Risky Prospects Research Articles

Risk and rationality: The effects of mood and decision rules on probability weighting

Abstract Empirical research has shown that people tend to overweight small probabilities and underweight large probabilities when valuing risky prospects, but little is known about factors influencing the shape of the probability weighting curve. Based on a laboratory experiment with monetary incentives, we demonstrate that pre-existing good mood is significantly associated with women’s probability weights: Women in a better than normal mood tend to weight probabilities relatively more optimistically. Many men, however, seem to be immunized against effects of incidental mood by applying a mechanical decision criterion such as maximization of expected value.

Information Integration in Risky Choice: Identification and Stability

How is information integrated across the attributes of an option when making risky choices? In most descriptive models of decision under risk, information about risk, and reward is combined multiplicatively (e.g., expected value; expected utility theory, Bernouli, 1738/1954; subjective expected utility theory, Savage, 1954; Edwards, 1955; prospect theory, Kahneman and Tversky, 1979; rank-dependent utility, Quiggin, 1993; decision field theory, Busemeyer and Townsend, 1993; transfer of attention exchange model, Birnbaum, 2008). That is, (some transform of) probability is multiplied by (some transform of) reward to give a value for a risky prospect, and the prospect with the maximum value is then chosen.

SELECTION INTO AUCTIONS FOR RISKY AND AMBIGUOUS PROSPECTS

We study experimentally the selection into first‐price sealed‐bid auctions for a risky or an ambiguous prospect. Most subjects chose to submit a bid for the risky prospect, leading to thinner markets for the ambiguous prospect. Transaction prices for both prospects were equal although subjects expected the ambiguous markets to be smaller. Evidence of a positive correlation between risk and ambiguity aversion suggests that the ambiguous markets were populated by relatively risk tolerant bidders. A control experiment with selection in a simple choice task shows that subjects correctly anticipate the effects of selection on market size and risk attitudes. (JEL C91, D44, D81)

Uncertainty and measurement error in welfare models for risk changes

Most welfare models of environmental or mortality risk reductions assume that risks are exogenously determined and known with certainty. However, a growing body of research suggests that uncertainty about risks can affect choices over risky prospects. I present a decision-weighted random-utility model that decomposes welfare losses into those attributable to an increase in the deterministic component of risk and those attributable to uncertainty about risk. I apply the model to an illustrative dataset of subjects' perceived mortality risk and willingness to accept the risk of nuclear-waste transport. I estimate the model using Lewbel's (2000) strictly exogenous regressor approach to account for endogeneity bias and measurement error. Subjects display aversion to both risk and uncertainty about the risk of a transport accident, so that increases in either leads to social-welfare losses. Roughly 12% of the external cost of nuclear-waste transport is attributable to the public's uncertainty about transport risk.

Stochastic dominance and risk measure: A decision-theoretic foundation for VaR and C-VaR

Is it possible to obtain an objective and quantifiable measure of risk backed up by choices made by some specific groups of rational investors? To answer this question, in this paper we establish some behavior foundations for various types of VaR models, including VaR and conditional-VaR, as measures of downside risk. In this paper, we will establish some logical connections among VaRs, conditional-VaR, stochastic dominance, and utility maximization. Though supported to some extents with unanimous choices by some specific groups of expected or non-expected-utility investors, VaRs as profiles of risk measures at various levels of risk tolerance are not quantifiable – they can only provide partial and incomplete risk assessments for risky prospects. We also include in our discussion the relevant VaRs and several alternative risk measures for investors; these alternatives use somewhat weaker assumptions about risk-averse behavior by incorporating a mean-preserving-spread. For this latter group of investors, we provide arguments for and against the standard deviation versus VaR and conditional-VaRs as objective and quantifiable measures of risk in the context of portfolio choice.

