Elicitation methods in decision-making under risk allow us to infer the utilities of outcomes as well as the probability weights from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes the inevitable distortion of preferences by random errors into account and minimizes the effect of such errors on the inferred utility and probability weighting functions. Under mild assumptions, the optimally efficient method for eliciting utilities and probability weights is the following three-stage procedure. (...) First, a probability is elicited whose subjective weight is one half. Second, the utility function is elicited through the midpoint chaining certainty equivalent method using the probability elicited at the first stage. Finally, the probability weighting function is elicited through the probability equivalent method. (shrink)

This paper contributes to the mathematical foundations of the model for utility theory developed by Richard Jeffrey in The Logic of Decision [5]. In it I discuss the relationship of Jeffrey's to classical models, state and interpret an existence theorem for numerical utilities and subjective probabilities and restate a theorem on their uniqueness.

The rule to maximize expected utility is intended for decisions where options involve risk. In those decisions the decision maker's attitude toward risk is important, and the rule ought to take it into account. Allais's and Ellsberg's paradoxes, however, suggest that the rule ignores attitudes toward risk. This suggestion is supported by recent psychological studies of decisions. These studies present a great variety of cases where apparently rational people violate the rule because of aversion or attraction to risk. Here I (...) attempt to resolve the issue concerning expected utility and risk. I distinguish two versions of the rule to maximize expected utility. One adopts a broad interpretation of the consequences of an option and has great intuitive appeal. The other adopts a narrow interpretation of the consequences of an option and seems to have certain technical and practical advantages. I contend that the version of the rule that interprets consequences narrowly does indeed neglect attitudes toward risk. That version of the rule excludes the risk involved in an option from the consequences of the option and, contrary to what is usually claimed, cannot make up for this exclusion through adjustments in probability and utility assignments. I construct a new, general argument that establishes this in a rigorous way. On the other hand, I contend that the version of the rule that interprets consequences broadly takes account of attitudes toward risk by counting the risk involved in an option among the consequences of the option. I rebut some objections to this version of the rules, in particular, the objection that the rule lacks practical interest. Drawing upon the literature on 'mean-risk' decision rules, I show that this version of the rule can be used to solve some realistic decision problems. (shrink)

Beliefs come in different strengths. An agent's credence in a proposition is a measure of the strength of her belief in that proposition. Various norms for credences have been proposed. Traditionally, philosophers have tried to argue for these norms by showing that any agent who violates them will be lead by her credences to make bad decisions. In this article, we survey a new strategy for justifying these norms. The strategy begins by identifying an epistemic utility function and a decision-theoretic (...) norm; we then show that the decision-theoretic norm applied to the epistemic utility function yields the norm for credences that we wish to justify. We survey results already obtained using this strategy, and we suggest directions for future research. (shrink)

Causal decision theory attends to probabilities used to obtain an option's expected utility but for completeness should also attend to utilities of possible outcomes. A suitable formula for an option's expected utility uses a certain type of conditional utility.

An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that (...) computation of an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement. (shrink)

Decision theory and the theory of rational choice have recently been the subjects of considerable research by philosophers and economists. However, no adequate anthology exists which can be used to introduce students to the field. This volume is designed to meet that need. The essays included are organized into five parts covering the foundations of decision theory, the conceptualization of probability and utility, pholosophical difficulties with the rules of rationality and with the assessment of probability, and causal decision theory. The (...) editors provide an extensive introduction to the field and introductions to each part. (shrink)

Probability is a central concept in utilitarian moral theory, almost impossible to do without. I attempt to clarify the role of probability, so that we can be clear about what we are aiming for when we apply utilitarian theory to real cases. I point out the close relationship between utilitarianism and expected-utility theory, a normative standard for individual decision-making. I then argue that the distinction between “ambiguity” and risk is a matter of perception. We do not need this distinction in (...) the theory itself. In order to make this argument I rely on the personalist theory of probability, and I try to show that, within this theory, we do not need to give up completely on the idea that a “true probability” exists. Finally, I discuss several examples of applied utilitarianism, emphasizing the role of probability in each example: reasonable doubt, the precautionary principle in risk regulation, charity, climate change, and voting. (shrink)

As I sit down to begin this essay, the strains of “Tristan und Isolde” are still ringing in my ears; meanwhile, another dozen or so Pakistanian refugees have died for lack of sufficient food, shelter, or medical attention, probably, during the time it will have taken to compose this paragraph. The Isolde in that performance commanded, probably, a fee of four or five thousand dollars; each member of the audience paid, on the average, perhaps ten dollars to see the performance. (...) This works out, probably, to an average of one year’s worth of refugees kept alive and in some sort of health for every two members of the audience, or about two hundred for the wages of the leading soprano for one evening. The arithmetic is doubtless inaccurate: possibly it would require as much as three opera tickets to keep our refugee going, and Isolde could manage but fifty. But the orders of magnitude are about right. (shrink)

