The Expected Shortfall or Conditional Value-at-Risk (CVaR) has been playing the role of main risk measure in the recent years and paving the way for an enormous number of applications in risk management due to its very intuitive form and important coherence properties. This work aims to explore this measure as a probability-dependent utility functional, introducing an alternative view point for its Choquet Expected Utility representation. Within this point of view, its main preference properties will be (...) characterized and its utility representation provided through local utilities with an explicit dependence on the assessed revenue’s distribution (quantile) function. Then, an intuitive interpretation for the related probability dependence and the piecewise form of such utility will be introduced on an investment pricing context, in which a CVaR maximizer agent will behave in a relativistic way based on his previous estimates of the probability function. Finally, such functional will be extended to incorporate a larger range of risk-averse attitudes and its main properties and implications will be illustrated through examples, such as the so-called Allais Paradox. (shrink)

Many philosophers accept that, as well as having a right that others not harm us, we also have a right that others not subject us to a risk of harm. And yet, when we attempt to spell out precisely what this ‘right against risk imposition’ involves, we encounter a series of notorious puzzles. Existing attempts to deal with these puzzles have tended to focus on the nature of rights – but I propose an approach that focusses instead on (...) the nature of risk. The key move is to distinguish two different ways in which to conceptualise the risk that a given action presents – one of which is linked to the notion of probability and the other to the notion of normalcy. (shrink)

This paper examines and evaluates a range of methodologies that have been proposed for making useful claims about the probability of phenomena that would contribute to existential risk. Section One provides a brief discussion of the nature of such claims, the contexts in which they tend to be made and the kinds of probability that they can contain. Section Two provides an overview of the methodologies that have been developed to arrive at these probabilities and assesses their (...) advantages and disadvantages. Section Three contains four suggestions to improve best practice in existential risk assessment. These suggestions centre on the types of probabilities used in risk assessment, the role of methodology rankings including the ranking of probabilistic information, the extended use of expert elicitation, and the use of confidence measures to better communicate uncertainty in probability assessments. Finally, Section Four provides an annotated literature review of catastrophic and existential risk probability claims as well as the methodologies that were used to produce each of them. (shrink)

This paper examines and evaluates a range of methodologies that have been proposed for making useful claims about the probability of phenomena that would contribute to existential risk. Section One provides a brief discussion of the nature of such claims, the contexts in which they tend to be made and the kinds of probability that they can contain. Section Two provides an overview of the methodologies that have been developed to arrive at these probabilities and assesses their (...) advantages and disadvantages. Section Three contains four suggestions to improve best practice in existential risk assessment. These suggestions centre on the types of probabilities used in risk assessment, the role of methodology rankings including the ranking of probabilistic information, the extended use of expert elicitation, and the use of confidence measures to better communicate uncertainty in probability assessments. Finally, Section Four provides an annotated literature review of catastrophic and existential risk probability claims as well as the methodologies that were used to produce each of them. (shrink)

This paper examines and evaluates a range of methodologies that have been proposed for making useful claims about the probability of phenomena that would contribute to existential risk. Section One provides a brief discussion of the nature of such claims, the contexts in which they tend to be made and the kinds of probability that they can contain. Section Two provides an overview of the methodologies that have been developed to arrive at these probabilities and assesses their (...) advantages and disadvantages. Section Three contains four suggestions to improve best practice in existential risk assessment. These suggestions centre on the types of probabilities used in risk assessment, the role of methodology rankings including the ranking of probabilistic information, the extended use of expert elicitation, and the use of confidence measures to better communicate uncertainty in probability assessments. Finally, Section Four provides an annotated literature review of catastrophic and existential risk probability claims as well as the methodologies that were used to produce each of them. (shrink)

