Risk perception, ambiguity, and nuclear-waste transport.

• Author: Riddel, Mary

1. Introduction

   Ellsberg (1961, p. 643) defines ambiguity as "a quality depending upon the amount, type, reliability and 'unanimity' of information, and giving rise to one's degree of 'confidence' in an estimate of relative likelihoods." Welfare models aimed at valuing changes from baseline mortality risk are typically based on the expected-utility (EU) model, where risk distributions are necessarily degenerate at some certain, predetermined risk. However, a growing body of work suggests that risk and ambiguity both affect risky choices and, therefore, the value of reducing mortality risks (Viscusi and Magat 1992; Cameron 2005; Riddel and Schwer 2006; Riddel and Shaw 2006). As a result, a comprehensive welfare model should recognize the influence of both risk and ambiguity on choices and behavior.

   Although ambiguity has received ample attention in the theoretical EU literature, measures of ambiguity are rare. Indeed, there is no clear consensus as to how to elicit and estimate ambiguity. In this paper, I present a framework for eliciting and estimating risk and ambiguity simultaneously using a risk ladder. The resulting risk and ambiguity measures can ultimately be used to value changes in risk resulting from public programs or policies. The model, based on a variant of the induced-distribution model of Hill, Perry, and Willis (2007), allows me to estimate risk and ambiguity jointly and derive the correlation between the two. It has the additional advantage of explicitly allowing for flexible heterogeneity and measurement error in the perceived risk distribution.

   I provide an empirical example of the method using data from a survey addressing mortality risks related to transporting high-level radioactive waste to the proposed Yucca Mountain storage facility in Nye County, Nevada. I estimate median perceived risk and ambiguity as a function of demographic variables, distance from the proposed nuclear-waste transport route, and knowledge of the project. Although numerous studies have used risk ladders to elicit subjective-risk estimates, this survey is the first, to my knowledge, to elicit ambiguity.

   The results suggest that, on average, the public perceives nuclear-waste transport risk well in excess of that estimated by the U.S. Department of Energy (DOE). Information is shown to be of vital importance in the formation of individual risk perception. Moreover, the number of sources of information that a subject has considered is positively related to subject uncertainty. I infer that subjects view conflicting information as evidence of ambiguity.

2. Past Research Concerning Ambiguity Elicitation and Estimation

   Elicitation

   Studies show that visual aids are often a critical component of risk elicitation (Lundgren and McMakin 2004). Standard visual aids include risk ladders (see Mitchell and Carson 1986; Hammitt 1990; Loomis and duVair 1993; and Corso, Hammitt, and Graham 2001), dot and pie charts (see Jones-Lee, Hammerton, and Philips 1985), and verbal analogies (Hammitt and Graham 1999). Each elicitation device has strengths and weaknesses, but ladders may be the most straightforward method of eliciting risk and ambiguity jointly. Risk ladders have the appealing property of eliciting willingness-to-pay estimates that are nearly proportionate to the change in risk (Corso, Hammitt, and Graham 2001). This property is not shared by pie charts. Moreover, the rungs of the ladder provide a visual expression of risk; whereas, the distance between rungs spans a range of uncertainty, or ambiguity, about the risk. As a result, the ladder naturally yields a visual aid for simultaneously depicting a "most likely" risk estimate together with uncertainty surrounding this estimate. Other risk-communication devices do not have this property.

   Models of Ambiguity

   In early experiments by Savage (1954) and Ellsberg (1961), subjects preferred known risks over equivalent risks that were perceived to be uncertain. Much of the subsequent work on ambiguity focused on how new information affects decision formation and perceived risk. In this vein, Viscusi and Magat (1992) create posterior risk distributions by analyzing preferences over ambiguous health lotteries. Subjects were familiarized with diseases associated with environmental degradation and presented with two pieces of contradicting risk information, both stated in terms of the number of disease cases per one million residents for some area of interest A. The conflicting information was meant to induce ambiguity about the perceived risk. Subjects were then asked to state the single risk level that would make certain risks in some prescribed area B equivalent to the ambiguous risk in A. The posterior probability is then a function of the influence of ambiguity on belief formation, the subject's prior beliefs, and the informational content presented to the subject. The authors construct and test alternative models of belief formation assuming that risk follows the beta distribution.

