Are risk preferences stable over time? To address this question we elicit risk preferences from the same pool of subjects at two different moments in time. To interpret the results, we use a Fechner stochastic choice model in which the revealed preference of individuals is governed by some underlying preference, together with a random error. We take cumulative prospect theory as the underlying preference model (Kahneman and Tversky, Econometrica 47:263–292, 1979; Tversky and Kahneman, Journal of Risk (...) and Uncertainty 5:297–323, 1992). We observe that the aggregate pattern of preferences is very similar in both sessions, and it matches the results reported in the literature. Most subjects are risk averse for gains, and risk seeking for losses. However, the subjects that jointly agree with the reflection effect of prospect theory are around 50%. The percentage of individuals that change their responses across sessions is quite high, 63%. Estimating the stochastic choice model we find that 72% of the subjects have an underlying preference which agrees with the reflection effect of prospect theory. The remaining 28% are mainly classified as risk averse for both gains and losses. The results reinforce the empirical validity of the reflection effect. Deviations from the reflection effect can be attributed to noise, as well as to the existence of a fraction of risk averse subjects. (shrink)

We obtain rich measures of the risk preferences of a sample of Vietnamese farmers, and revisit the link between risk preferences and economic well-being. Far from being particularly risk averse, our farmers are on average risk neutral and, thus, more risk tolerant than typical Western subject populations. This generalises recent findings indicating that students in poorer countries are more risk tolerant than students in richer countries to a general population sample. Risk aversion is, (...) furthermore, negatively correlated with income within our sample, but does not correlate with wealth. This also casts doubt on high levels of risk aversion causing failure to adopt new technologies, which we discuss. (shrink)

Risk preferences of Australian academics are elicited by analyzing the aggregate distribution of their retirement funds across available investment options. Not more than 10 % of retirement funds are invested as if their owners maximize expected utility under the assumption of constant relative risk aversion with an empirically plausible level of risk aversion. An implausibly high level of risk aversion is required to rationalize any investment into bonds when stocks are available. Not more than 36.54 % (...) of all investments can be rationalized by a model of loss averse preferences. Moreover, the levels of loss aversion typically reported in the experimental studies imply overinvestment in bonds, which is not observed in the data. Up to 67.18 % of all investments can be rationalized by rank-dependent utility or Yaari’s dual model with empirically plausible parameters. A median Australian academic behaves as if maximizing rank-dependent utility with parameter γ∈[0.76,0.79]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma \in [0.76, 0.79]$$\end{document} in a Tversky and Kahneman probability weighting function. (shrink)

In this paper, we analyse higher-order risky choices by the representative cumulative prospect theory (CPT) decision maker from three alternative reference points. These are the status quo, average payout and maxmin. The choice tasks we consider in our analysis include binary risks, and are the ones employed in the experimental literature on higher order risk preferences. We demonstrate that the choices made by the representative subject depend on the reference point. If the reference point is the status quo (...) and the lottery choices exhibit symmetric risk, we demonstrate that there is no third order reflection effect of lottery choices but there is a fourth order reflection effect. When the average payout is the reference point, we demonstrate that any third or fourth order lottery choice is possible dependent upon the lottery payoffs. However, under the assumption of maxmin reference point, the risky choices are prudent and temperate. In addition to these results, our analysis reveals that the representative CPT subject can choose combinations of second with third and fourth order risky options that differ from those in other major models of decision under risk. We contrast our theoretical predictions with the empirical results reported in the literature on higher order risk preferences and are able to reconcile some conflicting experimental evidence. (shrink)

We compare two different elicitation methods for measuring risk attitudes on a sample of French farmers. We consider the lottery tasks initially proposed by Holt and Laury (Econ Rev 92:1644–1655, 2002) and by Eckel and Grossman (Evol Hum Behav 23:281–295, 2002; J Econ Behav Org 68:1–7, 2008). The main empirical result from this within-subject study is that risk preference measures are affected by the type of mechanism used. We first show that this risk preference instability can be (...) related to non-expected utility preferences of farmers. Using a risk-taking psychometric questionnaire, we then demonstrate that risk preferences of farmers are context-dependent. This may be another explanation of the observed risk preference instability. (shrink)