Many scientists, businessmen, and government regulators believe that the criteria for acceptable societal risk are too stringent. Those who subscribe to this belief often accept the view which I call the probability-threshold position. Proponents of this stance maintain that society ought to ignore very small risks, i.e., those causing an average annual probability of fatality of less than 10–6.After examining the three major views in the risk-evaluation debate, viz., the probability-threshold position, the zero-risk position, (...) and the weighted-risk position, I focus on the arguments for the first of these views, since it is the position which currently undergirds most public policy (especially in the U.S.) regarding acceptable risk. After analyzing Arrow's argument from decision theory, Comar's and Gibson's argument from ontology, and Starr's and Whipple's argument from epistemology, I conclude that these defenses of the probability-threshold position err in a variety of ways. Most commonly, they fail because they tacitly accept the assumption that magnitude of probability, alone, provides a sufficient condition for judging the acceptability of a given risk. In the light of these errors, I suggest that it might be more desirable for risk assessors, decision theorists, and policymakers to weight various risk-cost-benefit parameters according to alternative ethical criteria, rather than to evaluate risks solely in terms of mathematical considerations. (shrink)

Probability transformation functions were introduced into modelsof behavior toward risk to allow them to accommodate violations of the expected utility hypothesis.This paper examines the shape of the probability transformation function, its interpretation asoptimism or pessimism, and how the ranking of outcomes becomes important when probability transformationsare used. It also explores two behavioral implications: the overweighting of unlikely, extremeoutcomes, and intertia around certainty. Finally, the rationality of transforming the probabilitydistribution is discussed.

Probability transformation functions were introduced into modelsof behavior toward risk to allow them to accommodate violations of the expected utility hypothesis.This paper examines the shape of the probability transformation function, its interpretation asoptimism or pessimism, and how the ranking of outcomes becomes important when probability transformationsare used. It also explores two behavioral implications: the overweighting of unlikely, extremeoutcomes, and intertia around certainty. Finally, the rationality of transforming the probabilitydistribution is discussed.

Women are commonly stereotyped as more risk averse than men in financial decision making. In this paper we examine whether this stereotype reflects gender differences in actual risk-taking behavior by means of a laboratory experiment with monetary incentives. Gender differences in risk taking may be due to differences in valuations of outcomes or in probability weights. The results of our experiment indicate that value functions do not differ significantly between men and women. Men and women differ (...) in their probability weighting schemes, however. In general, women tend to be less sensitive to probability changes. They also tend to underestimate large probabilities of gains more strongly than do men. This effect is particularly pronounced when the decisions are framed in investment terms. As a result, women appear to be more risk averse than men in specific circumstances. (shrink)

Beginning with an analysis of the "reluctant gambler problem"—in which the notion of guiding one's life by probability seems to conflict with the preferences of rational people—we draw a distinction between rule and act probabilism. Arguing that humans are rule probabilists by default, we show that reluctant gamblers can be viewed as rule probabilists. If so viewed, their reluctance to gamble is consistent with their rational use of probability judgments to guide their lives.The distinction between rule and act (...) probabilism suggests a way to analyze the risks stemming from the September 11 terrorist attacks. Assessing the risks posed by the new reality of terrorism in the U.S. in light of the rule versus act probabilist distinction shows the risks Americans face from a terrorist attack are essentially the same as they were before September 11, 2002. Yet empirical investigation indicates Americans exaggerate their personal risks from terrorism.The perception that the risks of terrorism mushroomed on September 11 is partially explained by the 24-hour news stations' TV coverage and the current administration's "interest" in diverting attention from their own questionable practices. While the risks of terrorism are not appreciably higher than they were prior to September 11, they might be further reduced. Unfortunately, our government's strategy to reduce the risks of terrorist strikes involves weakening the Constitution. Americans face the question how much it is appropriate to pay—in diminished rights and liberties—to reduce a risk that is essentially the same as it was prior to the attacks. (shrink)

The status of risk factors and disease remains a disputed question in the theory and practice of medicine and healthcare, and so does the related question of delineating disease boundaries. I present a framework based on Bernard Lonergan’s account of emergent probability for differentiating (1) generically distinct levels of systematic function within organisms and between organisms and their environments and (2) the methods of functional, genetic, and statistical investigation. I then argue on this basis that it is possible (...) to understand disease in terms of biological or higher intra-level dysfunction, risk factors—including genetic risk factors—in terms of statistical inter-level conditioning of a given stage or developmental sequence of systematic functioning, and the empirical boundaries of disease in terms of the limits of both functional categorization (from an epistemic standpoint) and upper-level integration of lower-level processes and events (from an ontological standpoint). (shrink)

