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)

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)

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)

This article argues that Lara Buchak’s risk-weighted expected utility (REU) theory fails to offer a true alternative to expected utility theory. Under commonly held assumptions about dynamic choice and the framing of decision problems, rational agents are guided by their attitudes to temporally extended courses of action. If so, REU theory makes approximately the same recommendations as expected utility theory. Being more permissive about dynamic choice or framing, however, undermines the theory’s claim to capturing a (...) steady choice disposition in the face of risk. I argue that this poses a challenge to alternatives to expected utility theory more generally. (shrink)

Risk-weighted expected utility theory is motivated by small-world problems like the Allais paradox, but it is a grand-world theory by nature. And, at the grand-world level, its ability to handle the Allais paradox is dubious. The REU model described in Risk and Rationality turns out to be risk-seeking rather than risk-averse on one natural way of formulating the Allais gambles in the grand-world context. This result illustrates a general problem with the case for REU (...) theory, we argue. There is a tension between the small-world thinking marshaled against standard expected utility theory, and the grand-world thinking inherent to the risk-weighted alternative. (shrink)

Some early phase clinical studies of candidate HIV cure and remission interventions appear to have adverse medical risk–benefit ratios for participants. Why, then, do people participate? And is it ethically permissible to allow them to participate? Recent work in decision theory sheds light on both of these questions, by casting doubt on the idea that rational individuals prefer choices that maximise expected utility, and therefore by casting doubt on the idea that researchers have an ethical obligation not to (...) enrol participants in studies with high risk–benefit ratios. This work supports the view that researchers should instead defer to the considered preferences of the participants themselves. This essay briefly explains this recent work, and then explores its application to these two questions in more detail. (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)

When you are indifferent between two options, it’s rationally permissible to take either. One way to decide between two such options is to flip a fair coin, taking one option if it lands heads and the other if it lands tails. Is it rationally permissible to employ such a tie-breaking procedure? Intuitively, yes. However, if you are genuinely risk-averse—in particular, if you adhere to risk-weighted expected utility theory (Buchak in Risk and rationality, Oxford University Press, (...) 2013) and have a strictly convex risk-function—the answer will often be no: the REU of deciding by coin-flip will be lower than the REU of choosing one of the options outright (so long as at least one of the options is a nondegenerate gamble). This turns out to be a significant worry for risk-weighted expected utility theory. I argue that it adds real bite to established worries about diachronic consistency afflicting views, like risk-weighted expected utility theory, that violate Independence. And that, while these worries might be surmountable, surmounting them comes at a price. (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)

In a recent paper Winsberg (2021) argued in favor of research into geoengineering by relying on Good’s theorem, which states that conducting research maximizes one’s expected utility. However, this result sometimes fails for risk-avoidant agents (Buchak 2010). Since risk avoidance captures some of the ’precautionary’ intuitions that critics of geoengineering share, it is important to see if geoengineering research would maximize one’s utility if risk avoidance is taken into account. I show that under some conditions (...) conducting geoengineering research would not maximize risk-weighted expected utility. (shrink)

Lara Buchak argues for a version of rank-weighted utilitarianism that assigns greater weight to the interests of the worse off. She argues that our distributive principles should be derived from the preferences of rational individuals behind a veil of ignorance, who ought to be risk averse. I argue that Buchak’s appeal to the veil of ignorance leads to a particular way of extending rank-weighted utilitarianism to the evaluation of uncertain prospects. This method recommends choices that violate the (...) unanimous preferences of rational individuals and choices that guarantee worse distributions. These results, I suggest, undermine Buchak’s argument for rank-weighted utilitarianism. (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)

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)

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)

Veritism says that the fundamental source of epistemic value for a doxastic state is the extent to which it represents the world correctly: that is, its fundamental epistemic value is deter...