The Internet and social media have opened niches for political exploitation of human dispositions to hyper-alarmed states that amplify perceived threats relative to their objective probabilities of occurrence. Researchers should aim to observe the dynamic “ramping up” of security threat mechanisms under controlled experimental conditions. Such research necessarily begins from a clear model of standard baseline states, and should involve adding treatments to established experimental protocols developed by experimental economists. We review these protocols, which allow for joint estimation of (...) class='Hi'>risk preferences and subjective beliefs about probabilities and their distributions. Results we have obtained on such estimates, from populations in various countries, are gathered for comparison. Most people show moderate risk aversion in non-alarmed states. We also find universal heterogeneity in risk preference structures, with substantial sub-samples weighting probabilities in such a way as to display “probability pessimism”, while others make risky choices in accordance with expected utility theory. (shrink)

This article presents a characterization of higher-order risk preferences such as prudence or temperance in terms of statistical moments. Our results, which are generalizations of Roger :27–44, 2011) and Ekern, 329–333, 1980), give a better understanding of how higher-order risk preferences relate to skewness preference and kurtosis aversion. While they are not based on expected utility theory, an implication within that theory is that all commonly used utility functions exhibit skewness preference and kurtosis aversion.

One fundamental assumption often made in the literature on unawareness is that risk preferences are invariant to changes of awareness. We study how exposure to unawareness affects choices under risk. Participants in our experiment choose repeatedly between varying sure outcomes and a lottery in three phases. All treatments are exactly identical in phase 1 and phase 3, but differ in phase 2. There are five different treatments pertaining to the lottery faced in phase 2: The control treatment, the (...) treatment with awareness of unawareness of lottery outcomes but known number of outcomes, the treatment with awareness of unawareness of outcomes but with unknown number of outcomes, the treatment with unawareness of unawareness of some outcomes, and the treatment with an ambiguous lottery. We study both whether behavior differs in phase 3 across treatments and whether differences of subjects’ behavior between phases 1 and phase 3 differ across treatments. We observe no significant treatment effects. (shrink)

In this paper, we use the risk apportionment technique of Eeckhoudt, Rey and Schlesinger (2007) to study higher order risk preferences for others’ health as well as ex-ante and ex-post inequality preferences for social risky distributions, and their interaction. In an experiment on a sample of university students acting as impartial spectators, we observe risk aversion towards social health losses and a dislike of ex-ante inequality. In addition, evidence for ex-post inequality seeking is much weaker than evidence (...) for ex-ante inequality aversion. Because ex-ante inequality aversion is unrelated to risk aversion, we conclude that simple forms of utilitarianism are not relevant for individual judgment of social risk over health. Last, our investigation of precautionary distribution, which would occur when one particular group in the society suffers from background health risk, shows substantial polarization of preferences. (shrink)

In this article, we elicit both individuals’ and couples’ preferences assuming prospect theory (PT) as a general theoretical framework for decision under risk. Our experimental method, based on certainty equivalents, allows to infer measurements of utility and probability weighting at the individual level and at the couple level. Our main results are twofold. First, risk attitude for couples is compatible with PT and incorporates deviations from expected utility similar to those found in individual decision making. Second, couples’ (...) attitudes towards risk are found to be consistent with a mix of individual attitudes, women being more influent on couples’ preferences at low probability levels. (shrink)

According to the ‘Description–Experience gap’, when people are provided with the descriptions of risky prospects they make choices as if they overweight the probability of rare events; but when making decisions from experience after exploring the prospects’ properties, they behave as if they underweight such probability. This study revisits this discrepancy while focusing on information-search in decisions from experience. We report findings from a lab-experiment with three treatments: a standard version of decisions from description and two versions of decisions from (...) experience: with and without a ‘history table’ recording previously sampled events. We find that people sample more from lotteries with rarer events. The history table proved influential; in its absence search is more responsive to cues such as a lottery’s variance while in its presence the cue that stands out is the table’s maximum capacity. Our analysis of risky choices captures a significant DE gap which is mitigated by the presence of the history table. We elicit probability weighting functions at the individual level and report that subjects overweight rare events in experience but less so than in description. Finally, we report a measure that allows us to compare the type of DE gap found in studies using choice patterns with that inferred through valuation and find that the phenomenon is similar but not identical across the two methods. (shrink)