Psychology-Compatible Elicitation Mechanisms: The Uncertainty Effect as a Case Study

This paper introduces the notion of ‘psychology-compatible’ to refer to elicitation mechanisms that do not interfere with the psychological processes behind the phenomenon being studied. Its importance is demonstrated with one of the most commonly used mechanisms in experimental economics, the multiple-price-list, where subjects answer yes/no to their willingness to pay each of a set of prices. Four experiments that manipulate how valuations are elicited show that the Uncertainty Effect, which occurs when people value a risky prospect less that its worst outcome, reliably fails to be replicated with the multiple-price-list. This is proposed to occur because such elicitation (i) facilitates the identification of dominated alternatives and (ii) induces a more analytical processing of information. A modified elicitation method that should not have such consequences, where (the same) prices are presented sequentially rather than simultaneously, reliably does replicate the Uncertainty Effect, and so do open ended elicitations.

Stochastic efficiency analysis with risk aversion bounds: a comment

A recent contribution by Meyer et al. (2009, p. 521) corrected an error of fact by Hardaker et al. (2004b, p. 253) about the comparison between stochastic dominance with respect to a function (SDRF) and stochastic efficiency with respect to a function (SERF). While both methods compare risky prospects for a bounded range of degrees of risk aversion, SERF, unlike SDRF, also demands an assumption that a chosen measure of risk aversion is constant over all levels of outcomes being evaluated. It is argued that it is generally reasonable to make such an assumption, especially when the form of the utility function and the bounds on the degree of risk aversion are carefully chosen. Then SERF has the advantage that it can lead to a smaller efficient set than that identified by SDRF. SERF also has advantages of ease and transparency in use.

The Endowment Effect in Groups with and without Strategic Incentives

Anticommons are a special kind of mixed-motive dilemma in which negative effects for society are caused by the excessive use of exclusion rights. In two fully incentivized experiments on trading goods with risky prospects, we disentangle three psychological sources that have been suggested to contribute to increased pricing in anticommons dilemmas: the effects of strategic incentives for overpricing, endowment effects, and interdependence of outcomes. Our results show that pricing of risky prospects in the anticommons is only marginally influenced by endowment status, while participants readily respond to incentives to overprice and to the interdependence of outcomes. Endowment effects are reduced both when strategic incentives to overprice are provided and when outcomes of subjects become interdependent. As a result, endowment effects for risky prospects are strongly reduced or even disappear completely in anticommons dilemmas. Our results render support for an interaction model instead of an additive effect model in which both incentives and endowment effects would drive up pricing.

Common ratio using delay

We present an experiment in which we add a common delay in a choice between two risky prospects. The results show that delay produces the same change in preferences as in the well-documented common ratio effect in risky lotteries. The added common delay acts as if the probabilities were divided by some common ratio. Moreover, we show that there is a strong magnitude effect, in the sense that the effect of delay depends on the magnitude of the outcome. The results are consistent with the recently introduced probability time trade-off (PTT) model by Baucells and Heukamp. We present a parameterization of the model based on the experimental results, showing that the value function exhibits increasing relative risk aversion, the weighting function is s-shaped, and the intrinsic discount rate is decreasing.

Neurobiological studies of risk assessment: A comparison of expected utility and mean-variance approaches

When modeling valuation under uncertainty, economists generally prefer expected utility because it has an axiomatic foundation, meaning that the resulting choices will satisfy a number of rationality requirements. In expected utility theory, values are computed by multiplying probabilities of each possible state of nature by the payoff in that state and summing the results. The drawback of this approach is that all state probabilities need to be dealt with separately, which becomes extremely cumbersome when it comes to learning. Finance academics and professionals, however, prefer to value risky prospects in terms of a trade-off between expected reward and risk, where the latter is usually measured in terms of reward variance. This mean-variance approach is fast and simple and greatly facilitates learning, but it impedes assigning values to new gambles on the basis of those of known ones. To date, it is unclear whether the human brain computes values in accordance with expected utility theory or with mean-variance analysis. In this article, we discuss the theoretical and empirical arguments that favor one or the other theory. We also propose a new experimental paradigm that could determine whether the human brain follows the expected utility or the mean-variance approach. Behavioral results of implementation of the paradigm are discussed.

