned parties, including the public; and to provide a method for explicitly including risk analysis in the process. A multiattribute utility theory analysis was used to select a strategy for protecting the population after a simulated nuclear accident. The value-focused approach and the use of a neutral facilitator were identified as being useful.     

On The Quantitative Definition of Risk

A quantitative definition of risk is suggested in terms of the idea of a "set of triplets". The definition is extended to include uncertainty and completeness, and the use of Bayes' theorem is described in this connection. The definition is used to discuss the notions of "relative risk", "relativity of risk", and "acceptability of risk".     

Quantifying Uncertainty in a Risk Assessment Using Human Data

A call for risk assessment approaches that better characterize and quantify uncertainty has been made by the scientific and regulatory community. This paper responds to that call by demonstrating a distributional approach that draws upon human data to derive potency estimates and to identify and quantify important sources of uncertainty. The approach is rooted in the science of decision analysis and employs an influence diagram, a decision tree, probabilistic weights, and a distribution of point estimates of carcinogenic potency. Its results estimate the likelihood of different carcinogenic risks (potencies) for a chemical under a specific scenario. For this exercise, human data on formaldehyde were employed to demonstrate the approach. Sensitivity analyses were performed to determine the relative impact of specific levels and alternatives on the potency distribution. The resulting potency estimates are compared with the results of an exercise using animal data on formaldehyde. The paper demonstrates that distributional risk assessment is readily adapted to situations in which epidemiologic data serve as the basis for potency estimates. Strengths and weaknesses of the distributional approach are discussed. Areas for further application and research are recommended.     

Risk Matrix Integrating Risk Attitudes Based on Utility Theory

Recent studies indicate that absence of the consideration of risk attitudes of decisionmakers in the risk matrix establishment process has become a major limitation. In order to evaluate risk in a more comprehensive manner, an approach to establish risk matrices that integrates risk attitudes based on utility theory is proposed. There are three main steps within this approach: (1) describing risk attitudes of decisionmakers by utility functions, (2) bridging the gap between utility functions and the risk matrix by utility indifference curves, and (3) discretizing utility indifference curves. A complete risk matrix establishment process based on practical investigations is introduced. This process utilizes decisionmakers’ answers to questionnaires to formulate required boundary values for risk matrix establishment and utility functions that effectively quantify their respective risk attitudes.     

Risk Analysis: Understanding “How Safe is Safe Enough?“

The basic characteristics of determining acceptable risk are discussed. Technical, political, and social aspects of the problem add much complexity. The appropriate manner to reach responsible decisions regarding acceptable risk is suggested. This explicitly addresses the alternatives, the objectives, the uncertainty, and the values which constitute the information necessary to arrive at any solution. The inappropriateness of many "solutions" currently in use or "suggested" is exposed.     

Decision Making Under Uncertainty—An Example for Seismic Risk Management

Decision-making techniques are used to select the "best" alternatives under multiple and often conflicting criteria. Multicriteria decision making (MCDM) necessitates to incorporate uncertainties in the decision-making process. The major thrust of this article is to extend the framework proposed by Yager^{( 1 )} for multiple decisionmakers and fuzzy utilities (payoffs). In addition, the concept of expert credibility factor is introduced. The proposed approach is demonstrated for an example of seismic risk management using a heuristic hierarchical structure. A step-by-step formulation of the proposed approach is illustrated using a hypothetical example and a three-story reinforced concrete building.     

A Value Measure for Public‐Sector Enterprise Risk Management: A TSA Case Study

This article presents a public value measure that can be used to aid executives in the public sector to better assess policy decisions and maximize value to the American people. Using Transportation Security Administration (TSA) programs as an example, we first identify the basic components of public value. We then propose a public value account to quantify the outcomes of various risk scenarios, and we determine the certain equivalent of several important TSA programs. We illustrate how this proposed measure can quantify the effects of two main challenges that government organizations face when conducting enterprise risk management: (1) short‐term versus long‐term incentives and (2) avoiding potential negative consequences even if they occur with low probability. Finally, we illustrate how this measure enables the use of various tools from decision analysis to be applied in government settings, such as stochastic dominance arguments and certain equivalent calculations. Regarding the TSA case study, our analysis demonstrates the value of continued expansion of the TSA trusted traveler initiative and increasing the background vetting for passengers who are afforded expedited security screening.     