In comparing different risk elicitation methods under the assumptions of expected utility theory, previous studies have found significant differences in the elicited risk attitudes. This paper extends this line of research to consider cumulative prospect theory by comparing risk attitudes and probability weightings determined using two elicitation methods: the method by Tanaka et al. :557–571, 2010; TCN method) and the method by Wakker and Deneffe :1131–1150, 1996; WD method). We demonstrate that the two methods reveal significantly (...) different mean values for the measured risk attitudes. Participants are classified on average as moderately risk-averse using the TCN method, whereas the same individuals are classified as nearly risk-neutral using the WD method. Moreover, we find that on average, participants overweight low probabilities and underweight high probabilities to a greater extent with the WD method than with the TCN method. Therefore, the different elicitation methods, that both consider probability weighting, can lead to different measured values of risk attitude and probability weighting. (shrink)

Women are commonly stereotyped as more risk averse than men in financial decision making. In this paper we examine whether this stereotype reflects gender differences in actual risk-taking behavior by means of a laboratory experiment with monetary incentives. Gender differences in risk taking may be due to differences in valuations of outcomes or in probability weights. The results of our experiment indicate that value functions do not differ significantly between men and women. Men and women differ (...) in their probability weighting schemes, however. In general, women tend to be less sensitive to probability changes. They also tend to underestimate large probabilities of gains more strongly than do men. This effect is particularly pronounced when the decisions are framed in investment terms. As a result, women appear to be more risk averse than men in specific circumstances. (shrink)

Second or higher order probabilities have commonly been viewed with scepticism by those working within the realm of probability and decision theory. The aim of the present note is to show how the notion of second order probabilities can add to our understanding of judgmental and decision processes and how the traditional framework of Bayesian decision theory can be extended in a fruitful way by taking such entities into account. Section one consists of a brief account of arguments put (...) forth against higher order probabilities as well as of counterarguments. In order to provide an example of the applicability of second order probabilities a decision theory encompassing such probabilities will be presented in section two. In section three I will try to emphasize the value of second order probabilities for a deeper and more complete understanding of the notion of risk. (shrink)

Many widely divergent accounts of luck have been offered or employed in discussing an equally wide range of philosophical topics. We should, then, expect to find some unified philosophical conception of luck of which moral luck, epistemic luck, and luck egalitarianism are species. One of the attempts to provide such an account is that offered by Duncan Pritchard, which he refers to as the modal account. This view commits us to calling an event lucky when it obtains in this world, (...) but fails to obtain in a wide class of nearby possible worlds. In support of this account, Pritchard argues that a theory of luck ought to capture the fact that luck comes in degrees and that luck is closely associated with risk. I argue against this claim by suggesting that an understanding of luck grounded in considerations of probability is better able to satisfy these demands, and that the probability theory better explains exemplary cases of luck like those brought up by Pritchard. (shrink)

In a controlled laboratory experiment we use one sample of college students and one of mature executives to investigate how positive skew influences risky choices. In reduced-form regressions we find that both students and executives make riskier choices when lotteries display positive skew. We estimate decision models to explore three explanations for skew seeking choices: risk-loving, optimism and likelihood insensitivity. We find no role for love for risk as neither students nor executives have convex utility. Both optimism and (...) likelihood insensitivity play a part in skew seeking choices. Likelihood insensitivity is larger for students than for executives. Executives have more concave utility and are more optimistic than students, but this is found to be largely due to them being older. (shrink)

In the probability literature, a martingale is often referred to as a “fair game.” A martingale investment is a stochastic sequence of wealth levels, whose expected value at any future stage is equal to the investor’s current wealth. In decision theory, a risk neutral investor would therefore be indifferent between holding on to a martingale investment, and receiving its payoff at any future stage, or giving it up and maintaining his current wealth. But a risk-averse decision maker (...) would not be indifferent between a martingale investment and his current wealth level, since he values uncertain deals less than their mean. A risk seeking decision maker, on the other hand, would readily accept a martingale investment in exchange for his current wealth, and would repeat this investment any number of times. These ideas lead us to introduce the notion of a “risk-adjusted martingale”; a stochastic sequence of wealth levels that a rational decision maker with any attitude toward risk would value constantly with time, and would be indifferent between receiving its pay-off at any future stage, or giving it up and maintaining his current wealth level. We show how to construct such risk-adjusted investments for any decision maker with a continuous monotonic utility function. The fundamental result we derive is that a pay-off structure of an investment (i) is a risk-adjusted martingale and (ii) can be represented by a lattice if and only if the pay-off functions are invariant transformations of the given utility function. (shrink)