We present experimental evidence that supports the thesis :602–625, 2015, Br J Philos Sci 70:77–102, 2019; Bradley in Decisions theory with a human face, Cambridge University Press, Cambridge, 2017; Goldschmidt and Nissan-Rozen in Synthese 198:7553–7575, 2021) that people might positively or negatively desire risky prospects conditional on only some of the prospects’ outcomes obtaining. We argue that this evidence has important normative implications for the central debate in normative decision theory between two general approaches on how to rationalize several common (...) patterns of preference, which are ruled out as irrational by orthodox decision theory, namely the re-individuation approach and the non-expected utility approach. (shrink)

Lara Buchak sets out a new account of rational decision-making in the face of risk. She argues that the orthodox view is too narrow, and suggests an alternative, more permissive theory: one that allows individuals to pay attention to the worst-case or best-case scenario, and vindicates the ordinary decision-maker.

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 risk-taking, (...) to derive the view. (shrink)

This poster presents results from applying agent-based modeling to an exploration of risk attitudes and rational decision making in the context of group interaction. We are also interested in the place of agent-based modeling and computational philosophy within the computational humanities. Computational philosophy has not typically been included in Digital Humanities; computational work has been done using philosophy texts as a source for analysis (Kinney 2022; Malaterre et al. 2021; Fletcher et al. 2021; Zahorec et al. 2022), but there (...) are few examples of philosophical arguments being made based on computation (Zahorec et al. 2022). Modeling is largely accepted as a computational humanist method (McCarty 2004; So 2022), but typically models are based on data rather than designed simulations as a method analogous to a thought experiment (Mayo-Wilson / Zollman 2021). Agent-based modeling is not as common in computational humanities, but we are interested in its potential; for instance, see work modeling correspondence networks to better understand lost information and biases in correspondence data sets (Buarque / Vogl 2023), or work simulating past human societies (Romanowska et al. 2021). Our project explores Lara Buchak’s theory of risk-weighted rational decision making by extending it to the context of group populations and interactions. Buchak has proposed risk-weighted expected utility maximization, which incorporates individual risk attitudes into the standard expected utility (EU) calculation based on utility and probability of outcomes (Buchak 2017). This theory provides an explanation for differences of behavior seen in human populations, while still allowing those different choices to be rational. Buchak’s theory has previously only been applied to individual decision making; our work uses agent-based modeling to develop and analyze simulations which incorporate a variety of risk attitudes (risk avoidance and risk seeking) into game theoretic interactions. This project is a collaboration between a philosopher and a research software engineer; we have worked together to develop simulations that implement agents with risk attitudes making risky choices. This presentation focuses on results from an implementation of a hawk/dove game with multiple risk attitudes and risk attitude adjustment. In the hawk/dove game cooperation, or playing dove, is better for the population, but acting aggressively, or playing hawk, is better for an individual if they are in a neighborhood of doves. To set up the game, we place agents on a grid and have them play against each of their neighbors, and accumulate payoffs based on the success of their plays. We define risk attitudes 0 through 9, where that number corresponds to the minimum number of neighbors playing dove for an agent to play hawk. An agent with risk attitude 0 is most risk seeking and always plays hawk; an agent with risk attitude 1 will play hawk if at least one neighbor plays dove; an agent with risk attitude 9 always takes the safe choice and plays dove; an agent with risk attitude 4 or 5 is risk neutral (breaking ties in different ways), which corresponds to expected utility. In this simulation we randomly set agent initial risk attitudes, and then every ten rounds agents compare their payoffs with their neighbors and adopt the most successful risk attitude in their neighborhood. The simulation is coded to stop once risk attitude adjustments stabilize. We define 13 different population states based on primary and second majority of risk averse, risk inclined, or risk moderate, and analysis of over 1 million runs indicate that while it’s more likely to stabilize with the population having become majority risk inclined, that is not the only outcome; we also see cases where the population stabilizes as risk neutral, risk avoidant, and many cases with no clear majority. This diversity of stable populations provides support for the argument that no one risk attitude is uniquely rational, but rather that risk attitudes are conventional. This matches what we observe in the real world: that different populations have different risk attitudes. Our simulations include numerous parameters to vary grid size; adjustment frequency, strategy, and wealth comparison; neighborhood sizes for observing previous choice, playing against, and comparing payoffs for adjusting risk attitudes; and different distributions for initializing risk attitudes. Analysis of parameters and adjusted risk attitudes shows that the strongest correlations are the initial distribution of risk attitudes, which tend to be preserved. * * * This poster was accepted and presented at the DH2024 conference in Washington, D.C. (shrink)