Preference Functions for Spatial Risk Analysis

When outcomes are defined over a geographic region, measures of spatial risk regarding these outcomes can be more complex than traditional measures of risk. One of the main challenges is the need for a cardinal preference function that incorporates the spatial nature of the outcomes. We explore preference conditions that will yield the existence of spatial measurable value and utility functions, and discuss their application to spatial risk analysis. We also present a simple example on household freshwater usage across regions to demonstrate how such functions can be assessed and applied.     

Presenting Uncertainty in Health Risk Assessment: Initial Studies of Its Effects on Risk Perception and Trust

Some analysts suggest that discussing uncertainties in health risk assessments might reduce citizens'perceptions of risk and increase their respect for the risk-assessing agency. We tested this assumption with simulated news stories varying simple displays of uncertainty (e.g., a range of risk estimates, with and without graphics). Subjects from Eugene, Oregon, read one story each, and then answered a questionnaire. Three studies tested between 180 and 272 subjects each. Two focus groups obtained more detailed responses to these stories. The results suggested that (1) people are unfamiliar with uncertainty in risk assessments and in science; (2) people may recognize uncertainty when it is presented simply; (3) graphics may help people recognize uncertainty; (4) reactions to the environmental problems in the stories seemed affected less by presentation of uncertainty than by general risk attitudes and perceptions; (5) agency discussion of uncertainty in risk estimates may signal agency honesty and agency incompetence for some people; and (6) people seem to see lower risk estimates (10^-6, as opposed to 10^-3) as less credible. These findings, if confirmed, would have important implications for risk communication.     

Decision Making for Group Risk Reduction: Dealing with Epistemic Uncertainty

Group risk is usually represented by FN curves showing the frequency of different accident sizes for a given activity. Many governments regulate group risk through FN criterion lines, which define the tolerable location of an FN curve. However, to compare different risk reduction alternatives, one must be able to rank FN curves. The two main problems in doing this are that the FN curve contains multiple frequencies, and that there are usually large epistemic uncertainties about the curve. Since the mid 1970s, a number of authors have used the concept of “disutility” to summarize FN curves in which a family of disutility functions was defined with a single parameter controlling the degree of “risk aversion.” Here, we show it to be risk neutral, disaster averse, and insensitive to epistemic uncertainty on accident frequencies. A new approach is outlined that has a number of attractive properties. The formulation allows us to distinguish between risk aversion and disaster aversion, two concepts that have been confused in the literature until now. A two‐parameter family of disutilities generalizing the previous approach is defined, where one parameter controls risk aversion and the other disaster aversion. The family is sensitive to epistemic uncertainties. Such disutilities may, for example, be used to compare the impact of system design changes on group risks, or might form the basis for valuing reductions in group risk in a cost‐benefit analysis.     

Integrated Uncertainty Analysis for Ambient Pollutant Health Risk Assessment: A Case Study of Ozone Mortality Risk

The U.S. Environmental Protection Agency (EPA) uses health risk assessment to help inform its decisions in setting national ambient air quality standards (NAAQS). EPA's standard approach is to make epidemiologically‐based risk estimates based on a single statistical model selected from the scientific literature, called the “core” model. The uncertainty presented for “core” risk estimates reflects only the statistical uncertainty associated with that one model's concentration‐response function parameter estimate(s). However, epidemiologically‐based risk estimates are also subject to “model uncertainty,” which is a lack of knowledge about which of many plausible model specifications and data sets best reflects the true relationship between health and ambient pollutant concentrations. In 2002, a National Academies of Sciences (NAS) committee recommended that model uncertainty be integrated into EPA's standard risk analysis approach. This article discusses how model uncertainty can be taken into account with an integrated uncertainty analysis (IUA) of health risk estimates. It provides an illustrative numerical example based on risk of premature death from respiratory mortality due to long‐term exposures to ambient ozone, which is a health risk considered in the 2015 ozone NAAQS decision. This example demonstrates that use of IUA to quantitatively incorporate key model uncertainties into risk estimates produces a substantially altered understanding of the potential public health gain of a NAAQS policy decision, and that IUA can also produce more helpful insights to guide that decision, such as evidence of decreasing incremental health gains from progressive tightening of a NAAQS.     