There are decision problems where the preferences that seem rational to many people cannot be accommodated within orthodox decision theory in the natural way. In response, a number of alternatives to the orthodoxy have been proposed. In this paper, I offer an argument against those alternatives and in favour of the orthodoxy. I focus on preferences that seem to encode sensitivity to risk. And I focus on the alternative to the orthodoxy proposed by Lara Buchak’s risk-weighted expected (...) utility theory. I will show that the orthodoxy can be made to accommodate all of the preferences that Buchak’s theory can accommodate. (shrink)

In his paper, ‘Patients, doctors and risk attitudes’, Makins argues that doctors, when choosing a treatment for their patient, need to follow their risk profile.1 He presents a pair of fictitious diseases facing a patient who either has ‘exemplitis’, which requires no treatment or ‘caseopathy’, which is severe and disabling and for which there is a treatment with unpleasant side effects. The doctor needs to decide whether the patient should pursue the unpleasant treatment, just in case he has (...) caseopathy. Makins believes that rational-choice theory is a productive way to approach this problem. This theory frames all decisions as gambles. Each possible gamble (eg, not to pursue treatment) leads, probabilistically, to a set of outcomes (life with no disease and no side effects, but also, possibly, life with a disabling disease, since no treatment is taken). Utilities of these outcomes and probabilities that they will happen are combined to yield a number—expected utility. One is supposed to gamble—to make a choice—in a way that maximises this expected utility. Makins takes this framework for granted and is focused on an additional complication, the patient’s risk preference. He believes that, in his hypothetical example, even if expected utility were exactly the same, withholding treatment …. (shrink)

To understand how small business entrepreneurs respond to government policy one has to know their risk and time preferences. Are they risk averse, or have high discount rates, such that they are hard to motivate? We have conducted a set of field experiments in Denmark that will allow a direct characterization of small business entrepreneurs in terms of these traits. We build on experimental tasks that are well established in the literature. The results do not suggest that small (...) business entrepreneurs are more or less risk averse than the general population under the assumption of Expected Utility Theory. However, we generally find an S-shaped probability weighting function for both small business entrepreneurs and non-entrepreneurs, with entrepreneurs being more optimistic about the chance of occurrence for the best outcome in lotteries with real monetary outcomes. The results also point to a significant difference in individual discount rates between entrepreneurs and non-entrepreneurs: entrepreneurs are willing to wait longer for certain rewards than the general population. (shrink)

I focus my discussion on the well-known Ellsberg paradox. I find good normative reasons for incorporating non-precise belief, as represented by sets of probabilities, in an Ellsberg decision model. This amounts to forgoing the completeness axiom of expected utility theory. Provided that probability sets are interpreted as genuinely indeterminate belief, such a model can moreover make the “Ellsberg choices” rationally permissible. Without some further element to the story, however, the model does not explain how an agent may come to (...) have unique preferences for each of the Ellsberg options. Levi holds that the extra element amounts to innocuous secondary “risk” or security considerations that are used to break ties when more than one option is rationally permissible. While I think a lexical choice rule of this kind is very plausible, I argue that it involves a greater break with xpected utility theory than mere violation of the ordering axiom. (shrink)

In a recent article entitled “Putting Risk in its Proper Place,” Eeckhoudt and Schlesinger (2006) established a theorem linking the sign of the n-th derivative of an agent’s utility function to her preferences among pairs of simple lotteries. We characterize these lotteries and show that, in a given pair, they only differ by their moments of order greater than or equal to n. When the n-th derivative of the utility function is positive (negative) and n is odd (even), the (...) agent prefers a lottery with higher (lower) n + 2p-th moments for p belonging to the set of positive integers. This result links the preference for disaggregation of risks across states of nature to the complete structure of moments preferred by mixed risk averse agents. It can be viewed as a generalization of a proposition appearing in Ekern (1980) which focused only on the differences in the n-th moments. (shrink)