A review of some major topics of debate in normative decision theory from circa 2007 to 2019. Topics discussed include the ongoing debate between causal and evidential decision theory, decision instability, risk-weighted expected utility theory, decision-making with incomplete preferences, and decision-making with imprecise credences.

Can it be rational to be risk-averse? It seems plausible that the answer is yes—that normative decision theory should accommodate risk aversion. But there is a seemingly compelling class of arguments against our most promising methods of doing so. These long-run arguments point out that, in practice, each decision an agent makes is just one in a very long sequence of such decisions. Given this form of dynamic choice situation, and the (Strong) Law of Large Numbers, they conclude (...) that those theories which accommodate risk aversion end up delivering the same verdicts as risk-neutral theories in nearly all practical cases. If so, why not just accept a simpler, risk-neutral theory? The resulting practical verdicts seem to be much the same. In this paper, I show that these arguments do not in fact condemn those risk-aversion-accommodating theories. Risk aversion can indeed survive the long run. (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)

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)

This study extends experimental tests of (cumulative) prospect theory (PT) over prospects with more than three outcomes and tests second-order stochastic dominance principles (Levy and Levy, Management Science 48:1334–1349, 2002; Baucells and Heukamp, Management Science 52:1409–1423, 2006). It considers choice behavior of people facing prospects of three different types: gain prospects (losing is not possible), loss prospects (gaining is not possible), and mixed prospects (both gaining and losing are possible). The data supports the distinction of risk behavior into these (...) three categories of prospects, Further, probability weighting and diminishing sensitivity of utility as predicted by PT are observed. Loss aversion is, however, less pronounced, except for choices where one prospect is degenerate. The data suggests that the probability of losing may be relevant for loss aversion. (shrink)

Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the (...) consequences of their decisions, and are given ample incentives to reflect on their decisions, as predicted by Plott’s Discovered Preference Hypothesis (DPH). The results of a laboratory experiment with N = 62 participants support this hypothesis. The elicited subjective probability weighting function converges significantly toward linearity when respondents are asked to make repeated choices and are given direct feedback after each choice. Such convergence to linearity is absent in an experimental treatment where respondents are asked to make repeated choices but do not experience the resolution of risk directly after each choice, as predicted by the DPH. (shrink)

My book Risk and Rationality argues for a new alternative to the orthodox theory of rational decision-making. This alternative, risk-weighted expected utility maximization, holds that there are three important components involved in rational decision-making: utilities, probabilities, and risk-attitudes. This essay explains the basic outline of the theory and precisely how it differs from the orthodox theory. It also summarizes the main threads of argument in the book.

Two key questions of normative decision theory are: 1) whether the probabilities relevant to decision theory are evidential or causal; and 2) whether agents should be risk-neutral, and so maximise the expected value of the outcome, or instead risk-averse (or otherwise sensitive to risk). These questions are typically thought to be independent---that our answer to one bears little on our answer to the other. But there is a surprising argument that they are not. In this paper, I (...) show that evidential decision theory implies risk neutrality, at least in moral decision-making and at least on plausible empirical assumptions. Take any risk-aversion-accommodating decision theory, apply it using the probabilities prescribed by evidential decision theory, and every verdict of moral betterness you reach will match those of expected value theory. (shrink)

Lara Buchak defends a Weight-Ranked Utilitarianism (WRU) that she says avoids the critique of Rawls’s that is sometimes thought fatal: utilitarianism unjustifiably blurs the distinction between persons. Buchak’s defence depends upon (i) a version of Harsanyi’s assumption that parties to a social contract should reason as if they have an equal chance of being anyone and (ii) a hypothesis she explores in a recent article. I argue that her assumption and hypothesis are untenable. WRU fails of the generality to which (...) Buchak aspires because it fails for one of her most important cases: the distributive question posed by Rawls. (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)