In this article, ambiguity attitude is measured through the maximum price a decision maker is willing to pay to know the probability of an event. Two problems are examined in which the decision maker faces an act: in one case, buying information implies playing a lottery, while, in the other case, buying information gives also the option to avoid playing the lottery. In both decision settings, relying on the Choquet expected utility model, we study how the decision maker’s (...) class='Hi'>risk and ambiguity attitudes affect the reservation price for ambiguity resolution. These effects are analyzed for different levels of ambiguity of the act. Operating instructions for the elicitation of the reservation price for ambiguity resolution in an experimental setting are provided at the end of the article. (shrink)

Some risks have extremely high stakes. For example, a worldwide pandemic or asteroid impact could potentially kill more than a billion people. Comfortingly, scientific calculations often put very low probabilities on the occurrence of such catastrophes. In this paper, we argue that there are important new methodological problems which arise when assessing global catastrophic risks and we focus on a problem regarding probability estimation. When an expert provides a calculation of the probability of an outcome, they are really (...) providing the probability of the outcome occurring, given that their argument is watertight. However, their argument may fail for a number of reasons such as a flaw in the underlying theory, a flaw in the modeling of the problem, or a mistake in the calculations. If the probability estimate given by an argument is dwarfed by the chance that the argument itself is flawed, then the estimate is suspect. We develop this idea formally, explaining how it differs from the related distinctions of model and parameter uncertainty. Using the risk estimates from the Large Hadron Collider as a test case, we show how serious the problem can be when it comes to catastrophic risks and how best to address it. (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 (...) class='Hi'>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)

Our understanding of the decisions made under scenarios where both descriptive and experience-based information are available is very limited. Underweighting of small probabilities was observed in the gain domain when both description and experience were provided. The divergence observed from the prospect theory suggests a need for a separate or modified theory of decision making under risk. Recent studies suggest a possible role of probability weighting in the choice behaviour under risk. We investigated both gain and loss (...) domains with and without feedback for small and large probability conditions. We characterized the shape of the probability weighting function by a two-parameter functional form representing discriminability (concave-convex shape) and attractiveness (level of absolute weights relative to objective probability). We replicated four-fold pattern of risk attitude on non-WEIRD population. We find that feedback leads to underweighting of small probabilities and overweighting of large probabilities in the gain domain and overall underweighting of probabilities in the loss domain. We find that underweighting of small probabilities is driven by changes in discriminability and attractiveness components in the gain domain and changes in the attractiveness component in the loss domain. We have interpreted the results by proposing an updated belief-based account of decisions under uncertainty in which feedback, when available, influences the probability weighting mediating the choice behaviour. (shrink)

This paper aims to scrutinize how the notion of risk should be understood and applied to possibly catastrophic cases. I begin with clarifying the standard usage of the notion of risk, particularly emphasizing the conceptual relation between risk and probability. Then, I investigate how to make decisions in the case of seemingly catastrophic disasters by contrasting the precautionary principle with the preventive (prevention) principle. Finally, I examine what kind of causal thinking tends to be actually adopted (...) when we make decisions on emergent cases. My arguments are mainly based on Japan's 2011 massive earthquake and nuclear power station accident. Masaki Ichinose. (shrink)

The relative input of payoffs and probabilities into risk judgment The study was designed to investigate the relative input of payoffs and probabilities into risk judgment on the basis of the analysis of information search pattern. The modified version of MouselabWeb software was used as an investigative tool. The amount, the kind and the order of information accessed by subjects to evaluate risk was collected from ordinary respondents and respondents trained in mathematics and statistics. In the latter (...) group were 75 students and young researchers working at National Aeronautics and Space Administration. The ordinary subjects were 67 Polish students of social sciences. As expected, the NASA group considered more information than ordinary students and searched for more information about probabilities. However, the ratio of information about payoffs to probabilities was close to 1 in both groups. Moreover, average risk rates were similar in both groups. It was also observed that risk rates were positively related with the amount of information about probabilities considered by subjects. (shrink)

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)