Variability and Uncertainty Meet Risk Management and Risk Communication

In the past decade, the use of probabilistic risk analysis techniques to quantitatively address variability and uncertainty in risks increased in popularity as recommended by the 1994 National Research Council that wrote Science and Judgment in Risk Assessment. Under the 1996 Food Quality Protection Act, for example, the U.S. EPA supported the development of tools that produce distributions of risk demonstrating the variability and/or uncertainty in the results. This paradigm shift away from the use of point estimates creates new challenges for risk managers, who now struggle with decisions about how to use distributions in decision making. The challenges for risk communication, however, have only been minimally explored. This presentation uses the case studies of variability in the risks of dying on the ground from a crashing airplane and from the deployment of motor vehicle airbags to demonstrate how better characterization of variability and uncertainty in the risk assessment lead to better risk communication. Analogies to food safety and environmental risks are also discussed. This presentation demonstrates that probabilistic risk assessment has an impact on both risk management and risk communication, and highlights remaining research issues associated with using improved sensitivity and uncertainty analyses in risk assessment.     

Uncertainty in Cancer Risk Estimates

Several existing databases compiled by Gold et al.^(1–3) for carcinogenesis bioassays are examined to obtain estimates of the reproducibility of cancer rates across experiments, strains, and rodent species. A measure of carcinogenic potency is given by the TD₅₀ (daily dose that causes a tumor type in 50% of the exposed animals that otherwise would not develop the tumor in a standard lifetime). The lognormal distribution can be used to model the uncertainty of the estimates of potency (TD₅₀) and the ratio of TD₅₀'s between two species. For near-replicate bioassays, approximately 95% of the TD₅₀'s are estimated to be within a factor of 4 of the mean. Between strains, about 95% of the TD₅₀'s are estimated to be within a factor of 11 of their mean, and the pure genetic component of variability is accounted for by a factor of 6.8. Between rats and mice, about 95% of the TD₅₀'s are estimated to be within a factor of 32 of the mean, while between humans and experimental animals the factor is 110 for 20 chemicals reported by Allen et al.⁽⁴⁾ The common practice of basing cancer risk estimates on the most sensitive rodent species-strain-sex and using interspecies dose scaling based on body surface area appears to overestimate cancer rates for these 20 human carcinogens by about one order of magnitude on the average. Hence, for chemicals where the dose-response is nearly linear below experimental doses, cancer risk estimates based on animal data are not necessarily conservative and may range from a factor of 10 too low for human carcinogens up to a factor of 1000 too high for approximately 95% of the chemicals tested to date. These limits may need to be modified for specific chemicals where additional mechanistic or pharmacokinetic information may suggest alterations or where particularly sensitive subpopu-lations may be exposed. Supralinearity could lead to anticonservative estimates of cancer risk. Underestimating cancer risk by a specific factor has a much larger impact on the actual number of cancer cases than overestimates of smaller risks by the same factor. This paper does not address the uncertainties in high to low dose extrapolation. If the dose-response is sufficiently nonlinear at low doses to produce cancer risks near zero, then low-dose risk estimates based on linear extrapolation are likely to overestimate risk and the limits of uncertainty cannot be established.     

Implications of Excessive Precision for Risk Comparisons: Lessons from the Past Four Decades

This article reviews five published "second-order" risk comparisons from the past four decades that implied precise understanding, and hence clear relationships or orderings, of the underlying risks. "Second order" here refers to efforts that extract information from original sources with the goal of relating diverse findings. All five of these publications have frequently been cited in the peer-reviewed literature and/or in risk regulatory debate in the United States. Each is associated with at least one contemporaneous critique that the findings were excessively precise. None of these critiques suggested that an alternative relationship or ordering of the risks evaluated was more appropriate. Instead, each critique concluded that alternative, contradictory relationships were at least as plausible given data and/or analytical limitations. In one case, the critique led to the withdrawal of the original publication. The original findings have been propagated or used uncritically in subsequent literature, including political support for cost-effectiveness analysis. In other cases, the critiques have been used to discredit quantitative risk analysis in general, especially in the cases of nuclear power and cost-benefit analysis. Both of these outcomes are undesirable. Future risk comparisons should avoid excessive precision, include explicit discussion of uncertainty, and differentiate between plausible estimates and expected values.     