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)

Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the (...) consequences of their decisions, and are given ample incentives to reflect on their decisions, as predicted by Plott’s Discovered Preference Hypothesis (DPH). The results of a laboratory experiment with N = 62 participants support this hypothesis. The elicited subjective probability weighting function converges significantly toward linearity when respondents are asked to make repeated choices and are given direct feedback after each choice. Such convergence to linearity is absent in an experimental treatment where respondents are asked to make repeated choices but do not experience the resolution of risk directly after each choice, as predicted by the DPH. (shrink)

Risk-weighted expected utility theory permits preferences which violate the Sure-Thing Principle. But preferences that violate the STP can lead to bad decisions in sequential choice problems. In particular, they can lead decision-makers to adopt a strategy that is dominated – i.e. a strategy such that some available alternative leads to a better outcome in every possible state of the world.

We propose a task for eliciting attitudes toward risk that is close to real-world risky decisions which typically involve gains and losses. The task consists of accepting or rejecting gambles that provide a gain with probability p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document} and a loss with probability 1-p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1-p$$\end{document}. We employ finite mixture models to uncover heterogeneity in risk preferences and find that behavior is heterogeneous, with (...) one half of the subjects behaving as expected utility maximizers, for the others, reference-dependent models perform better than those where subjects derive utility from final outcomes, models with sign-dependent decision weights perform better than those without, and there is no evidence for loss aversion. The procedure is sufficiently simple so that it can be easily used in field or lab experiments where risk elicitation is not the main experiment. (shrink)

This paper merges the non-expected utility approach (Tversky and Kahneman, J Risk Uncertain 5:297–323, 1992 and Quiggin, J Econ Behav Organ 3:323–343, 1982) into Akerlof’s (Quart J Econ 84:488–500, 1970) model of Market for Lemons. We derive the results for different probability weighting functions and analyze the phenomenon of market failure in light of non-expected utility maximization. Our main finding suggests that when the proportion of traded lemons is high (low), the problem of market failure is mitigated (...) (enhanced). In addition, for the case of Cumulative Prospect Theory, we show that (a) the higher the loss aversion is, the more pronounced is the market failure; (b) gain-domain elevation is negatively related to the extent of market failure; and (c) the value function is (i) negatively monotonic in the gain-domain diminishing sensitivity parameter when the market is characterized by a high proportion of “peaches,” and (ii) positively monotonic in the loss-domain diminishing sensitivity parameter when the market is characterized by a high proportion of “lemons.”. (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)

Ellsberg (The Quarterly Journal of Economics 75, 643–669 (1961); Risk, Ambiguity and Decision, Garland Publishing (2001)) argued that uncertainty is not reducible to risk. At the center of Ellsberg’s argument lies a thought experiment that has come to be known as the three-color example. It has been observed that a significant number of sophisticated decision makers violate the requirements of subjective expected utility theory when they are confronted with Ellsberg’s three-color example. More generally, such decision makers are (...) in conflict with either the ordering assumption or the independence assumption of subjective expected utility theory. While a clear majority of the theoretical responses to these violations have advocated maintaining ordering while relaxing independence, a persistent minority has advocated abandoning the ordering assumption. The purpose of this paper is to consider a similar dilemma that exists within the context of multiattribute models, where it arises by considering indeterminacy in the weighting of attributes rather than indeterminacy in the determination of probabilities as in Ellsberg’s example. (shrink)

