Risk in Decision Theory

Ever since the Harsanyi-Sen debate, it is controversial whether someone's welfare should be measured by her von-Neumann-Morgenstern (VNM) utility, for instance when analysing welfare intensity, social welfare, interpersonal welfare comparisons, or welfare inequality. We prove that natural working hypotheses lead to a different welfare measure. It addresses familiar concerns about VNM utility, by faithfully capturing non-ordinal welfare features such as welfare intensity, despite resting on purely ordinal evidence such as revealed preferences or self-reported welfare comparisons. Using this welfare measure instead (...) of VNM utility alters social welfare analysis -- for instance, Harsanyi's `utilitarian theorem' now effectively supports prioritarianism. VNM utility is shown to be a hybrid object, determined by an interplay of two factors: welfare and attitude to intrinsic risk, i.e., to risk in welfare rather than outcomes. (shrink)

A decision theory is self-recommending if, when you ask it which decision theory you should use, it considers itself to be among the permissible options. I show that many alternatives to expected utility theory are not self-recommending, and I argue that this tells against them.

Orthodox causal decision theory is unstable. Its advice changes as you make up your mind about what you will do. Several have objected to this kind of instability and explored stable alternatives. Here, I'll show that explorers in search of stability must part with a vestige of their homeland. There is no plausible stable decision theory which satisfies Savage's Sure Thing Principle. So those in search of stability must learn to live without it.

A novel theory of comparative risk is developed and defended. Extant theories are criticized for failing the tests of extensional and formal adequacy. A unified diagnosis is proposed: extant theories consider risk to be a univariable function, but risk is a multivariate function. According to the theory proposed, which we call the unified theory of risk, the riskiness of a proposition is a function of both the proportion and the modal closeness of the possible worlds at which the proposition holds. (...) It is argued the theory passes the tests of extensional and formal adequacy. (shrink)

There are infinitely many ways the world might be, and there may well be infinitely many people in it. These facts raise moral paradoxes. We explore a conflict between two highly attractive principles: a Pareto principle that says that what is better for everyone is better overall, and a statewise dominance principle that says that what is sure to turn out better is better on balance. We refine and generalize this paradox, showing that the problem is faced by many theories (...) of interpersonal aggregation besides utilitarianism, and by many decision theories besides expected value theory. Considering the range of consistent responses, we find all of them to be quite radical. (shrink)

I present a new puzzle about choice under uncertainty for agents whose preferences are sensitive to multiple dimensions of outcomes in such a way as to be incomplete. In response, I develop a new theory of choice under uncertainty for incomplete preferences. I connect the puzzle to central questions in epistemology about the nature of rational requirements, and ask whether it shows that preferences are rationally required to be complete.

A moral requirement R1 is said to be lexically prior to a moral requirement R2 just in case we are morally obliged to uphold R1 at the expense of R2 – no matter how many times R2 must be violated thereby. While lexical priority is a feature of many ethical theories, and arguably a part of common sense morality, attempts to model it within the framework of decision theory have led to a series of problems – a fact which is (...) sometimes spun as a ‘decision theoretic critique’ of lexical priority. In this paper, I develop an enriched decision theoretic framework that is capable of modelling lexical priority while avoiding all extant problems. This will involve introducing several new ingredients into the standard decision theoretic framework, including multidimensional utilities, de minimis risks, and the means to represent two different conceptions of risk. (shrink)

In a recent paper, Björn Lundgren and H. Orri Stefánsson (forthcoming) present three objections to normic de minimis expected utility theory (NDEUT) – a decision theoretic framework defended in Smith (2024). In this paper, I respond to these objections and outline some possible ways in which NDEUT might be modified or further developed. Like any de minimis framework, NDEUT employs a risk threshold to sort possibilities into those that must be considered when making a decision, and those that can be (...) legitimately ignored – the so-called ‘de minimis risks’. While this threshold would usually take the form of a probability value, in NDEUT the de minimis risks are identified instead on the basis of their abnormality. In the first section I will set up some of the formalism used in NDEUT and consider Lundgren and Stefánsson’s first objection – which is essentially formal in nature. In the second section I will delve further into the interpretation of NDEUT and consider the second and third objections, which turn on particular examples. (shrink)