Prospect Theory (PT) is widely regarded as the most promising descriptive model for decision making under uncertainty. Various tests have corroborated the validity of the characteristic fourfold pattern of risk attitudes implied by the combination of probability weighting and value transformation. But is it also safe to assume stable PT preferences at the individual level? This is not only an empirical but also a conceptual question. Measuring the stability of preferences in a multi-parameter decision model such as PT (...) is far more complex than evaluating single-parameter models such as Expected Utility Theory under the assumption of constant relative risk aversion. There exist considerable interdependencies among parameters such that allegedly diverging parameter combinations could in fact produce very similar preference structures. In this paper, we provide a theoretic framework for measuring the (temporal) stability of PT parameters. To illustrate our methodology, we further apply our approach to 86 subjects for whom we elicit PT parameters twice, with a time lag of 1 month. While documenting remarkable stability of parameter estimates at the aggregate level, we find that a third of the subjects show significant instability across sessions. (shrink)

Political philosophers working on ideal and non-ideal theory sometimes seem to be stuck in a bind: while ideal theory risks being too ideal to be useful in the real world, non-ideal theory risks being so non-ideal that it stops far short of justice. In this paper, I highlight a third – and equally unappealing – possibility: that non-ideal theory, precisely because of its obvious engagement with real-world problems, might fail to recognize the unacceptable ways in which (...) it is itself problematically idealized. I highlight this problem through the case-study of adaptive preferences. Although work in adaptive preferences obviously fits into non-ideal theory, the actual work being done in the literature is idealized in that it takes only the circumstances and needs of adults into account. In the best case, this means that the needs of one of our most vulnerable populations – that is, children – are ignored. In the worst case, where the needs of children and adults conflict, the needs of children will be actively frustrated. In this way, non-ideal theory can fail to approximate justice precisely because it fails to recognize the idealizations that it itself employs. (shrink)

No existing normative decision theory adequately handles risk. Expected Utility Theory is overly restrictive in prohibiting a range of reasonable preferences. And theories designed to accommodate such preferences (for example, Buchak's (2013) Risk‐Weighted Expected Utility Theory) violate the Betweenness axiom, which requires that you are indifferent to randomizing over two options between which you are already indifferent. Betweenness has been overlooked by philosophers, and we argue that it is a compelling normative constraint. Furthermore, neither Expected (...) nor Risk‐Weighted Expected Utility Theory allow for stakes‐sensitive risk‐attitudes—they require that risk matters in the same way whether you are gambling for loose change or millions of dollars. We provide a novel normative interpretation of Weighted‐Linear Utility Theory that solves all of these problems. (shrink)

We explore how risk preferences affect pro-social behavior under uncertainty. We analyze a modified dictator game in which the dictator can, by reducing her own sure payoff, increase the odds that an unknown recipient wins a lottery. We first augment a standard social preferences model with reference-dependent risk attitudes and then test the model’s predictions for the dictator’s giving behavior using a laboratory experiment. Consistent with the predictions of the model, we find that the relationship between giving behavior (...) and a giver’s loss aversion is mediated by the strength of the giver’s pro-social preferences. Among more pro-social dictators, an increase in loss aversion increases the likelihood that a dictator contributes to a recipient. (shrink)

Ramsey (1926) sketches a proposal for measuring the subjective probabilities of an agent by their observable preferences, assuming that the agent is an expected utility maximizer. I show how to extend the spirit of Ramsey's method to a strictly wider class of agents: risk-weighted expected utility maximizers (Buchak 2013). In particular, I show how we can measure the risk attitudes of an agent by their observable preferences, assuming that the agent is a risk-weighted expected utility maximizer. Further, (...) we can leverage this method to measure the subjective probabilities of a risk-weighted expected utility maximizer. (shrink)