Experimental studies suggest that individuals exhibit more risk aversion in choices among prospects when the payment and resolution of uncertainty are immediate relative to when it is delayed. This leads to preference reversals that cannot be attributed to discounting. When data suggest that utility is time-independent, probability weighting functions, such as those used to model prospect theory preferences, can accommodate such reversals. We propose a simple descriptive model with a two-parameter probability weighting function where one of these parameters (...) depends on the time at which a prospect is resolved. The time-dependent parameter is responsible for the curvature of the probability weighting function and is regarded as an index of sensitivity towards changes in probabilities. We provide conditions that characterize increased sensitivity towards more distant probabilities; this can account for the observed relatively less risk aversion towards delayed prospects. In our framework, the discount function is unrestricted, such that the model is compatible with empirical findings of non-constant discounting. In a simple application to bargaining we illustrate when it is advantageous for an individual to advance or delay the bargaining resolution time if an opponent displays increased sensitivity towards probability changes with delay. (shrink)

I reply to two commentaries—one by Johanna Thoma and Jonathan Weisberg and one by James M. Joyce—concerning how risk-weighted expected utility theory handles the Allais preferences and Dutch books.

In many real-world gambles, a non-trivial amount of time passes before the uncertainty is resolved but after a choice is made. An individual may have a preference between gambles with identical probability distributions over final outcomes if they differ in the timing of resolution of uncertainty. In this domain, utility consists not only of the consumption of outcomes, but also the psychological utility induced by an unresolved gamble. We term this utility anxiety. Since a reflective decision maker (...) may want to include anxiety explicitly in analysis of unresolved lotteries, a multiple-outcome model for evaluating lotteries with delayed resolution of uncertainty is developed. The result is a rank-dependent utility representation (e.g., Quiggin, 1982), in which period weighting functions are related iteratively. Substitution rules are proposed for evaluating compound temporal lotteries. The representation is appealing for a number of reasons. First, probability weights can be interpreted as the cognitive attention allocated to certain outcomes. Second, the model disaggregates strength of preference from temporal risk aversion and thus provides some insight into the old debate about the relationship between von Neumann–Morgenstern utility functions and strength of preference value functions. (shrink)

This paper addresses the question of whether gathering additional evidence is always rationally required, both from the point of view of instrumental rationality and of epistemic rationality. It is shown that in certain situations, it is not instrumentally rational to look for more evidence before making a decision. These are situations in which the risk of “misleading” evidence – a concept that has both instrumental and epistemic senses – is not offset by the gains from the possibility of non-misleading (...) evidence. These situations also undermine a particular argument for the claim that it is epistemically rational to look for more evidence, though it is argued that the relationship between instrumental and epistemic rationality makes such arguments flawed to begin with. Furthermore, these situations show us that our epistemic and our practical goals sometimes point us in different directions, not merely because of our limited resources or because our desires are sometimes best served by being in particular epistemic states, but because of the nature of rational action. (shrink)

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the (...) obtained loss-aversion coefficient of 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome. (shrink)

This paper reviews the most common approaches that have been adopted to analyze and describe loss aversion under prospect theory. Subsequently, it is argued that loss aversion is a property of observable choice behavior and two new definitions of loss averse behavior are advocated. Under prospect theory, the new properties hold if the commonly used utility based measures of loss aversion are corrected by a probability based measure of loss aversion and their product exceeds 1. It is shown that (...) prominent parametric families of weighting functions, while successful in accommodating empirical findings on probabilistic risk attitudes, may not fit well with the theoretical implications of the new loss averse behavior conditions. (shrink)