Unternehmensbewertung unter Unsicherheit: Zur entscheidungstheoretischen Fundierung der Risikoanalyse

Zusammenfassung  Zur Bewertung von Unternehmen beziehungsweise von risikobehafteten Zahlungsstr?men gibt es im Wesentlichen vier Ans?tze, n?mlich erstens der rein individualistische Ansatz unter ausschlie?licher Verwendung multiattributiver (= multivariater) Risikonutzenfunktionen, zweitens hybride Ans?tze, die den individualistischen Ansatz mit einem perfekten Geldmarkt zu verbinden suchen, drittens die CAPM-basierte Methodik und schlie?lich viertens der auf der no-arbitrage Bedingung aufbauende Ansatz im Rahmen eines reichhaltigen (perfekten und vollst?ndigen) Kapitalmarkts. Die Arbeit besch?ftigt sich mit einem wichtigen Aspekt des hybriden (semi-subjektiven, semi-objektiven, ...) Ansatzes. Bei Existenz eines perfekten Geldmarkts kann der zu bewertende Zahlungsstrom durch risikolose Anlage-beziehungsweise Verschuldungsaktivit?ten transformiert werden; dabei bleibt die intertemporale Abh?ngigkeitsstruktur unberührt. Beeinflussen derartige Transformationen das für Bewertungsfragen relevante Sicherheits?quivalent nicht, so bezeichnen wir die zu Grunde liegende multiattributive Risikonutzenfunktion als geldmarktinvariant. Die Klasse der geldmarktinvarianten Risikonutzenfunktionen wird vollst?ndig charakterisiert. Ferner wird die entscheidungstheoretische Fundierung der Risikoanalyse gekl?rt.

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On the evaluation of risky streams: theoretical underpinnings of the risk analysis

Summary  There are several approaches to the valuation of risky streams: Firstly, the pure individualistic approach stemming from multiperiod (= multiattributed, multivariate) utility functions, secondly, the individualistic approach combined with the ingredients (risk-free rate) of a perfect money market, thirdly, CAPM-based approaches, and finally, the no-arbitrage valuation in the framework of perfect and complete capital markets. The paper deals with an important aspect of the second approach. A multiperiod utility function is called moneymarket invariant if the (time zero) certainty equivalent is independent of (arbitrary but non-stochastic) borrowing and lending activities. The invariant utility functions are completely characterized. Moreover, the paper clarifies the theoretical underpinnings of the risk analysis.

     

How Business Interests and Government Inaction Led to the Humidifier Disinfectant Disaster in South Korea: Implications for Better Risk Governance

Humidifier sterilizers were regarded as innovative and health-promoting products; they were widespread in South Korea until 2011. However, hospitals reported mysterious deaths, and a legal investigation in April 2016 found that hundreds of people have died due to use of the sterilizing disinfectant. This article takes up that topic, discussing the government's role in dealing with the risk regarding the humidifier disinfectant. We pay particular attention to the unequal nature of the uncertainty produced by the distorted socioeconomic structure. Through in-depth interviews with key informants and an examination of relevant documents from the government, civic groups, and newspapers, we find that the government had increasingly acknowledged the risk, yet their inaction failed to stop the high number of casualties, and they have only recently responded proactively. The uncertainty of the risk was unevenly distributed between companies, the government, experts, and citizens. We argue that the proactive and transparent role of the government with the precautionary principle could fix the unequal structure of knowledge production and preserve public health.     

Equity in Social Risk: Some Empirical Observations

In societal risk analysis the equity of the distribution of risks is often an important consideration owing to the special nature of health risks. We empirically validate some assumptions about equity that have been discussed in the decision analytic literature. Our results show that the way fatalities are distributed throughout a society is considered along with the number of fatalities in evaluating alternative policies involving mortality risks. The concepts of ex ante equity and ex post equity are both shown to be important in judgments of fairness. We next present a decision model based on multiattribute preference theory incorporating the number of fatalities, as well as ex ante equity and ex post equity. When ex ante equity and ex post equity are positively weighted in this fair-risk model , options with more equal risk distributions are ranked higher. Next we empirically show that the distribution of benefits has an impact on judgments of fairness. The fair-risk model does not include information on the benefits distribution, so it would apply when benefits are distributed equally or when the decision maker wishes to not include benefits in the model. We briefly discuss how the notion of proportional equity can incorporate benefits into judgments of the fairness of risk distributions. We then include benefits in a more general model in which fair risk-benefit combinations are those that are exchange equitable. A key implication of this envy-free risk–benefit model is that an unequal distribution of risks may be preferred if it is accompanied by a compensatory differential in benefits consistent with peoples' preference tradeoffs between received benefits and assumed risks. Finally, we discuss how perceived deservedness may influence judgments about equity. We conclude with a discussion of the implications of research on alternative notions of equity for policy makers dealing with social risks.