Showing papers in "Journal of Risk and Uncertainty in 1992"

Advances in prospect theory: cumulative representation of uncertainty

Abstract: We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk attitudes: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability. Expected utility theory reigned for several decades as the dominant normative and descriptive model of decision making under uncertainty, but it has come under serious question in recent years. There is now general agreement that the theory does not provide an adequate description of individual choice: a substantial body of evidence shows that decision makers systematically violate its basic tenets. Many alternative models have been proposed in response to this empirical challenge (for reviews, see Camerer, 1989; Fishburn, 1988; Machina, 1987). Some time ago we presented a model of choice, called prospect theory, which explained the major violations of expected utility theory in choices between risky prospects with a small number of outcomes (Kahneman and Tversky, 1979; Tversky and Kahneman, 1986). The key elements of this theory are 1) a value function that is concave for gains, convex for losses, and steeper for losses than for gains,

Recent developments in modeling preferences: Uncertainty and ambiguity

Abstract: In subjective expected utility (SEU), the decision weights people attach to events are their beliefs about the likelihood of events. Much empirical evidence, inspired by Ellsberg (1961) and others, shows that people prefer to bet on events they know more about, even when their beliefs are held constant. (They are averse to ambiguity, or uncertainty about probability.) We review evidence, recent theoretical explanations, and applications of research on ambiguity and SEU.

Status-Quo and Omission Biases

Abstract: Bias toward the status quo, found in choice and in emotional reactions to adverse outcomes, has been confounded with bias toward omission. We unconfounded these effects with scenarios in which change occurs unless action is taken. Subjects reacted more strongly to adverse outcomes caused by action, whether the status quo was maintained or not, and subjects preferred inaction over action even when inaction was associated with change. No status-quo bias was found in a matching task, which did not require action. The observed status-quo bias is at least partly caused by a bias toward omissions.

The effect of information on health risk valuations

Abstract: This article examines the effect of familiarity with chronic lung disease on people's willingness to pay to reduce their risk of contracting chronic bronchitis, and on their willingness to increase their risk of auto death to reduce chronic bronchitis risk. We find that persons who have a relative with chronic lung disease are willing to give up more income to reduce their risk of chronic bronchitis than persons with no first-hand knowledge of the disease; however, their willingness to increase their risk of auto death to reduce their risk of chronic bronchitis is no different, on average, than persons with no first-hand knowledge of lung disease. This suggests that responses to risk-risk tradeoffs may be more stable than responses to risk-income choices.

Reinsurance and the liability insurance crisis

Abstract: Insurance-industry accounts of the liability insurance crisis of the mid-1980s often cite disruption of supply in reinsurance markets as an important contributing factor. Economic theories of the crisis have not explored this explanation for the severity of the crisis. This article investigates the extent to which events in reinsurance markets affected liability insurance market outcomes. It documents significant shocks to reinsurance supply in the early 1980s and finds evidence of subsequent disruptions to the price and availability of reinsurance. Regression analysis of liability insurance profitability over the time period supports the hypothesis that problems in reinsurance markets played an important role in the crisis.

Bayesian decisions with ambiguous belief aversion

Abstract: This study provides an empirical perspective on the effect of ambiguous environmental risk information on lottery preferences using a sample of 646 adults. The learning process follows a Bayesian expected utility model in terms of the overall magnitude and sign of the weights that respondents place on the risk information. Significant ambiguous belief aversion that is consistent with the Ellsberg paradox is also evident. The extent of this aversion increases with the size of the risk spread, but at a decreasing rate. These results are consistent with both probability-based and preference-based models of ambiguous probabilities. The findings also indicate the presence of cognitive limitations in the processing of risk information, but lead to rejection of more extreme models in which individuals respond in alarmist fashion or do not learn at all.

Reference Points, Loss Aversion, and Contingent Values for Auto Safety

Abstract: This article is concerned with the possible role of reference points and loss aversion (as suggested by prospect theory) in subjects' judgments about the value of increments and decrements in automobile safety. The contingent valuation method is employed in two experiments, both of which consider subjects' willingness-to-pay (WTP) for increased safety and compensation demanded (CD) for decreased safety in hypothetical new vehicle purchases. The results establish that disparities exist in subjects' WTP and CD values for the same increment of auto safety, even for a close-to-market context such as hypothetical new vehicle purchases. The results also indicate that evaluations can be manipulated by changing the perception of the reference point: losses can be recast as forgone gains and forgone gains as losses, altering (or even eliminating) differences between WTP and CD values.