Decisions from Experience and the Effect of Rare Events in Risky Choice

When people have access to information sources such as newspaper weather forecasts, drug-package inserts, and mutual-fund brochures, all of which provide convenient descriptions of risky prospects, they can make decisions from description. When people must decide whether to back up their computer's hard drive, cross a busy street, or go out on a date, however, they typically do not have any summary description of the possible outcomes or their likelihoods. For such decisions, people can call only on their own encounters with such prospects, making decisions from experience. Decisions from experience and decisions from description can lead to dramatically different choice behavior. In the case of decisions from description, people make choices as if they overweight the probability of rare events, as described by prospect theory. We found that in the case of decisions from experience, in contrast, people make choices as if they underweight the probability of rare events, and we explored the impact of two possible causes of this underweighting-reliance on relatively small samples of information and overweighting of recently sampled information. We conclude with a call for two different theories of risky choice.

How do we evaluate future gambles? Experimental evidence on path dependency in risky intertemporal choice

AbstractThis study reports three experiments which demonstrate path dependency in risky intertemporal choice. Consider a lottery to be resolved and paid in a future time period. One can obtain the present value of this lottery in three different ways: (1) eliciting directly the present certainty equivalent (CE) of the future lottery (direct path); (2) eliciting the future CE and then discounting this amount to the present (risk‐time path); and (3) eliciting the present value of the risky prospect and then determining the CE of this current lottery (time‐risk path). Standard rational choice models such as the discounted expected utility model, assume a multiplicative model, where all three methods mentioned above would yield the same value. We conducted three studies to examine if this is the case: Experiments 1 and 2 were based on a set of matching‐task questions and Experiment 3 used a process‐tracing design to analyze the natural sequence of decision making by the subjects. These three studies show that the evaluation of future gambles is path‐dependent. The present values elicited under the time‐risk and direct paths are, on average, higher than those reported under the risk‐time path. In addition, we found evidence for a two‐stage evaluation of risky future prospects: When evaluating a future gamble, individuals first assess the present value of the gamble (time discounting) and then they determine a certainty equivalent (probability discounting). Copyright © 2008 John Wiley & Sons, Ltd.

Non‐Monotonicity of the Tversky‐Kahneman Probability‐Weighting Function: A Cautionary Note

Abstract Cumulative Prospect Theory has gained a great deal of support as an alternative to Expected Utility Theory as it accounts for a number of anomalies in the observed behavior of economic agents. Expected Utility Theory uses a utility function and subjective or objective probabilities to compare risky prospects. Cumulative Prospect Theory alters both of these aspects. The concave utility function is replaced by a loss‐averse utility function and probabilities are replaced by decision weights. The latter are determined with a weighting function applied to the cumulative probability of the outcomes. Several different probability weighting functions have been suggested. The two most popular are the original proposal of Tversky and Kahneman and the compound‐invariant form proposed by Prelec. This note shows that the Tversky‐Kahneman probability weighting function is not increasing for all parameter values and therefore can assign negative decision weights to some outcomes. This in turn implies that Cumulative Prospect Theory could make choices not consistent with first‐order stochastic dominance.

Orders and inventory commodities with price and demand uncertainty in complete markets

The purpose of this paper is to price an order (inventory control) policy when both the demand and the price are uncertain and markets are complete. Inventory management is assumed to be equivalent to an investment for future and risky prospects for which a risk premium is required. Optimization of this risk premium defines the optimal-order policy. A number of examples are solved and we show how a zero-inventory policy can be replicated by a portfolio of options and of course an optimal-order quantity. The approach developed in this paper underlies as well a common practice by certain firms who use materials that are traded in speculative financial markets. In these situations, managers combine their production-based activities with speculations regarding their potential demand and the associated price of materials. For demonstration purposes and to highlight the practicality of this approach an extensive application and numerical results are used. In particular, we consider a two-period problem with an exponential utility function and a mean exponential demand, which is a function of price.

Risk attributes theory: Decision making under risk

In this paper, some limitations in the conventional theories and models of the decision making under risk are presented from a new angle. To eliminate those limitations, a theoretical framework is proposed, in which the risk preference relation is constructed on a set of risk attributes instead of risky prospects. The axioms are presented to ensure the existence of the representation function for this risk preference relation through employing the Multi-attribute Utility Theory (MAUT). In our framework, we construct a risk decision model with four risk attributes. One of these attributes measured by a newly defined attribute measurement, the Relative Maximum Absolute Value (RMAV), can be employed in our model to explain the experimental result more intuitively compared with the overweighting of small probability proposed by Kahneman and Tversky in their Prospect Theory. In addition, the validity of the model is testified by applying it to explain the Allais Paradox and the Fourfold Pattern of Risk Attitudes. The advantages of our theory are summarized to complete this paper. Since our model is based on an axiomatized preference relation and has a good descriptive ability, it can either serve as a normative or a descriptive decision model under risk.