   Delavande (2008) examines how women use new information to update prior pregnancy expectations while using birth control. Subjects are queried about their beliefs concerning the overall likelihood of getting pregnant using a new, fictitious birth-control method. Assuming that effectiveness is a random variable, Delavande then elicits three points along the prior subjective cumulative distribution function. Subjects are then given information about the pregnancy outcomes for other women using the method, and the posterior distribution is elicited in a similar manner. Like Viscusi and Magat (1992), she assumes that the prior and posterior expectations follow the beta distribution.

   A more recent study by Cameron (2005), designed to estimate welfare values for mitigating global-warming risks, elicits the distribution of future mean global temperatures. She first elicits expected mean global temperatures for the years 2011-2020. For the dispersion measure, she asks subjects to state "plus" and "minus" amounts that yield a 95% confidence interval around their stated expected value. After subjects read information from scientific and advocacy groups about global warming, she elicits the new risk distribution and analyzes the effects of new information.

   Riddel and Shaw (2006) and Riddel and Schwer (2006) study perceived risks from nuclear-waste transport using a phone-mail-phone survey. (1) Risk and ambiguity are elicited using the risk-ladder approach described below. As in previous studies, they assume that perceived risk follows the beta distribution. They use the estimates of risk and ambiguity to obtain welfare estimates for reducing the perceived mortality risk from transport.

   The elicitation methods, particularly those used by Cameron (2005) and Delavande (2008), may be inappropriate when surveying the general public. Cameron's subjects were undergraduate students in summer-session economics courses at the University of California, Los Angeles, while Delavande uses subjects primarily composed of college students at Northwestern University and Truman College. College students are more likely to be familiar with the concept of confidence intervals and distribution functions than the general public. Indeed, subjects in my survey-design focus groups displayed a strong preference for the risk ladder and eschewed the cumulative distribution function method as complicated and difficult to understand. In one multiyear study of risk communication, media outlets overwhelmingly preferred to portray ambiguity using a series of ranges rather than a cumulative distribution function, even when both methods were provided, suggesting that ranges are a more manageable communication device (Lundgren and McMakin 2004, p. 239).

   The choice of risk distributions in these earlier studies is also problematic. Cameron (2005) assumes a symmetric normal distribution. Indeed, my findings show that the risk distribution for nuclear-waste transport risk is markedly positively skewed, and the normal distribution would be inappropriate. Viscusi and Magat (1992), Riddel and Shaw (2006), and Delavande (2008) use the beta distribution. While the beta distribution's flexible shape and natural bounding on the zero-one interval make it a candidate for estimating perceived risk, it has significant drawbacks, both in terms of estimation and motivating theory. Because so many shapes are possible, the likelihood surface may have many local maxima, and a global maximum is not assured. Convergence can be a problem, and atypical estimation schemes, like that used by Riddel and Shaw (2006), are often necessary. An even more serious drawback is that the fixed relationship between the mean (perceived risk) and variance (ambiguity) requires that the marginal impact of any independent variable on risk and ambiguity be constrained by the relationship between the mean and variance of the beta distribution. In other words, the model does not allow different forces to determine perceived risk and ambiguity.

   In response to these concerns, Hill, Perry, and Willis (2007) estimate the risk distribution for a subject's beliefs about the likelihood of survival to a predetermined age based on an index function model using data from the Health and Retirement Study. This induced-distribution (ID) approach, like that in Heckman and Willis (1977), explicitly accounts for subject heterogeneity and measurement errors that are likely to occur when using survey data. Further, it readily allows different variables to determine risk and ambiguity while permitting flexible correlation between the two.

   In the current study, I propose a variant of the model described by Hill, Perry, and Willis (2007) that is modified to accommodate range data elicited using the risk ladder. I apply the model to a survey-based study of the determinants of the perceived risk distribution related to nuclear-waste transport to the proposed repository at Yucca Mountain, Nevada. The...