In this essay, I argue that environmental risk is a strategic situation that places the individual citizen in the position of an imprisoned rider who is being exploited without his or her knowledge by the preferences of others. I contend that what is at stake in policy decisions regarding environmental risk is not numerical probabilities or consistent, complete, transitive preferences for individual welfare, but rather respect for the human agency of the individual. Human agency is a prerequisite to (...) one’s utility function and is threatened and exploited in the strategic situation that produces the imprisoned rider. This problem is created by the policy maker’s assumption that his or her task is to assume rational preferences and aggregate them. The guidelines for evaluation and justification of policy should move beyondwelfare preferences and involve an active state protecting human agency and empowering the imprisoned rider. Only in this way can we free all citizens from fear of exploitation by those who would impose collective and irreversible risk on each of them in violation of their unconditional right to their own agency. (shrink)

In this essay, I argue that environmental risk is a strategic situation that places the individual citizen in the position of an imprisoned rider who is being exploited without his or her knowledge by the preferences of others. I contend that what is at stake in policy decisions regarding environmental risk is not numerical probabilities or consistent, complete, transitive preferences for individual welfare, but rather respect for the human agency of the individual. Human agency is a prerequisite to (...) one’s utility function and is threatened and exploited in the strategic situation that produces the imprisoned rider. This problem is created by the policy maker’s assumption that his or her task is to assume rational preferences and aggregate them. The guidelines for evaluation and justification of policy should move beyondwelfare preferences and involve an active state protecting human agency and empowering the imprisoned rider. Only in this way can we free all citizens (a priori) from fear of exploitation by those who would impose collective and irreversible risk on each of them in violation of their unconditional right to their own agency. (shrink)

I have claimed that risk-weighted expected utility maximizers are rational, and that their preferences cannot be captured by expected utility theory. Richard Pettigrew and Rachael Briggs have recently challenged these claims. Both authors argue that only EU-maximizers are rational. In addition, Pettigrew argues that the preferences of REU-maximizers can indeed be captured by EU theory, and Briggs argues that REU-maximizers lose a valuable tool for simplifying their decision problems. I hold that their arguments do not succeed and (...) that my original claims still stand. However, their arguments do highlight some costs of REU theory. (shrink)

According to the orthodox treatment of risk preferences in decision theory, they are to be explained in terms of the agent's desires about concrete outcomes. The orthodoxy has been criticised both for conflating two types of attitudes and for committing agents to attitudes that do not seem rationally required. To avoid these problems, it has been suggested that an agent's attitudes to risk should be captured by a risk function that is independent of her utility and (...) probability functions. The main problem with that approach is that it suggests that attitudes to risk are wholly distinct from people's (non-instrumental) desires. To overcome this problem, we develop a framework where an agent's utility function is defined over chance propositions (i.e., propositions describing objective probability distributions) as well as ordinary (non-chance) ones, and argue that one should explain different risk attitudes in terms of different forms of the utility function over such propositions. (shrink)

Traditional portfolio selection models mainly obtain the optimized portfolio ratio by focusing on the prices of financial products. However, investors’ multiple preferences and risk appetites are also significant factors that should be taken into account. In consideration of these two factors simultaneously, we propose a double-hierarchy model in this paper. Specifically, the first hierarchy quantifies investors’ risk appetite based on a historical simulation method and probabilistic preference theory. This hierarchy can be utilized to describe investors’ variable (...) class='Hi'>risk appetites and ensure the obtained investment ratios meet investors’ immediate risk requirements. Then, using the cross-efficiency evaluation principle, the optimal investment ratios can be derived by fusing investors’ multiple preferences and risk appetites in the second hierarchy. Lastly, an illustrative example about evaluating the 10 largest capitalized stocks on the Shenzhen Stock Exchange is given to verify the feasibility and effectiveness of our newly proposed model. We make the theoretical contribution to improve the traditional portfolio selection model, especially considering investors’ subjective preferences and risk appetite. Moreover, the proposed model can be practical for assisting investors with their investment strategies in real life. (shrink)