Should you be willing to forego any sure good for a tiny probability of a vastly greater good? Fanatics say you should, anti-fanatics say you should not. Anti-fanaticism has great intuitive appeal. But, I argue, these intuitions are untenable, because satisfying them in their full generality is incompatible with three very plausible principles: acyclicity, a minimal dominance principle, and the principle that any outcome can be made better or worse. This argument against anti-fanaticism can be turned into a positive argument (...) for a weak version of fanaticism, but only from significantly more contentious premises. In combination, these facts suggest that those who find fanaticism counterintuitive should favor not anti-fanaticism, but an intermediate position that permits agents to have incomplete preferences that are neither fanatical nor anti-fanatical. (shrink)

Expected value maximization gives plausible guidance for moral decision‐making under uncertainty in many situations. But it has unappetizing implications in ‘Pascalian’ situations involving tiny probabilities of extreme outcomes. This paper shows, first, that under realistic levels of ‘background uncertainty’ about sources of value independent of one's present choice, a widely accepted and apparently innocuous principle—stochastic dominance—requires that prospects be ranked by the expected value of their consequences in most ordinary choice situations. But second, this implication does not hold when differences (...) in expected value are driven by tiny probabilities of extreme outcomes. Stochastic dominance therefore lets us draw a surprisingly principled line between ‘ordinary’ and ‘Pascalian’ situations, providing a powerful justification for de facto expected value maximization in the former context while permitting deviations in the latter. Drawing this distinction is incompatible with an in‐principle commitment to maximizing expected value, but does not require too much departure from decision‐theoretic orthodoxy: it is compatible, for instance, with the view that moral agents must maximize the expectation of a utility function that is an increasing function of moral value. (shrink)

Cost-effectiveness analysis for health interventions is traditionally conducted in a risk-neutral way, insensitive to risk attitudes in the population, which are potentially non-neutral. While the standard outcome metric of quality-adjusted life years (QALYs) aims to be deferential to people's valuations of health states, cost-effectiveness analysis of risky interventions using the QALY metric is not similarly deferential to people's risk attitudes. I argue that there is no good justification for this practice. Non-neutral attitudes to risk, especially where they concern individually life-changing (...) interventions need not be irrational, and so imposing neutrality is not justifiable as a way of debiasing preferences. Many common justifications for deference to health state preferences extend to risk attitudes. But even if reasons for deference do not extend, imposition of risk neutrality as opposed to any other rationally permissible risk attitude is under-motivated as default practice. Thus, either methods for measuring risk attitudes separately and incorporating them into cost-effectiveness analysis should be used more widely or a richer set of information should be presented to political decision-makers and the public to enable them to decide how to take into account the individual risks faced by members of the population, on top of aggregate effects on population health. (shrink)

Various decision theories share a troubling implication. They imply that, for any finite amount of value, it would be better to wager it all for a vanishingly small probability of some greater value. Counterintuitive as it might be, this _fanaticism_ has seemingly compelling independent arguments in its favour. In this paper, I consider perhaps the most _prima facie_ compelling such argument: an _Egyptology argument_ (an analogue of the Egyptology argument from population ethics). I show that, despite recent objections from Russell (...) (Noûs, 2023) and Goodsell (Analysis 81(3):420–426, 2021), the argument’s premises can be justified and defended, and the argument itself remains compelling. (shrink)

A social planner who evaluates risky public policies in light of the other risks with which their society will be faced should judge favourably some such policies even though they would deem them too risky when considered in isolation. I suggest that a longtermist would—or at least should—evaluate risky polices in light of their prediction about future risks; hence, longtermism supports social risk-taking. I consider two formal versions of this argument, discuss the conditions needed for the argument to be valid, (...) and briefly compare these conditions to some risky policy options with which actual public decision-makers are faced. (shrink)

Since the 1970’s there has been a major increase in adventure sports participation but it seems that engagement in such sports comes with a stigma: adventure sports participants are often regarded as reckless ‘daredevils’. We approach the questions about people’s perception of risk and recklessness in adventure sports by combining empirical research with philosophical analysis. First, we provide empirical evidence that suggests that laypeople tend to assess the danger of adventure sports as greater than more mundane sports and judge adventure (...) sports participants as more reckless than participants in non-adventure sports. We contextualise these findings within existing psychological risk perception paradigms and outline new philosophical explanations of the identified pattern in laypeople’s risk perception. (shrink)

