Measurement error, skewness, and risk analysis: coping with the long tail of the distribution.

Probabilistic risk analyses often construct multistage chance trees to estimate the joint probability of compound events. If random measurement error is associated with some or all of the estimates, we show that resulting estimates of joint probability may be highly skewed. Joint probability estimates based on the analysis of multistage chance trees are more likely than not to be below the true probability of adverse events, but will sometimes substantially overestimate them. In contexts such as insurance markets for environmental risks, skewed distributions of risk estimates amplify the "winner's curse" so that the estimated risk premium for low-probability events is likely to be lower than the normative value. Skewness may result even in unbiased estimators of expected value from simple lotteries, if measurement error is associated with both the probability and pay-off terms. Further, skewness may occur even if the error associated with these two estimates is symmetrically distributed. Under certain circumstances, skewed estimates of expected value may result in risk-neutral decisionmakers exhibiting a tendency to choose a certainty equivalent over a lottery of equal expected value, or vice versa. We show that when distributions of estimates of expected value are, positively skewed, under certain circumstances it will be optimal to choose lotteries with nominal values lower than the value of apparently superior certainty equivalents. Extending the previous work of Goodman (1960), we provide an exact formula for the skewness of products.     

Patterns of Conflict About Risky Technologies

This paper examines taxonomies for classifying risks and conflicts about risky technologies. First, we describe six levels of conflict that represent various " shades of gray" between purely factual and purely value laden conflicts in technology disputes. Subsequently, we survey several recent taxonomies of risks and hazards that were at least partly intended to clarify the nature of the public conflicts about technologies and their risks. After pointing out that non-risk features frequently shape technology debates, we develop a taxonomy of the disputes themselves, based on a collection of 162 cases. Our taxonomy of technological controversies is related to the recent risk taxonomies and to the different levels of conflict. It turns out that the different technological disputes create quite different levels of conflict ranging from mainly factual (consumer products, drugs) to extremely value laden (nuclear power, genetic engineering). Depending on the type of controversy and level of conflict we suggest alternative conflict management strategies.     

突发事件公众准备意愿的影响因素——基于实证数据的分析

突发事件是"低概率、高损失"的极端事件。突发事件风险客观存在,公众的应对准备意愿及行为对减缓突发事件风险及降低突发事件损失有着重要影响。但实际上,公众普遍表现出较弱的准备意愿,很少主动采取准备措施及行为。为了解释公众为避免突发事件损失而事先采取应对准备的行为差异,本文基于实证调查数据,将保护动机理论（PMT）应用于公众准备意愿的预测研究,建立突发事件公众认知与准备意愿理论模型,运用多元回归分析及结构方程模型方法,验证公众风险认知、应对认知与准备意愿之间的路径关系。其中风险认知包括可能性和严重性认知两个变量,应对认知包括应对效能、自我效能和应对成本认知三个变量。实证数据通过问卷调查的方式获取,调查对象涉及湖北省武汉市七大行政区域共405位城区居民。数据分析结果表明,公众的准备意愿受到风险认知及应对认知的共同影响,相比于风险认知,应对认知对准备意愿有更大的解释效力;年龄、教育程度、收入等三类人口统计学特征对准备意愿有一定的解释效力。研究结论显示,为了促使公众形成准备意愿,风险沟通不仅应考虑突发事件风险发生的可能性及后果的严重性,更需要关注应对效能、自我效能以及应对成本等对公众准备意愿有着显著影响的因素。     

Public Distrust and Hazard Management Success at the Rocky Flats Nuclear Weapons Plant

Based on experience gained while serving a public oversight commission appointed by the governor of Colorado, hazard management at the Department of Energy's Rocky Flats nuclear weapons plant is reviewed. Specific reference is made to the plant's history of controversy, its defense-in-depth strategy of hazard control, occupational health issues, public exposure to plutonium, and the assessment of low-probability, high-consequence risks. This leads to the conclusion that Rocky Flats is, by any objective standard, a hazard management success. It follows that public distrust of Rocky Flats arises as much from fear and loathing of nuclear weapons themselves as from the manufacturing process by which they are made.     

Further Effects of Lottery Odds on Responding

Lotteries (i.e., probabilistic bonus contingencies) are an established intervention in Organizational Behavior Management. Although common, there are many permutations of lotteries used in literature and they are often combined with other interventions. One key variable that may influence the effectiveness of lotteries are the odds that the lottery will pay out to those who earn entry. The current investigation evaluated a lottery intervention with varied payout chances (25%, 12%, 6%, or 3%). A 6% chance of winning was the lowest odds of winning where responding was reliably maintained across two participants. Implications of these results and future direction for research are discussed below.     