The orthodox theory of instrumental rationality, expected utility (EU) theory, severely restricts the way in which risk-considerations can figure into a rational individual's preferences. It is argued here that this is because EU theory neglects an important component of instrumental rationality. This paper presents a more general theory of decision-making, risk-weighted expected utility (REU) theory, of which expected utility maximization is a special case. According to REU theory, the weight that each outcome (...) gets in decision-making is not the subjective probability of that outcome; rather, the weight each outcome gets depends on both its subjective probability and its position in the gamble. Furthermore, the individual's utility function, her subjective probability function, and a function that measures her attitude towards risk can be separately derived from her preferences via a Representation Theorem. This theorem illuminates the role that each of these entities plays in preferences, and shows how REU theory explicates the components of instrumental rationality. (shrink)

A natural view in distributive ethics is that everyone's interests matter, but the interests of the relatively worse off matter more than the interests of the relatively better off. I provide a new argument for this view. The argument takes as its starting point the proposal, due to Harsanyi and Rawls, that facts about distributive ethics are discerned from individual preferences in the "original position." I draw on recent work in decision theory, along with an intuitive principle about (...) class='Hi'>risk-taking, to derive the view. (shrink)

This paper presents a new decision theory for modelling choice under risk. The new theory is a two-parameter generalization of expected utility theory. The proposed theory assumes that a decision maker: behaves as if maximizing expected utility; but may experience disappointment when the utility of a lottery’s outcome falls short of the expected utility of the lottery; and may have a preference for gambling. The proposed theory can rationalize the fourfold pattern of risk (...) attitudes; the common ratio effect and the reverse thereof ; the Allais paradox in classical common consequence problems and the reverse Allais paradox—in common consequence problems with an even split of a probability mass; violations of the betweenness axiom; switching behavior in the Samuelson’s example; violations of ordinal, upper and lower cumulative independence ; and preference reversals between valuations and choice. In application to insurance, the theory can rationalize full insurance with an actuarially unfair premium and aversion to probabilistic insurance. In application to optimal portfolio investment, the theory can rationalize the equity premium puzzle. (shrink)

This paper uses duality to elaborate Slutzky equations of risks in quasi-linear decision models extended by independent background risks. Wealth, substitution and total effects are characterized in terms of mean-variance preferences. It is shown that both Pratt and Zeckhauser’s proper risk aversion and Kimball’s standard risk aversion are sufficient for negative substitution effects.

It is widely held that the influence of risk on rational decisions is not entirely explained by the shape of an agent’s utility curve. Buchak (Erkenntnis, 2013, Risk and rationality, Oxford University Press, Oxford, in press) presents an axiomatic decision theory, risk-weighted expected utility theory (REU), in which decision weights are the agent’s subjective probabilities modified by his risk-function r. REU is briefly described, and the global applicability of r is discussed. Rabin’s (Econometrica 68:1281–1292, (...) 2000) calibration theorem strongly suggests that plausible levels of risk aversion cannot be fully explained by concave utility functions; this provides motivation for REU and other theories. But applied to the synchronic preferences of an individual agent, Rabin’s result is not as problematic as it may first appear. Theories that treat outcomes as gains and losses (e.g. prospect theory and cumulative prospect theory) account for risk sensitivity in a way not available to REU. Reference points that mark the difference between gains and losses are subject to framing, many instances of which cannot be regarded as rational. However, rational decision theory may recognize the difference between gains and losses, without endorsing all ways of fixing the point of reference. In any event, REU is a very interesting theory. (shrink)

Existence value refers to the value humans ascribe to the existence of something, regard­less of whether it is or will be of any particular use to them. This existence value based on preference satisfaction should be taken into account in evaluating activities that come with a risk of species extinction. There are two main objections. The first is that on the preference satisfaction interpretation, the concept lacks moral importance because satisfying people’s preferences may involve no good or well-being for (...) them. However, existence value can be based on a restricted version of the preference satisfaction theory, which is not vulnerable to the skeptical arguments about the link between preference satisfaction and well-being. The second objection is that even if preference satisfaction can be linked to well-being, understanding existence value in terms of individual preference satisfaction is incoherent, because existence value reflects disinterested preferences that involve no benefits to the individual. However, the fact that existence value may involve disinterested preferences does not threaten the coherence of the concept, but suggests that it does not fit smoothly into the “utilitarian” or “welfarist” framework it is commonly considered within. A pluralistic normative approach based on prima facie duties can be an alternative to standard utilitarian-style approaches for considering existence value in concrete cases involving a risk of species extinction, such as through deep sea mining. (shrink)

