A tractable method to measure utility and loss aversion under prospect theory

This paper provides an efficient method to measure utility under prospect theory. Our method minimizes both the number of elicitations required to measure utility and the cognitive burden for subjects, being based on the elicitation of certainty equivalents for two-outcome prospects. We applied our method in an experiment and were able to replicate the main findings on prospect theory, suggesting that our method measures what it is intended to. Our data confirmed empirically that risk seeking and concave utility can coincide under prospect theory. Utility did not depend on the probability used in the elicitation, which offers support for the validity of prospect theory.

Stochastic expected utility theory

This paper proposes a new decision theory of how individuals make random errors when they compute the expected utility of risky lotteries. When distorted by errors, the expected utility of a lottery never exceeds (falls below) the utility of the highest (lowest) outcome. This assumption implies that errors are likely to overvalue (undervalue) lotteries with expected utility close to the utility of the lowest (highest) outcome. Proposed theory explains many stylized empirical facts such as the fourfold pattern of risk attitudes, common consequence effect (Allais paradox), common ratio effect and violations of betweenness. Theory fits the data from ten well-known experimental studies at least as well as cumulative prospect theory.

Third-generation prospect theory

We present a new theory of decision under uncertainty: third-generation prospect theory (PT³). This retains the predictive power of previous versions of prospect theory, but extends that theory by allowing reference points to be uncertain while decision weights are specified in a rank-dependent way. We show that PT³ preferences respect a state-conditional form of stochastic dominance. The theory predicts the observed tendency for willingness-to-accept valuations of lotteries to be greater than willingness-to-pay valuations. When PT³ is made operational by using simple functional forms with parameter values derived from existing experimental evidence, it predicts observed patterns of the preference reversal phenomenon.

An experimental investigation of violations of transitivity in choice under uncertainty

Several models of decision-making imply systematic violations of transitivity of preference. Our experiments explored whether people show patterns of intransitivity predicted by regret theory and majority rule. To distinguish “true” violations from those produced by “error,” a model was fit in which each choice can have a different error rate and each person can have a different pattern of true preferences that need not be transitive. Error rate for a choice is estimated from preference reversals between repeated presentations of that same choice. Our results showed that very few people repeated intransitive patterns. We can retain the hypothesis that transitivity best describes the data of the vast majority of participants.

Eliciting decision weights by adapting de Finetti’s betting-odds method to prospect theory

This paper extends de Finetti’s betting-odds method for assessing subjective beliefs to ambiguous events. Thus, a tractable manner for measuring decision weights under ambiguity is obtained. De Finetti’s method is so transparent that decision makers can evaluate the relevant tradeoffs in complex situations. The resulting data can easily be analyzed, using nonparametric techniques. Our extension is implemented in an experiment on predicting next-day’s performance of the Dow Jones and Nikkei stock indexes, where we test the existence and nature of rank dependence, finding usual patterns. We also find violations of rank dependence.

Can ranking techniques elicit robust values?

This paper reports two experiments which examine the use of ranking methods to elicit ‘certainty equivalent’ values. It investigates whether such methods are able to eliminate the disparities between choice and value which constitute the ‘preference reversal phenomenon’ and which thereby pose serious problems for both theory and policy application. The results show that ranking methods are vulnerable to distorting effects of their own, but that when such effects are controlled for, the preference reversal phenomenon, previously so strong and striking, is very considerably attenuated.

Probability weighting and the ‘level’ and ‘spacing’ of outcomes: An experimental study over losses

The main goal of the experimental study described in this paper is to investigate the sensitivity of probability weighting to the payoff structure of the gambling situation—namely the level of consequences at stake and the spacing between them—in the loss domain. For that purpose, three kinds of gambles are introduced: two kinds of homogeneous gambles (involving either small or large losses), and heterogeneous gambles involving both large and small losses. The findings suggest that at least for moderate/high probability of loss do both ‘level’ and ‘spacing’ effects reach significance, with the impact of ‘spacing’ being both opposite to and stronger than the impact of ‘level’. As compared to small-loss gambles, large-loss gambles appear to enhance probabilistic optimism, while heterogeneous gambles tend to increase pessimism.

Self-protection and insurance with interdependencies

We study optimal investment in self-protection of insured individuals when they face interdependencies in the form of potential contamination from others. If individuals cannot coordinate their actions, then the positive externality of investing in self-protection implies that, in equilibrium, individuals underinvest in self-protection. Limiting insurance coverage through deductibles or selling “at-fault” insurance can partially internalize this externality and thereby improve individual and social welfare.

Risk aversion in the small and in the large: Calibration results for betweenness functionals

A reasonable level of risk aversion with respect to small gambles leads to a high, and absurd, level of risk aversion with respect to large gambles. This was demonstrated by Rabin (Econometrica 68:1281–1292, 2000) for expected utility theory. Later, Safra and Segal (Econometrica, 2008) extended this result by showing that similar arguments apply to many non-expected utility theories, provided they are Gateaux differentiable. In this paper we drop the differentiability assumption and by restricting attention to betweenness theories we show that much weaker conditions are sufficient for the derivation of similar calibration results.