A New Theoretical Discrete Growth Distribution with Verification for Microbial Counts in Water

Living microbes are discrete, not homogeneously distributed in environmental media, and the form of the distribution of their counts in drinking water has not been well established. However, this count may "scale" or range over orders of magnitude over time, in which case data representing the tail of the distribution, and governing the mean, would be represented only in impractically long data records. In the absence of such data, knowledge of the general form of the full distribution could be used to estimate the true mean accounting for low-probability, high-consequence count events and provide a basis for a general environmental dose-response function. In this article, a new theoretical discrete growth distribution (DGD) is proposed for discrete counts in environmental media and other discrete growth systems. The term growth refers not to microbial growth but to a general abiotic first-order growth/decay of outcome sizes in many complex systems. The emergence and stability of the DGD in such systems, defined in simultaneous work, are also described. The DGD is then initially verified versus 12 of 12 simulated long-term drinking water and short-term treated and untreated water microbial count data sets. The alternative Poisson lognormal (PLN) distribution was rejected for 2 (17%) of the 12 data sets with 95% confidence and, like other competitive distributions, was not found stable (in simultaneous work). Sample averages are compared with means assessed from the fitted DGD, with varying results. Broader validation of the DGD for discrete counts arising as outcomes of mathematical growth systems is suggested.     

Risk Perception and Social Acceptability of Technologies: The French Case

The authors present results of a February 1987 survey on judged frequency of mortality causes and risk perception of technologies in a representative sample of the French population. Although the French context is very different, and the impact of public controversies have been very limited on technological choices such as the nuclear energy program, strong similarities in risk perception of technologies are observed with results from U.S. surveys. Results, which could be worthwhile for other countries, suggest that risk perception is influenced by two different types of components. The first influence is the global feeling of "security" that society procures to its members. Such feeling depends on the individual's socioeconomic status, subjective state of health, and personal discomfort in daily life, and explains individual aversion to risk independently of the mortality causes or technologies involved. The second influence is the degree of perceived social legitimization of the activities involving risks. Risks of medical and transportation activities are strongly opposed to illegitimate risky behaviors (smoking, drugs, alcohol); technologies which have been an object of public debate (nuclear plants, the chemical industry, lead in gasoline) have an intermediate position reflecting the remaining uncertainties of public opinion about their risk–benefit balancing. Tentative conclusions for risk communication are proposed.     

The Effect of School Choice on Participants: Evidence from Randomized Lotteries

School choice has become an increasingly prominent strategy for enhancing academic achievement. To evaluate the impact on participants, we exploit randomized lotteries that determine high school admission in the Chicago Public Schools. Compared to those students who lose lotteries, students who win attend high schools that are better in a number of dimensions, including peer achievement and attainment levels. Nonetheless, we find little evidence that winning a lottery provides any systematic benefit across a wide variety of traditional academic measures. Lottery winners do, however, experience improvements on a subset of nontraditional outcome measures, such as self‐reported disciplinary incidents and arrest rates.     

Scale invariance of incident size distributions in response to sizes of their causes.

Incidents can be defined as low-probability, high-consequence events and lesser events of the same type. Lack of data on extremely large incidents makes it difficult to determine distributions of incident size that reflect such disasters, even though they represent the great majority of total losses. If the form of the incident size distribution can be determined, then predictive Bayesian methods can be used to assess incident risks from limited available information. Moreover, incident size distributions have generally been observed to have scale invariant, or power law, distributions over broad ranges. Scale invariance in the distributions of sizes of outcomes of complex dynamical systems has been explained based on mechanistic models of natural and built systems, such as models of self-organized criticality. In this article, scale invariance is shown to result also as the maximum Shannon entropy distribution of incident sizes arising as the product of arbitrary functions of cause sizes. Entropy is shown by simulation and derivation to be maximized as a result of dependence, diversity, abundance, and entropy of multiplicative cause sizes. The result represents an information-theoretic explanation of invariance, parallel to those of mechanistic models. For example, distributions of incident size resulting from 30 partially dependent causes are shown to be scale invariant over several orders of magnitude. Empirical validation of power law distributions of incident size is reviewed, and the Pareto (power law) distribution is validated against oil spill, hurricane, and insurance data. The applicability of the Pareto distribution, in particular, for assessment of total losses over a planning period is discussed. Results justify the use of an analytical, predictive Bayesian version of the Pareto distribution, derived previously, to assess incident risk from available data.     

Random Expected Utility

We develop and analyze a model of random choice and random expected utility. A decision problem is a finite set of lotteries that describe the feasible choices. A random choice rule associates with each decision problem a probability measure over choices. A random utility function is a probability measure over von Neumann–Morgenstern utility functions. We show that a random choice rule maximizes some random utility function if and only if it is mixture continuous, monotone (the probability that a lottery is chosen does not increase when other lotteries are added to the decision problem), extreme (lotteries that are not extreme points of the decision problem are chosen with probability 0), and linear (satisfies the independence axiom).     