A fruit in the hand or two in the bush? Divergent risk preferences in chimpanzees and bonobos

Human and non-human animals tend to avoid risky prospects. If such patterns of economic choice are adaptive, risk preferences should reflect the typical decision-making environments faced by organisms. However, this approach has not been widely used to examine the risk sensitivity in closely related species with different ecologies. Here, we experimentally examined risk-sensitive behaviour in chimpanzees (Pan troglodytes) and bonobos (Pan paniscus), closely related species whose distinct ecologies are thought to be the major selective force shaping their unique behavioural repertoires. Because chimpanzees exploit riskier food sources in the wild, we predicted that they would exhibit greater tolerance for risk in choices about food. Results confirmed this prediction: chimpanzees significantly preferred the risky option, whereas bonobos preferred the fixed option. These results provide a relatively rare example of risk-prone behaviour in the context of gains and show how ecological pressures can sculpt economic decision making.

Risk Attitude in Real Decision Problems

Abstract We use data from 298 showings of the television program "Affari Tuoi," which involves contestants making decisions between risky prospects with possible prizes of up to half a million euros, to estimate three models of decision-making under risk: Expected Utility, Rank-Dependent Expected Utility and Regret-Rejoice. We find that Regret-Rejoice does not significantly improve upon Expected Utility, while Rank-Dependent outperforms it. Interestingly, we find that the CARA specification fits significantly better than the conventionally-adopted CRRA specification. Crucially, we find a significant role for unobserved heterogeneity, implying that our estimates provide more superior estimates of risk attitude and of probability weighting than other studies.

Valuing a Risky Prospect Less than its Worst Outcome: Uncertainty Effect or Task Ambiguity?

Gneezy, List and Wu [Q. J. Econ. 121 (2006) 1283-1309] document that lotteries are often valued less than the lotteries’ worst outcomes. We show how to undo this result.

Axiomatization of stochastic models for choice under uncertainty

This paper develops a theory of probabilistic models for risky choices. This theory can be viewed as an extension of the expected utility theory. One probabilistic version of the Archimedean Axiom and two versions of the Independence Axiom are proposed. In addition, additional axioms are proposed of which one is Luce's Independence from Irrelevant Alternatives (IIA). It is demonstrated that different combinations of the axioms yield different characterizations of the probabilities for choosing the respective risky prospects. Particular dimensional invariance axioms are postulated for the case with monetary rewards. It is demonstrated that when probabilistic versions of the Archimedean and the Independence Axioms are combined with Dimensional Invariance axioms explicit functional forms of the utility function follow. It is also proved that a random utility representation exists in the particular case when IIA holds for choice among lotteries. An interesting feature of the models developed is that they allow for violations of the expected utility theory known as the common consequence effect and the common ratio effect.

On the Descriptive Value of Loss Aversion in Decisions under Risk

Previous studies of loss aversion in decisions under risk have led to mixed results. Losses appear to loom larger than gains in some settings, but not in others. The current paper clarifies these results by highlighting six experimental manipulations that tend to increase the likelihood of the behavior predicted by loss aversion. These manipulations include: (1) framing of the safe alternative as the status quo; (2) ensuring that the choice pattern predicted by loss aversion maximizes the probability of positive (rather than zero or negative) outcomes; (3) the use of high nominal (numerical) payoffs; (4) the use of high stakes; (5) the inclusion of highly attractive risky prospects that creates a contrast effect; and (6) the use of long experiments in which no feedback is provided and in which the computation of the expected values is difficult. In addition, the results suggest the possibility of learning in the absence of feedback: The tendency to select simple strategies, like ``maximize the worst outcome'' which implies ``loss aversion'', increases when this behavior is not costly. Theoretical and practical implications are discussed.