Where Does Subjective Expected Utility Fail Descriptively

Abstract: Subjective expected utility (SEU) rests on and implies four tenets of rational preferences; transitivity, monotonicity of consequences, independence of a common consequence, and accounting equivalences. Empirical evidence against transitivity and monotonicity is reevaluated and the opposite conclusion drawn using more recent data. The more complex accounting equivalences are descriptively implausible. The three simplest—idempotence, complementarity, and event commutativity—seem to be the only ones that may be descriptive. These, coupled with the postulate of an interval scale representation, result in a rank-dependent, weighted linear generalization of SEU. Further generalizations to nonbinary mixtures and to rank-and sign-dependent representations are also described. Problems in testing these theories are discussed.

Violations of dominance in pricing judgments

Abstract: The dominance principle states that the judged price of gamble A should be equal to or greater than the judged price of gamble B whenever A's outcomes are equal to or better than the corresponding outcomes of B, holding everything else constant Subjects often violate the dominance principle by assigning a higher price to a gamble with some probability of winning a positive amount, Y, otherwise zero, than to a superior gamble with the same chances of winning Y, otherwise winning X Violations also occur with losses Results are consistent with a configural-weight theory in which the decision weight for each outcome depends on the rank of the outcome with respect to the other outcomes in the lottery and the value of the outcome (zero vs nonzero)

Propitious selection in insurance

Abstract: The theory of propitious selection suggests that there are risk-avoiding personalities who both take physical precautions and buy financial security (insurance). Conversely, there are risk seekers who tend to do neither. Survey evidence is presented that is consistent with the theory. Individuals who obtain motor vehicle liability coverage are less likely than others to drink-and-drive, and are more likely to engage in health-beneficial (risk-avoiding) behaviors. Propitious selection may be a general phenomenon promoting favorable selection in many real world insurance markets.

Ambiguity and decision modeling: A preference-based approach

Abstract: In this article, we develop a model that permits a decision maker's preferences to depend on the decision maker's ambiguity about the probability of an event that is relevant for decision-making purposes. We deal with ambiguity through preference modeling, with ambiguity leading to modifications in the utilities of outcomes. The behavior of ambiguity premiums and probability premiums as the payoffs are varied depends on the nature of the modifications in utilities. Particular forms of the model that arise under different sets of assumptions about preferences include additive, bilinear, and ratio forms. We conclude with a brief example and some thoughts about potential generalizations and implications of the model.

State-independent subjective expected lexicographic utility

Abstract: By enriching the set of acts deemed available at least as objects of assessment, we obtain a significant tightening of the linear lexicographic representation described in LaValle and Fishburn (1991a). Under the state-independent assumption that every outcome is available in every state, each state must be either completely null or completely essential (rather than lexicographically essential), and the matrices characterizing subjective probabilities of the states must be square and lower triangular with positive diagonal entries. It follows that there are straightforward generalizations of real-valued-probability relationships such as Bayes' theorem. Even in the tighter case, the matrix probabilities cannot be reduced to scalar matrices or even fully diagonal matrices. Nevertheless, they are easy to work with and permit fully consequentialist decision analysis of problems in which preferences are non-Archimedean.

An intransitive expectations-based bayesian variant of prospect theory

Abstract: Psychological experiments have established that the classical expected utility model appears descriptively inadequate. Viscusi's prospective reference theory attempts to reconcile the expected utility model with many of these experiments by supposing that individuals have prior expectations about the utility they can expect to get from lottery payoffs. Bayesian theory then implies that individuals revise lottery probabilities in light of these prior expectations before choosing among lotteries so as to maximize expected utility. But Viscusi's theory cannot account for nonmonotonic or intransitive behavior. This article develops an extension of Viscusi's model with correlated prior beliefs that does account for nonmonotonic and intransitive behavior.

The value of job safety for railroad workers

Abstract: The value of reducing job risk is estimated using a hedonic wage model and a risk variable that is matched by occupation and state of residence. This study is the first to use the hedonic wage approach to estimate the value of safety in a single industry. Industry-specific estimates will help researchers and labor policymakers better understand the distribution of compensating wage differentials across industries. Our estimated value of job safety for railroad workers is between $21,000 and $26,000 (1980 dollars) per statistical disabling injury, which is somewhat larger than the average of values estimated in previous studies that use cross-industry or crossoccupation aggregate risk data.