Natural Disasters in the United States as Release Agents of Oil, Chemicals, or Radiological Materials Between 1980-1989: Analysis and Recommendations

Generally, hazards research and literature has treated natural and technological disasters as separate entities. This study attempts to determine how frequently interaction between these two types of disaster took place in the United States from 1980-1989. Data were collected by performing a literature review, contacting organizations and individuals active in hazards research and mitigation, and through a questionnaire sent to the emergency management agencies of all 50 states. The consensus derived from the data is that the number of incidents where natural and technological disasters interact is rising while preparations, which recognize the complications inherent in such combined events, remain cursory. There is a pressing need for states to record, and make available to managers, information regarding the number of combined natural/technological events affecting their areas. Only when such data are available will it be possible to make appropriate decisions regarding the best way to reduce the effects of a natural disaster causing a catastrophic release of hazardous materials.     

LP/HC and LULUs: The Political Uses of Risk Analysis in Land-Use Planning1

This paper examines how LP/HC (low-probability/high-consequence) risk analysis is used in planning for locally unwanted land uses, or LULUs. LULUs are development projects that are predictably objectionable to many of their neighbors. Examples are nuclear power plants, hazardous waste facilities, refineries, and airports. The paper begins by elaborating the idea of LULUs, focussing on those whose planning typically requires or invokes some form of LP/HC risk analysis. It then discusses how land planning and planners actually use the LP/HC approach to deal with LULUs. It argues that in practice land-use planners and their associates employ a concept of risk different from that of economists, scientists, and engineers and more like that of political decision-makers and the public at large. It concludes with a political interpretation that offers some suggestions for productively reducing this divergence in the treatment of LULUs that pose LP/HC risks.     

Implicit Attitudes Toward Nuclear Power and Mobile Phone Base Stations: Support for the Affect Heuristic

The implicit association test (IAT) measures automatic associations. In the present research, the IAT was adapted to measure implicit attitudes toward technological hazards. In Study 1, implicit and explicit attitudes toward nuclear power were examined. Implicit measures (i.e., the IAT) revealed negative attitudes toward nuclear power that were not detected by explicit measures (i.e., a questionnaire). In Study 2, implicit attitudes toward EMF (electro-magnetic field) hazards were examined. Results showed that cell phone base stations and power lines are judged to be similarly risky and, further, that base stations are more closely related to risk concepts than home appliances are. No differences between experts and lay people were observed. Results of the present studies are in line with the affect heuristic proposed by Slovic and colleagues. Affect seems to be an important factor in risk perception.     

Taxonomic Analysis of Perceived Risk: Modeling Individual and Group Perceptions Within Homogeneous Hazard Domains

Previous studies of risk perception have typically focused on the mean judgments of a group of people regarding the riskiness (or safety) of a diverse set of hazardous activities, substances, and technologies. This paper reports the results of two studies that take a different path. Study 1 investigated whether models within a single technological domain were similar to previous models based on group means and diverse hazards. Study 2 created a group taxonomy of perceived risk for only one technological domain, railroads, and examined whether the structure of that taxonomy corresponded with taxonomies derived from prior studies of diverse hazards. Results from Study 1 indicated that the importance of various risk characteristics in determining perceived risk differed across individuals and across hazards, but not so much as to invalidate the results of earlier studies based on group means and diverse hazards. In Study 2, the detailed analysis of railroad hazards produced a structure that had both important similarities to, and dissimilarities from, the structure obtained in prior research with diverse hazard domains. The data also indicated that railroad hazards are really quite diverse, with some approaching nuclear reactors in their perceived seriousness. These results suggest that information about the diversity of perceptions within a single domain of hazards could provide valuable input to risk-management decisions.     

Bridging the Gap between Social Acceptance and Ethical Acceptability

New technology brings great benefits, but it can also create new and significant risks. When evaluating those risks in policymaking, there is a tendency to focus on social acceptance. By solely focusing on social acceptance, we could, however, overlook important ethical aspects of technological risk, particularly when we evaluate technologies with transnational and intergenerational risks. I argue that good governance of risky technology requires analyzing both social acceptance and ethical acceptability. Conceptually, these two notions are mostly complementary. Social acceptance studies are not capable of sufficiently capturing all the morally relevant features of risky technologies; ethical analyses do not typically include stakeholders’ opinions, and they therefore lack the relevant empirical input for a thorough ethical evaluation. Only when carried out in conjunction are these two types of analysis relevant to national and international governance of risky technology. I discuss the Rawlsian wide reflective equilibrium as a method for marrying social acceptance and ethical acceptability. Although the rationale of my argument is broadly applicable, I will examine the case of multinational nuclear waste repositories in particular. This example will show how ethical issues may be overlooked if we focus only on social acceptance, and will provide a test case for demonstrating how the wide reflective equilibrium can help to bridge the proverbial acceptance‐acceptability gap.     