Sutton ( 2010 ) claims that on our analysis (2007), the problem in the two-envelope paradox is an error in counterfactual reasoning. In fact, we distinguish two formulations of the paradox, only one of which, on our account, involves an error in conditional reasoning. According to Sutton, it is conditional probabilities rather than subjunctive conditionals that are essential to the problem. We argue, however, that his strategy for assigning utilities on the basis of conditional probabilities leads to (...) absurdity. In addition, we show that a crucial presupposition of Sutton’s argument — namely, that one can know that envelope A contains n simply on the basis of a stipulation — is mistaken. (shrink)

We find suggestive evidence that emotional balance has an impact on probability weighting incremental to demographic controls. Specifically, low negative affectivity (implying high emotional balance) tends to be a characteristic of those whose probability weighting functions exhibit lower curvature and more neutral elevation. In other words, emotional balance seems to push people in the direction of normative expected utility theory.

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)

Richard Jeffrey is beyond dispute one of the most distinguished and influential philosophers working in the field of decision theory and the theory of knowledge. His work is distinctive in showing the interplay of epistemological concerns with probability and utility theory. Not only has he made use of standard probabilistic and decision theoretic tools to clarify concepts of evidential support and informed choice, he has also proposed significant modifications of the standard Bayesian position in order that it provide a better (...) fit with actual human experience. Probability logic is viewed not as a source of judgment but as a framework for explaining the implications of probabilistic judgments and their mutual compatability. This collection of essays spans a period of some 35 years and includes what have become some of the classic works in the literature. There is also one completely new piece, while in many instances Jeffrey includes afterthoughts on the older essays. (shrink)

This note is a postscript to Ramsey's 'Truth and Probability'. It replaces that article's psychological reading of subjective probability with a reading of it as a consistency condition on the theory that we act to maximise expected utility.

We argue that indeterminate probabilities are not only rationally permissible for a Bayesian agent, but they may even be rationally required . Our first argument begins by assuming a version of interpretivism: your mental state is the set of probability and utility functions that rationalize your behavioral dispositions as well as possible. This set may consist of multiple probability functions. Then according to interpretivism, this makes it the case that your credal state is indeterminate. Our second argument begins with (...) our describing a world that plausibly has indeterminate chances. Rationality requires a certain alignment of your credences with corresponding hypotheses about the chances. Thus, if you hypothesize the chances to be indeterminate, your will inherit their indeterminacy in your corresponding credences. Our third argument is motivated by a dilemma. Epistemic rationality requires you to stay open-minded about contingent matters about which your evidence has not definitively legislated. Practical rationality requires you to be able to act decisively at least sometimes. These requirements can conflict with each other-for thanks to your open-mindedness, some of your options may have undefined expected utility, and if you are choosing among them, decision theory has no advice to give you. Such an option is playing Nover and Hájek’s Pasadena Game , and indeed any option for which there is a positive probability of playing the Pasadena Game. You can serve both masters, epistemic rationality and practical rationality, with an indeterminate credence to the prospect of playing the Pasadena game. You serve epistemic rationality by making your upper probability positive-it ensures that you are open-minded. You serve practical rationality by making your lower probability 0-it provides guidance to your decision-making. No sharp credence could do both. (shrink)

Background:The management of challenging behaviours in inpatient with intellectual disability and/or autism spectrum disorders can lead to an escalation of control measures. In these complex situations where patients have an intellectual disability/autism spectrum disorder accompanied by a psychiatric comorbidity, the experiences of caregivers related to the crisis management have rarely been studied.Purpose:This study examined the moral experiences of caregivers related to challenging behaviours’ management and alternatives to control measures.Research design:Using Charles Taylor’s hermeneutic framework, a 2-month focused ethnography with a participatory (...) approach was used.Participants and research context:Sixteen caregivers were interviewed in a Canadian mental health setting for adults with intellectual disability/autism spectrum disorder and psychiatric comorbidity.Ethical considerations:The research was conducted in compliance with the Declaration of Helsinki and local Research Ethics Board approval. Written informed consent was collected systematically from participants.Findings:By accounting for caregivers’ moral experiences, this study sheds light on a neglected dimension of the care relationship: the vulnerability of the caregiver. We highlight the main barriers and facilitators to alternatives to control measures. First, a caregiver’s vulnerability was characterised by the overall impact of challenging behaviours and the moral distress associated with the use of control measures and exclusion mechanisms of intellectual disability/autism spectrum disorder patients. Second, a strong ambiguity between care and control measures and a lack of inclusive approaches were identified as the two main barriers to challenging behaviour management. Third, the involvement, both professional and personal, of caregivers was deemed necessary to implement alternatives to control measures.Discussion:A conflict of values opposes two conceptions of autonomy: a rational autonomy, which is counterproductive to the reduction of control measures, versus a relational autonomy based on shared vulnerability.Conclusion:The recognition of caregiver’s vulnerability is a benchmark to create alternative approaches, which defuse the logic of control and promote an ethics of care within which caregivers’ self-concern can be understood as fostering mutual respect. (shrink)