In this paper I argue that the rationality of law and legal decision making would be enhanced by a systematic attempt to recognize and respond to the implications of empirical uncertainty for policy making and decision making. Admission of uncertainty about the accuracy of facts and the validity of assumptions relied on to make inferences of fact is commonly avoided in law because it raises the spectre of paralysis of the capacity to decide issues authoritatively. The roots of this short-sighted (...) view are found in primitive mechanical models of relationships in the empirical and social world – those of objective causality and determinism. Insofar as it is believed that if we had sufficient data a clear and unequivocal answer would be available to each question, admission of uncertainty is seen as a sign of insufficiency, incompetence, impotence, and is avoided whenever a decision that must be seen to be based on valid reasons, cannot be avoided. Avoidance of some decisions, duplicity in others, is the result. -/- Decision-making must be restructured to recognize the provisional and context-bound validity and relevance of the models we use to conceptualize and order our understanding of phenomena, and to utilize this awareness as an instrument in the production of legal policies and decisions that will be authoritative precisely because they are honestly accurate and socially responsible. The paper makes a start on such a re-structuring of the legal process by exploring the implications of the observation that if law is to be “just”: 1) legal policy must be based on accurate information and rationally related to social goals; and 2) decisions applying policy to individual fact situations must be based on assumptions that are both relevant and accurate. -/- Reasons for determinations of fact must be given, otherwise the presumption that the trier of fact is “reasonable” is an unconditional licence to use private modes of logic and theories of social and natural science. What is not disclosed cannot be challenged on grounds of invalidity or irrelevance. -/- Use of “objective validity” as a standard to evaluate conclusions made by the trier of fact in contentious cases would only serve to beg all important questions by concealing: 1) fundamental normative conflict, and 2) the limited nature and applicability of many validity claims. -/- Our use of the phrases “undue risk,” “public interest,” “reasonable,” and “necessary,” reflects the weight we choose to give conflicting social values and goals when we must make decisions in relative ignorance of all the consequences. “Objective criteria” are of limited utility in legal decision-making because their social meaning is derivative. Policy generation in the absence of any coherent conceptual-normative framework, use of vague terminology in legislation stating policy, and the absence of rational means to distinguish between individual cases to which decision-makers are required by law to apply policy, make it inevitable that many legal “decisions” made in the guise of determinations of objective fact, are charades, an arbitrary, capricious, intuitive, subjective (and thus private) use of public decision-making power. -/- Law must alter its aspirations and recognize that rational decision-making is a process that can occur only within parameters set by present knowledge and societal preference structures. Only by working with the constraints imposed by these parameters is it possible to achieve “just” decisions. Where no rational basis for differentiating cases exists, “individualized justice” must be avoided and public policy articulated in law applied uniformly to all cases in a class. The terms “reasonable” and “necessary,” used to describe policy and its consequences for specific cases, must be understood to represent provisional societal assessments, attempts to implement societal preference structures in the face of limited knowledge. Heightened awareness of the limited nature of our knowledge can only result in legal policies that have a more explicit normative basis. -/- The volume is is published with an introduction by Michael D. Bayles. It is available in hardback, paperback, and as an ebook. (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)

Longtermism is the view that the most urgent global priorities, and those to which we should devote the largest portion of our resources, are those that focus on (i) ensuring a long future for humanity, and perhaps sentient or intelligent life more generally, and (ii) improving the quality of the lives that inhabit that long future. While it is by no means the only one, the argument most commonly given for this conclusion is that these interventions have greater expected goodness (...) per unit of resource devoted to them than each of the other available interventions, including those that focus on the health and well-being of the current population. In this paper, I argue that, even if we grant the consequentialist ethics upon which this argument depends, and even if we grant one of the axiologies that are typically paired with that ethics to give the argument, we are not morally required to choose an option that maximises expected utility; indeed, we might not even be permitted to do so. Instead, I will argue, if the argument's consequentialism is correct, we should choose using a decision theory that is sensitive to risk, and allows us to give greater weight to worse-case outcomes than expected utility theory does. And, I will show, such decision theories do not always recommend longtermist interventions. Indeed, sometimes, they recommend exactly the opposite: sometimes, they recommend hastening human extinction. Many, though not all, will take this as a reductio of the consequentialism or the axiology of the argument. I remain agnostic on the conclusion we should draw. (shrink)

Various U.S. laws, such as the Clean Air Act and the Food Quality Protection Act, require additional protections for susceptible subpopulations who face greater environmental health risks. The main ethical rationale for providing these protections is to ensure that environmental health risks are distributed fairly. In this article, we (1) consider how several influential theories of justice deal with issues related to the distribution of environmental health risks; (2) show that these theories often fail to provide specific guidance concerning policy (...) choices; and (3) argue that an approach to public decision making known as accountability for reasonableness can complement theories of justice in establishing acceptable environmental health risks for the general population and susceptible subpopulations. Since accountability for reasonableness focuses on the fairness of the decision-making process, not the outcome, it does not guarantee that susceptible subpopulations will receive a maximum level of protection, regardless of costs or other morally relevant considerations. (shrink)