Preferences for One‐Shot Resolution of Uncertainty and Allais‐Type Behavior

Experimental evidence suggests that individuals are more risk averse when they perceive risk that is gradually resolved over time. We address these findings by studying a decision maker who has recursive, nonexpected utility preferences over compound lotteries. The decision maker has preferences for one‐shot resolution of uncertainty if he always prefers any compound lottery to be resolved in a single stage. We establish an equivalence between dynamic preferences for one‐shot resolution of uncertainty and static preferences that are identified with commonly observed behavior in Allais‐type experiments. The implications of this equivalence on preferences over information systems are examined. We define the gradual resolution premium and demonstrate its magnifying effect when combined with the usual risk premium.     

Cautious Expected Utility and the Certainty Effect

Many violations of the independence axiom of expected utility can be traced to subjects' attraction to risk‐free prospects. The key axiom in this paper, negative certainty independence ([Dillenberger, 2010]), formalizes this tendency. Our main result is a utility representation of all preferences over monetary lotteries that satisfy negative certainty independence together with basic rationality postulates. Such preferences can be represented as if the agent were unsure of how to evaluate a given lottery p; instead, she has in mind a set of possible utility functions over outcomes and displays a cautious behavior: she computes the certainty equivalent of p with respect to each possible function in the set and picks the smallest one. The set of utilities is unique in a well defined sense. We show that our representation can also be derived from a “cautious” completion of an incomplete preference relation.     

Risk Management Solutions for Climate Change–Induced Disasters

In honor of the 40th anniversary of Risk Analysis, this article suggests ways of linking risk assessment and risk perception in developing risk management strategies that have a good chance of being implemented, focusing on the problem of reducing losses from natural hazards in the face of climate change. Following a checklist for developing an implementable risk management strategy, Section 2 highlights the impact that exponential growth of CO₂ emissions is likely to have on future disaster losses as assessed by climate and social scientists. Section 3 then discusses how people perceive the risks of low-probability adverse events and the cognitive biases that lead them to underprepare for future losses. Based on this empirical evidence, Section 4 proposes a risk management strategy for reducing future losses using the principles of choice architecture to communicate the likelihood and consequences of disasters, coupled with economic incentives and well-enforced regulations.     

Personal Values, Beliefs, and Ecological Risk Perception

A mail survey on ecological risk perception was administered in the summer of 2002 to a randomized sample of the lay public and to selected risk professionals at the U.S. Environmental Protection Agency (US EPA). The ranking of 24 ecological risk items, from global climate change to commercial fishing, reveals that the lay public is more concerned about low-probability, high-consequence risks whereas the risk professionals are more concerned about risks that pose long-term, ecosystem-level impacts. To test the explanatory power of the value-belief-norm (VBN) theory for risk perception, respondents were questioned about their personal values, spiritual beliefs, and worldviews. The most consistent predictors of the risk rankings are belief in the new ecological paradigm (NEP) and Schwartz's altruism. The NEP and Schwartz's altruism explain from 19% to 46% of the variance in the risk rankings. Religious beliefs account for less than 6% of the variance and do not show a consistent pattern in predicting risk perception although religious fundamentalists are generally less concerned about the risk items. While not exerting as strong an impact, social-structural variables do have some influence on risk perception. Ethnicities show no effect on the risk scales but the more educated and financially well-off are less concerned about the risk items. Political leanings have no direct influence on risk rankings, but indirectly affect rankings through the NEP. These results reveal that the VBN theory is a plausible explanation for the differences measured in the respondents' perception of ecological risk.     

When Does Information about Probability Count in Choices Under Risk?

The question addressed in the present research is whether in naturalistic risky decision environments people are sensitive to information about the probability parameter. In Study 1, we showed that in naturalistic scenarios participants generally revealed little interest in obtaining information about the outcomes and probabilities. Moreover, participants asked fewer questions about probabilities for scenarios containing moral considerations. In Study 2, it was shown that, when supplied with information on probabilities, people could be sensitive to this information. This sensitivity depends on two factors. People were less sensitive to probabilities in scenarios perceived as containing ethical considerations. People were also less sensitive to probabilities when they were faced with a single-choice situation than when they were faced with a series of lotteries with different probabilities. This can be accounted for in terms of the evaluability principle.