Several authors have argued that act–utilitarianism cannot provide an adequate critique of buying meat because a single meat purchase will not actually cause more farm animals to be raised or slaughtered. Thus, regardless of whether or not the production of meat is inhumane to animals, someone who buys meat is doing nothing wrong. This argument fails to show that meat purchases are morally permissible, however, because it assumes that act–utilitarians would use actual utility in their decision to buy or not (...) to buy meat. I show that act–utilitarians cannot use actual utility as a decision procedure and must instead use expected utility to prescribe or proscribe actions. I then demonstrate how expected utility can be applied to cases of contributory causation, where many people seem morally responsible for causing something to happen. Buying meat is one case of contributory causation where the probability of any single individual's affecting meat production is slight, but the expected disutility of affecting that production is substantial. Thus, in its expected utility form, act–utilitarianism defeats the ‘causal inefficacy’ defence of buying meat [1]. (shrink)

The response mode bias, in which subjects exhibit different risk attitudes when assessing certainty equivalents versus indifference probabilities, is a well-known phenomenon in the assessment of utility functions. In this empirical study, we develop and apply a cardinal measure of risk attitudes to analyze not only the existence, but also the strength of this phenomenon. Since probability levels involved in decision problems are already known to have a strong impact on behavior, we use this approach to study the impact (...) of probabilities on the extent of the response mode bias. We find that the direction in which probabilities influence measured risk aversion is the opposite in the certainty equivalence (CE) method versus in the probability equivalence (PE) method. Utilizing the CE elicitation approach leads to an increase of risk seeking for gambles involving high probabilities. For the PE method, subjects tend to behave risk averse with gambles of high probabilities. This behavior is reversed in the gain domain. This “tailwhip” effect is consistently replicated in several experiments, involving both loss and gain domains of lotteries. (shrink)

Probability can be used to measure degree of belief in two ways: objectively and subjectively. The objective measure is a measure of the rational degree of belief in a proposition given a set of evidential propositions. The subjective measure is the measure of a particular subject’s dispositions to decide between options. In both measures, certainty is a degree of belief 1. I will show, however, that there can be cases where one belief is stronger than another yet both beliefs are (...) plausibly measurable as objectively and subjectively certain. In ordinary language, we can say that while both beliefs are certain, one belief is more certain than the other. I will then propose second, non probabilistic dimension of measurement, which tracks this variation in certainty in such cases where the probability is 1. A general principle of rationality is that one’s subjective degree of belief should match the rational degree of belief given the evidence available. In this paper I hope to show that it is also a rational principle that the maximum stake size at which one should remain certain should match the rational weight of certainty given the evidence available. Neither objective nor subjective measures of certainty conform to the axioms of probability, but instead are measured in utility. This has the consequence that, although it is often rational to be certain to some degree, there is no such thing as absolute certainty. (shrink)

A generalization of the usual approach to the expected utility theory is given, with the aim of representing the state of belief of an agent who may decline on grounds of ignorance to express a preference between a given pair of acts and would, therefore, be considered irrational from a Bayesian point of view. Taking state, act, and outcome as primitive concepts, a utility function on the outcomes is constructed in the usual way. Each act is represented by a utility-valued (...) function on the states — but not all such functions are taken to represent acts. A weaker than usual set of axioms on preferences between acts is now postulated. It is shown that any agent can be represented by a risk function that assigns to each (mixed) state a number that gives the maximum loss (in utility) the agent might expect should be the actual state of the world. The form of the risk function is determined, both in general and in important particular cases. The results show that any rational agent behaves as though he were acting under the guidance of a set of Bayesian (or, more generally, pseudo-Bayesian) advisors. (shrink)

I argue that information is a goal-relative concept for Bayesians. More precisely, I argue that how much information is provided by a piece of evidence depends on whether the goal is to learn the truth or to rank actions by their expected utility, and that different confirmation measures should therefore be used in different contexts. I then show how information measures may reasonably be derived from confirmation measures, and I show how to derive goal-relative non-informative and informative priors given background (...) information. Finally, I argue that my arguments have important implications for both objective and subjective Bayesianism. In particular, the Uniqueness Thesis is either false or must be modified. Moreover, objective Bayesians must concede that pragmatic factors systematically influence which priors are rational, and subjective Bayesians must concede that pragmatic factors sometimes partly determine which prior distribution most accurately represents an agent’s epistemic state. (shrink)

This essay gives necessary and sufficient conditions for recovering expected utility from choice behavior in several popular models of uncertainty. In particular, these techniques handle a finite state model; a model for which the choice space consists of probability densities and the expected utility representation requires bounded, measurable utility; and a model for which the choice space consists of Borel probability measures and the expected utility representation requires bounded, continuous utility. The key result is the identification of the continuity condition (...) necessary for the revelation of linear utility. (shrink)