Paying for permanence: Public preferences for contaminated site cleanup

We use conjoint choice questions to investigate the preferences of people in four cities in Italy for income and future/permanent mortality risk reductions delivered by contaminated site remediation policies. The VSL is €5.6 million for an immediate risk reduction. If the risk reduction takes place 20 years from now, the implied VSL is €1.26 million. Respondents’ implicit discount rate is 7%. The VSL depends on respondent characteristics, familiarity with contaminated sites, concern about the health effects of exposure to toxicants, having a family member with cancer, perceived usefulness of public programs and beliefs about the goals of government remediation programs.

Valuing a homeland security policy: Countermeasures for the threats from shoulder mounted missiles

This paper reports estimates for the ex ante tradeoffs for three specific homeland security policies that all address a terrorist attack on commercial aircraft with shoulder mounted missiles. Our analysis focuses on the willingness to pay for anti-missile laser jamming countermeasures mounted on commercial aircraft compared with two other policies as well as the prospect of remaining with the status quo. Our findings are based a stated preference conjoint survey conducted in 2006 and administered to a sample from Knowledge Networks’ national internet panel. The estimates range from $100 to $220 annually per household. Von Winterfeldt and O’Sullivan’s (2006) analysis of the same laser jamming plan suggests that the countermeasures would be preferred if economic losses are above $74 billion, the probability of attack is larger than 0.37 in 10 years, and if the cost of the measures is less than about $14 billion. Our results imply that, using the most conservative of our estimates, a program with a cost consistent with their thresholds would yield significant aggregate net benefits.

Environmental disasters as risk regulation catalysts? The role of Bhopal,Chernobyl, Exxon Valdez,Love Canal,and Three Mile Island in shaping U.S. environmental law

Unexpected events such as environmental catastrophes capture wide public attention. Soon after five major shocks—Three Mile Island, Love Canal, Bhopal, Chernobyl, and the Exxon Valdez oil spill—Congress voted on new risk regulation. This paper conducts an event study to test whether individual congressional representatives were “shocked” by these environmental disasters into increasing their probability of voting in favor of risk legislation. On average, representatives were less likely to vote in favor of bills tied to these five events. Significant heterogeneity in representatives’ responses to these shocks is documented. Liberal Northeast representatives were most likely to increase their pro-environment voting in the aftermath of these shocks.

Myopic risk-seeking: The impact of narrow decision bracketing on lottery play

In two experiments conducted with low-income participants, we find that individuals are more likely to buy state lottery tickets when they make several purchase decisions one-at-a-time, i.e. myopically, than when they make one decision about how many tickets to purchase. These results extend earlier findings showing that “broad bracketing” of decisions encourages behavior consistent with expected value maximization. Additionally, the results suggest that the combination of myopic decision making and the “peanuts effect”—greater risk seeking for low stakes than high stakes gambles—can help explain the popularity of state lotteries.

Statistical vs. identified lives in benefit-cost analysis

Evaluation of projects that affect mortality risk usually assumes that risk changes are small and similar across individuals. In reality, risks differ among individuals and information about risk heterogeneity determines the extent to which affected lives are “statistical” or “identified” and influences the outcome of benefit-cost analysis (BCA). The effects of information about risk heterogeneity on BCA depend on, inter alia, whether information concerns heterogeneity of baseline or change in risk and whether valuation uses compensating or equivalent variation. BCA does not systematically favor identified over statistical lives. We suggest some political factors that may explain the apparent public bias.

The sensitivity of subjective probability to time and elicitation method

The paper reports the results of a survey designed to elicit probability judgements for different types of events: ‘pure chance’ events, for which objective probabilities can be calculated; ‘public’ events, about which there may be some discussion in social groups and the media; and ‘personal’ events, such as those relating to crime or accidental injury. Even among respondents deemed to be ‘well-calibrated’ in the domain of pure chance events we find limited sensitivity to the ‘temporal scope’ of public and personal events—this being especially marked for personal events. We discuss possible reasons and some implications for policy-related survey work.

Cancer premiums and latency effects: A risk tradeoff approach for valuing reductions in fatal cancer risks

Many studies estimate individuals’ values for avoiding fatality risks; however, most value-of-statistical-life studies focus on accident-related deaths. Consequently, little is known about preferences for avoiding other fatal risks, such as cancer. Cancer may engender strong feelings of dread, leading to a “cancer premium,” but cancer latency periods may have the opposite effect. Using a national survey, we elicit relative preferences for avoiding fatal cancer and auto-accident risks. We find strong preferences for avoiding cancer risks. With a 5-year latency, they are valued roughly three times greater than immediate accident risks, declining to 50% greater for a 25-year latency.

Preferences and decision errors in the winner’s curse

The problem of asymmetric information causes a winner’s curse in many environments. Given many unsuccessful attempts to eliminate it, we hypothesize that some people ‘prefer’ the lotteries underlying the winner’s curse. Study 1 shows that after removing the hypothesized cause of error, asymmetric information, half the subjects still prefer winner’s curse lotteries, implying past efforts to de-bias the winner’s curse may have been more successful than previously recognized since subjects prefer these lotteries. Study 2 shows risk-seeking preferences only partially explain lottery preferences, while non-monetary sources of utility may explain the rest. Study 2 suggests lottery preferences are not independent of context, and offers methods to reduce the winner’s curse.