Perhaps the topic of acceptable risk never had a sexier and more succinct introduction than the one Edward Norton, playing an automobile company executive, gave it in Fight Club: “Take the number of vehicles in the field (A), multiply it by the probable rate of failure (B), and multiply the result by the average out of court settlement (C). A*B*C=X. If X is less than the cost of the recall, we don’t do one.” Of course, this dystopic scene also (...) gets to the heart of the issue in another way: acceptable risk deals with mathematical calculations about the value of life, injury, and emotional wreckage, making calculation a difficult matter ethically, politically, and economically. This entry will explore the history of this idea, focusing on its development alongside statistics into its wide importance today. (shrink)

With the ascent of modern epidemiology in the Twentieth Century came a new standard model of prediction in public health and clinical medicine. In this article, we describe the structure of the model. The standard model uses epidemiological measures-most commonly, risk measures-to predict outcomes (prognosis) and effect sizes (treatment) in a patient population that can then be transformed into probabilities for individual patients. In the first step, a risk measure in a study population is generalized or extrapolated to (...) a target population. In the second step, the risk measure is particularized or transformed to yield probabilistic information relevant to a patient from the target population. Hence, we call the approach the Risk Generalization-Particularization (Risk GP) Model. There are serious problems at both stages, especially with the extent to which the required assumptions will hold and the extent to which we have evidence for the assumptions. Given that there are other models of prediction that use different assumptions, we should not inflexibly commit ourselves to one standard model. Instead, model pluralism should be standard in medical prediction. (shrink)

In this paper, we illustrate some serious difficulties involved in conveying information about uncertain risks and securing informed consent for risky interventions in a clinical setting. We argue that in order to secure informed consent for a medical intervention, physicians often need to do more than report a bare, numerical probability value. When probabilities are given, securing informed consent generally requires communicating how probability expressions are to be interpreted and communicating something about the quality and quantity of the (...) evidence for the probabilities reported. Patients may also require guidance on how probability claims may or may not be relevant to their decisions, and physicians should be ready to help patients understand these issues. (shrink)

It is argued that the standard way that the criminal justice debate regarding the permissible extent of wrongful convictions is cast is fundamentally flawed. In particular, it is claimed that there is an inherent danger in focussing our attention in this debate on different ways of measuring the probabilistic likelihood of wrongful conviction and then evaluating whether these probabilities are unacceptably high. This is because such probabilistic measures are clumsy ways of capturing the level of risk involved, to the (...) extent that a defendant can be subject to an unacceptably high level of legal risk in this regard even where the relevant probabilities are very low. An alternative conception of legal risk – one that is primarily cast along modal rather than probabilistic lines – is set out which offers a much better way of framing the debate regarding what would be an acceptable level of wrongful conviction. It is further argued that with this modal conception of legal risk in play we can capture an important necessary condition that should be imposed on legal evidence, one that has application beyond the context of the criminal trial. (shrink)

The notion of risk plays a central role in economics, finance, health, psychology, law and elsewhere, and is prevalent in managing challenges and resources in day-to-day life. In recent work, Duncan Pritchard (2015, 2016) has argued against the orthodox probabilistic conception of risk on which the risk of a hypothetical scenario is determined by how probable it is, and in favour of a modal conception on which the risk of a hypothetical scenario is determined by how (...) modally close it is. In this article, we use Pritchard’s discussion as a springboard for a more wide-ranging discussion of the notion of risk. We introduce three different conceptions of risk: the standard probabilistic conception, Pritchard’s modal conception, and a normalcy conception that is new (though it has some precursors in the psychological literature on risk perception). Ultimately, we argue that the modal conception is ill-suited to the roles that a notion of risk is required to play and explore the prospects for a form of pluralism about risk, embracing both the probabilistic and the normalcy conceptions. (shrink)