In this paper I argue that the rationality of law and legal decision making would be enhanced by a systematic attempt to recognize and respond to the implications of empirical uncertainty for policy making and decision making. Admission of uncertainty about the accuracy of facts and the validity of assumptions relied on to make inferences of fact is commonly avoided in law because it raises the spectre of paralysis of the capacity to decide issues authoritatively. The roots of this short-sighted (...) view are found in primitive mechanical models of relationships in the empirical and social world – those of objective causality and determinism. Insofar as it is believed that if we had sufficient data a clear and unequivocal answer would be available to each question, admission of uncertainty is seen as a sign of insufficiency, incompetence, impotence, and is avoided whenever a decision that must be seen to be based on valid reasons, cannot be avoided. Avoidance of some decisions, duplicity in others, is the result. -/- Decision-making must be restructured to recognize the provisional and context-bound validity and relevance of the models we use to conceptualize and order our understanding of phenomena, and to utilize this awareness as an instrument in the production of legal policies and decisions that will be authoritative precisely because they are honestly accurate and socially responsible. The paper makes a start on such a re-structuring of the legal process by exploring the implications of the observation that if law is to be “just”: 1) legal policy must be based on accurate information and rationally related to social goals; and 2) decisions applying policy to individual fact situations must be based on assumptions that are both relevant and accurate. -/- Reasons for determinations of fact must be given, otherwise the presumption that the trier of fact is “reasonable” is an unconditional licence to use private modes of logic and theories of social and natural science. What is not disclosed cannot be challenged on grounds of invalidity or irrelevance. Use of “objective validity” as a standard to evaluate conclusions made by the trier of fact in contentious cases would only serve to beg all important questions by concealing: 1) fundamental normative conflict, and 2) the limited nature and applicability of many validity claims. -/- Our use of the phrases “undue risk,” “public interest,” “reasonable,” and “necessary,” reflects the weight we choose to give conflicting social values and goals when we must make decisions in relative ignorance of all the consequences. “Objective criteria” are of limited utility in legal decision-making because their social meaning is derivative. Policy generation in the absence of any coherent conceptual-normative framework, use of vague terminology in legislation stating policy, and the absence of rational means to distinguish between individual cases to which decision-makers are required by law to apply policy, make it inevitable that many legal “decisions” made in the guise of determinations of objective fact, are charades, an arbitrary, capricious, intuitive, subjective (and thus private) use of public decision-making power. -/- Law must alter its aspirations and recognize that rational decision-making is a process that can occur only within parameters set by present knowledge and societal preference structures. Only by working with the constraints imposed by these parameters is it possible to achieve “just” decisions. Where no rational basis for differentiating cases exists, “individualized justice” must be avoided and public policy articulated in law applied uniformly to all cases in a class. The terms “reasonable” and “necessary,” used to describe policy and its consequences for specific cases, must be understood to represent provisional societal assessments, attempts to implement societal preference structures in the face of limited knowledge. Heightened awareness of the limited nature of our knowledge can only result in legal policies that have a more explicit normative basis. (shrink)

Opposing the tendency to read Thucydides as a strong realist, committed to a theory of behaviour that assumes rationality as expected utility maximization, Ned Lebow and Clifford Orwin emphasize Thucydides’ attentiveness to deviations from rationality by individuals and states. This paper argues that Thucydides grasped the principles underlying contemporary prospect theory, which explains why people over-weight small probabilities and under-weight near certain ones. Thucydides offers salient examples of excessive risk-aversion in the face of probable gains and excessive (...) class='Hi'>risk-seeking by decision-makers faced with high probability losses. Thucydides suggests that in a democracy, leaders’ rhetoric can limit or exacerbate the political effects of bias in risk assessment. (shrink)

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the (...) obtained loss-aversion coefficient of 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome. (shrink)