A philosophical account of risk, such as this book provides, states what risk is, which attitudes to it are rational, and which acts affecting risks are rational. Attention to the nature of risk reveals two types of risk, first, a chance of a bad event, and, second, an act’s risk in the sense of the volatility of its possible outcomes. The distinction is normatively significant because different general principles of rationality govern attitudes to these two (...) types of risk. Rationality strictly regulates attitudes to the chance of a bad event and is more permissive about attitudes to an act’s risk. Principles of rationality governing attitudes to risk also justify evaluating an act according to its expected utility given that the act’s risk, if any, belongs to every possible outcome of the act. For a rational ideal agent, the expected utilities of the acts available in a decision problem explain the agent’s preferences among the acts. Maximizing expected utility is just following preferences among the acts. This view takes an act’s expected utility, not just as a feature of a representation of preferences among acts, but also as a factor in the explanation of preferences among acts. The view extends to evaluations of combination of acts, either simultaneous or in a sequence. It takes account of an agent’s attitudes to an act’s risk without weakening the standard of expected-utility maximization. The book’s theory of risk also grounds a justification of the risk-return evaluation of investments that finance advances, and a generalized version of this type of evaluation that a professional may use to advise clients about risks and that a government regulatory agency may use to make decisions about risks on behalf of the public. (shrink)

In this paper, we consider the composition of an optimal portfolio made of two dependent risky assets. The investor is first assumed to be a risk-averse expected utility maximizer, and we recover the existing conditions under which all these investors hold at least some percentage of their portfolio in one of the assets. Then, we assume that the decision maker is not only risk-averse, but also prudent and we obtain new minimum demand conditions as well as intuitively appealing (...) interpretations for them. Finally, we consider the general case of investor’s preferences exhibiting risk apportionment of any order and we derive the corresponding minimum demand conditions. As a byproduct, we obtain conditions such that an investor holds either a positive quantity of one of the assets or a proportion greater than 50 %. (shrink)

This paper investigates hypotheses drawn from two sources: (1) Belsky, Steinberg, and Draper’s (1991) attachment theory model of the development of reproductive strategies, and (2) recent life history models and comparative data suggesting that environmental risk and uncertainty may be potent determinants of the optimal tradeoff between current and future reproduction. A retrospective, self-report study of 136 American university women aged 19–25 showed that current recollections of early stress (environmental risk and uncertainty) were related to individual differences (...) in adult time preference and adult sexual behavior, and that individual differences in time preference were related to adult attachment organization and sexual behavior. These results are consistent with the hypothesis that perceptions of early stress index environmental risk and uncertainty and mediate the attachment process and the development of reproductive strategies. On this view individual differences in time preference are considered to be part of the attachment theoretical construct of an internal working model, which itself is conceived as an evolved algorithm for the contingent development of alternative reproductive strategies. (shrink)

Risk attitude is known to be a key determinant of various economic and financial choices. Behavioral studies that aim to evaluate the role of risk attitudes in contexts of this type, therefore, require tools for measuring individual risk tolerance. Recent developments in decision theory provide such tools. However, the methods available can be time consuming. As a result, some practitioners might have an incentive to prefer “fast and frugal” methods to clean but more costly methods. In (...) this article, we focus on a tractable procedure initially proposed by Holt and Laury (2002) to elicit risk attitude. We generalize this method to measure utility and risk aversion as follows. First, we allow measurement of probabilistic risk attitude through violations of expected utility due to probability weighting. Second, we use the outcome scale rather than the probability scale in the menu of choices. Third, we compare sure payoffs with lotteries instead of comparing non-degenerate lotteries. A within-subject experimental study illustrates the gains in tractability and bias minimization that can result from such an extension. (shrink)