How much does rationality constrain what we should believe on the basis of our evidence? According to this book, not very much. For most people and most bodies of evidence, there is a wide range of beliefs that rationality permits them to have in response to that evidence. The argument, which takes inspiration from William James' ideas in 'The Will to Believe', proceeds from two premises. The first is a theory about the basis of epistemic rationality. It's called epistemic utility (...) theory, and it says that what it is epistemically rational for you to believe is what it would be rational for you to choose if you were given the chance to pick your beliefs and, when picking them, you were to care only about their epistemic value. So, to say which beliefs are permitted, we must say how to measure epistemic value, and which decision rule to use when picking your beliefs. The second premise is a claim about attitudes to epistemic risk, and it says that rationality permits many different such attitudes. These attitudes can show up in epistemic utility theory in two ways: in the way you measure epistemic value; and in the decision rule you use to pick beliefs. This book explores the latter. The result is permissivism about epistemic rationality: different attitudes to epistemic risk lead to different choices of prior beliefs; given most bodies of evidence, different priors lead to different posteriors; and even once we fix your attitudes to epistemic risk, if they are at all risk-inclined, there is a range of different priors and therefore different posteriors they permit. (shrink)

The dominance of the modern concept of risk and calculability is challenged by and has to be distinguished from “manufactured uncertainties.” Typically today, conflict and controversy flare up around this particular type of new manufactured risk. Neither natural disasters – threats – coming from the outside and thus attributable to God or nature have this effect any longer. Nor do the specific calculable uncertainties – “risks” – which are determinable with actuarial precision interms of a probability calculus (...) backed up by insurance and monetary compensation fall in this category. At the centre of attention today, by contrast, are “manufactured uncertainties.” They are distinguished by the fact that they are dependent on human decisions, created by society itself, immanent to society and thus non-externalizable, collectively imposed and thus individually unavoidable. (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)

Epistemic closure under known implication is the principle that knowledge of "p" and knowledge of "p implies q", together, imply knowledge of "q". This principle is intuitive, yet several putative counterexamples have been formulated against it. This paper addresses the question, why is epistemic closure both intuitive and prone to counterexamples? In particular, the paper examines whether probability theory can offer an answer to this question based on four strategies. The first probability-based strategy rests on the accumulation of (...) risks. The problem with this strategy is that risk accumulation cannot accommodate certain counterexamples to epistemic closure. The second strategy is based on the idea of evidential support, that is, a piece of evidence supports a proposition whenever it increases the probability of the proposition. This strategy makes progress and can accommodate certain putative counterexamples to closure. However, this strategy also gives rise to a number of counterintuitive results. Finally, there are two broadly probabilistic strategies, one based on the idea of resilient probability and the other on the idea of assumptions that are taken for granted. These strategies are promising but are prone to some of the shortcomings of the second strategy. All in all, I conclude that each strategy fails. Probability theory, then, is unlikely to offer the account we need. (shrink)

Having children is probably as old as the first successful organism. It is often done thoughtlessly. This book is an argument for giving procreating some serious thought, and a theory of how, when, and why procreation may be permissible.Rivka Weinberg begins with an analysis of the kind of act procreativity is and why we might be justifiably motivated to engage in it. She then proceeds to argue that, by virtue of our ownership and control of the hazardous material that is (...) our gametes, we are parentally responsible for the risks we take with our gametes and for the persons that develop when we engage in activity that allows our gametes to unite with others and develop into persons. Further argument establishes that when done respectfully, and in cases where the child's chances of leading a life of human flourishing are high, procreation may be permissible. Along the way, Weinberg argues that the non-identity problem is a curiously common mistake. Arguments intending to show that procreation is impermissible because life is bad for people and imposed on them without their consent are shown to have serious flaws. Yet because they leave us with lingering concerns, Weinberg argues that although procreation is permissible under certain conditions, it is not only a welfare risk but also a moral risk. Still, it is a risk that is often permissible for us to take and impose, given our high level of legitimate interest in procreativity. In order to ascertain when the procreative risk is permissible to impose, contractualist principles are proposed to fairly attend to the interests prospective parents have in procreating and the interests future people have in a life of human flourishing. The principles are assessed on their own merits and in comparison with rival principles. They are then applied to a wide variety of procreative cases. (shrink)

Suppose we want to do the most good we can with a particular sum of money, but we cannot be certain of the consequences of different ways of making use of it. This article explores how our attitudes towards risk and ambiguity bear on what we should do. It shows that risk-avoidance and ambiguity-aversion can each provide good reason to divide our money between various charitable organizations rather than to give it all to the most promising one. It (...) also shows how different attitudes towards risk and ambiguity affect whether we should give to an organization which does a small amount of good for certain or to one which does a large amount of good with some small or unknown probability. (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)