Subjective probabilities and utility with event-dependent preferences

Abstract: This article generalizes Savage's theory to include event-dependent preferences. The state space is partitioned into finitely many events. The induced preferences over consequences are assumed independent of the underlying states within, but not across, these events. This results in an additively separable representation of preferences over acts. The dependence of the preference relation over consequences on the events is represented by event-dependent mappings of the set of consequences onto itself. Given these mappings, the preferences on acts are represented by the expectation of event-dependent utilities on the consequences with respect to unique subjective probabilities on the states.

Adverse selection and equilibrium in liability insurance markets

Abstract: Models of asymmetric information in insurance markets typically consider insurance buyers with Bernoulli loss distributions differing in expected loss. This article analyzes markets where buyer loss distributions are characterized by mean-preserving spreads and insurers can classify applicants in terms of expected values but not by risk. Because liability losses are characterized by skewed continuous probability distributions, both discrete and continuous loss distributions are considered. In contrast to the single separating equilibrium in the classic Rothschild-Stiglitz insurance market, multiple separating equilibria are identified in this article: three in the discrete case and four in the continuous case. The possibility of extreme discontinuities in insurer policy offers provides a new explanation for crises in liability insurance markets.

Different frames for the independence axiom: An experimental investigation in individual decision making under risk

Abstract: This article classifies three classes of generalized expected utility preferences according to the justifications for the independence axiom and for the reduction principle that they subscribe to or reject. The results of an experiment designed to test the three classes show that some substantial proportions of responses are consistent with each class. In view of this finding, it is suggested that the different theories belonging to the three classes should be considered complementary, rather than alternative, in order to explain individual behavior under risk.

Evaluating the injury risk associated with All-Terrain Vehicles: An application of Bayes' rule

Abstract: This article discusses several technical and conceptual issues relating to the regulation of All-Terrain Vehicles (ATVs). Qualitative response models are used to analyze a survey of injured persons and a survey of the general population of users. Because the latter did not distinguish injured and noninjured persons, an application of Bayes' rule is used to make inferences about the relationship between the two injury categories, and to consistently estimate injury risk. The article concludes with a discussion of the problem of risk awareness and some policy implications.

Multidimensional Bargains and the Desirability of Ex Post Inefficiency

Abstract: In multidimensional bargaining situations where individuals possess relevant private information, say about preferences, allocational efficiency is a central concern Even if there is no squabbling over distribution—for example, if contingent commitments on allocations can be made before private information is secured—honest revelation comes only by sacrificing efficiency Indeed, the incentive-compatible, second-best outcomes generally require that some allocations be off the contract curve (ex post inefficient) The potential for recontracting, by ruling out such inefficient allocations and the second-best equilibria they support, would hurt matters further

A note on Savage's theorem with a finite number of states

Abstract: This article gives a preference-based characterization of subjective expected utility for the general equilibrium model with a finite number of states. The characterization follows Savage (1954) as closely as possible but has to abandon his axiom (P6), atomlessness of events, since this requires an infinite state space. To introduce continuity we replace (P6) with a continuity assumption on the set of consequences and assume the preferences are smooth. Then we apply Savage's sure-thing principle and his state-independence axiom to get an additively separable utility representation. Finally, to separate subjective probabilities from basic tastes, we apply a new axiom, which states that for each pair of states the marginal rate of substitution is constant along the certainty line.

The Pioneer's Curse: Selection Bias and Agricultural Land Degradation

Abstract: Expansion of agriculture into new regions has often been followed by land degradation. In this article, it is argued that the process of land development involves the selection of pioneer's with optimistic expectations about the robustness and carrying capacity of new land. Hence, there is a systematic bias towards overexploitation and land degradation. The argument is shown to be an extension of the winner's curse analysis in the theory of auctions.

A subjectivist approach to consecutive conflict

Abstract: An easily applied approach is developed to provide one participant in a sequence of conflicts with an optimal strategy. A goal of this article is to demonstrate that it is mathematically feasible to incorporate a decision maker's subjective distributions over the effects his actions will have on the outcomes of future conflicts. Unlike many other approaches, the model of this article does not restrict the beliefs that the participant is allowed to express. The participant, not the decision theorist, decides on what is relevent. Model assumptions required for updating rules, such as Bayesian updating, are not required unless they really are appropriate for the situation.