Personalistic Bayesian decision theory provides a simple, roomy framework for hypothesis-testing and choice under uncertainty. Call the theory Bayesianism, for short. It’s the line that L. J. Savage made respectable among statisticians and economists. It’s the same thing as the expected utility hypothesis, in this form: preference does or should go by personal probabilistic expectation of utility. The question of whether to say “does” or “should” is the question of whether the theory is meant to be normative (...) or descriptive. (shrink)

The use of risk assessment tools has come to play an increasingly important role in sentencing decisions in many jurisdictions. A key issue in the theoretical discussion of risk assessment concerns the predictive accuracy of such tools. For instance, it has been underlined that most risk assessment instruments have poor to moderate accuracy in most applications. However, the relation between, on the one hand, judgements of the predictive accuracy of a risk assessment tool and, on the (...) other, conclusions concerning the justified use of such an instrument in sentencing practice, is often very unclear. The purpose of this paper is to examine this relation. More precisely, it is argued that the relation between predictive accuracy and the question as to whether a new risk assessment tool should be introduced in sentencing practice is highly complicated. For instance, there may be cases in which a new risk assessment tool is more accurate than those currently in use, but should nevertheless not be introduced; and conversely, where a new tool is less accurate, but where its introduction instead of current tools would be morally preferable. (shrink)

In contrast to the assumptions of standard economic theory, recent experimental evidence shows that the income of peers has a systematic impact on observed degrees of risk aversion. This paper reports the findings of two experiments examining the impact of income inequality on risk preferences and whether the knowledge of inequality mediates the decisions. In Experiment 1, participants who were recruited for a real-effort task were paid either a low wage or a high wage. Half of the (...) participants were aware of the income inequality, while the other half were not. After completing their task, they were invited to invest a part of their salary in a risky asset. In Experiment 2, we replicated the same experiment in the laboratory with windfall endowments to test the consistency of results in the laboratory settings. The results of the first experiment show that high-wage subjects take higher risks than low-wage participants do if they are aware of the inequality in wages. This finding supports the idea that income comparisons shape risky decisions. In Experiment 2, on the other hand, we did not observe any significant differences in decisions. This may suggest that the income comparison is sensitive to house-money effect. (shrink)

Expected-utility theory advances representation theorems that do not take the risk an act generates as a consequence of the act. However, a principle of expected-utility maximization that explains the rationality of preferences among acts must, for normative accuracy, take the act’s risk as a consequence of the act if the agent cares about the risk. I defend this conclusion against the charge that taking an act’s consequences to comprehend all the agent cares about trivializes the principle (...) of expected-utility maximization. (shrink)

Downside risk aversion (downside RA) and decreasing absolute risk aversion (DARA) are different concepts that describe preferences for which the harm from bearing risk is lessened by an increase in wealth. This note presents some intuitive explanations of the difference between the two concepts using simple lotteries and graphical analysis. All risk-averse utility functions exhibit downside risk aversion, except those that exhibit sufficiently strong increasing absolute risk aversion. In a sense, downside RA is to (...) be expected: adding downside risk to a baseline lottery is analogous to increasing risk while adding upside risk is analogous to decreasing risk. The difference between the two concepts can be attributed to the use of different measures of the harm from risk bearing: downside RA measures harm using the utility premium and DARA measures harm using the risk premium. The two premia can change at different rates and even in different directions as wealth increases. (shrink)

There exists no completely satisfactory theory of risk attitude in current normative decision theories. Existing notions confound attitudes to pure risk with unrelated psychological factors such as strength of preference for certain outcomes, and probability weighting. In addition traditional measures of risk attitude frequently cannot be applied to non-numerical consequences, and are not psychologically intuitive. I develop Pure Risk theory which resolves these problems – it is consistent with existing normative theories, and both internalises (...) and generalises the intuitive notion of risk being related to the probability of not achieving one’s aspirations. Existing models which ignore pure risk attitudes may be misspecified, and effects hitherto modelled as loss aversion or utility curvature may be due instead to Pure Risk attitudes. (shrink)