Recent claims that artificial intelligence (AI) systems demonstrate “emergent abilities” have fueled excitement but also fear grounded in the prospect that such systems may enable a wider range of parties to make unprecedented advances in areas that include the development of chemical or biological weapons. Ambiguity surrounding the term “emergent abilities” has added avoidable uncertainty to a topic that has the potential to destabilize the strategic landscape, including the perception of key parties about the viability of nonproliferation efforts. To avert (...) these problems in the future, scientists, developers, policymakers, and other parties should take credible steps to strengthen the health of the scientific ecosystem around AI. (shrink)

A de minimis risk is defined as a risk that is so small that it may be legitimately ignored when making a decision. While ignoring small risks is common in our day-to-day decision making, attempts to introduce the notion of a de minimis risk into the framework of decision theory have run up against a series of well-known difficulties. In this paper, I will develop an enriched decision theoretic framework that is capable of overcoming two major obstacles to the modelling (...) of de minimis risk. The key move is to introduce, into decision theory, a non-probabilistic conception of risk known as normic risk. (shrink)

Bartha and DesRoches (Synthese 199(3–4):8701–8740, 2021) and Steel and Bartha (Risk Analysis 43(2):260–268, 2023) argue that we should understand the precautionary principle as the injunction to maximise lexical utilities. They show that the lexical utility model has important pragmatic advantages. Moreover, the model has the theoretical advantage of satisfying all axioms of expected utility theory except continuity. In this paper I raise a trilemma for any attempt at modelling the precautionary principle with lexical utilities: it permits choice cycles or leads (...) to paralysis or implies that the smallest value difference that is possible in a context has extreme axiological implications. (shrink)

Suppose an agent is choosing between rescuing more people with a lower probability of success, and rescuing fewer with a higher probability of success. How should they choose? Our moral judgments about such cases are not well-studied, unlike the closely analogous non-moral preferences over monetary gambles. In this paper, I present an empirical study which aims to elicit the moral analogues of our risk preferences, and to assess whether one kind of evidence—concerning how they depend on outcome probabilities—can debunk them. (...) I find significant heterogeneity in our moral risk preferences—in particular, moral risk-seeking and risk-neutrality are surprisingly popular. I also find that subjects’ judgments aren't probability-dependent, thus providing an empirical defense against debunking arguments from probability dependence. (shrink)

According to a common judgement, a social planner should often use a lottery to decide which of two people should receive a good. This judgement undermines one of the best-known arguments for utilitarianism, due to John C. Harsanyi, and more generally undermines axiomatic arguments for utilitarianism and similar views. In this paper we ask which combinations of views about (a) the social planner’s attitude to risk and inequality, and (b) the subjects’ attitudes to risk are consistent with the aforementioned judgement. (...) We find that the class of combinations of views that can plausibly accommodate this judgement is quite limited. But one theory does better than others: the theory of chance-sensitive utility. (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)

All ordinary decisions involve some risk. If I go outside for a walk, I may trip and injure myself. But if I don’t go for a walk, I slightly increase my chances of cardiovascular disease. Typically, we disregard most small risks. When, for practical purposes, is it appropriate for one to ignore risk? This issue looms large because many activities performed by those in wealthy societies, such as driving a car, in some way risk contributing to climate harms. Are these (...) activities morally appropriate? -/- In this paper, I first summarize and respond to some arguments that purport to show that it is appropriate to ignore or discount very small risks. I argue that because our rationality is bounded, it is impossible for us to include every small risk in our decision-making process, and so we may reasonably use heuristics to guide many decisions. However, contrary to some thinkers, I argue that this does not violate the spirit of expected value theory; it merely shows that we should adopt a so-called "two-level" view. Our use of heuristics allows for the reasonable ignoring of some risks, and this perhaps explains why one might be inclined to think that individual climate-related risks are negligible. However, virtually all greenhouse-gas emitting activities in fact have some climate risk on the negative side of the ledger, and the use of heuristics does not permit the general ignoring of climate-change-related risk by individuals on grounds of expediency of judgment and decision-making. (shrink)

Underscoring the economic significance of the Knightian distinction between risk and uncertainty, Don Katzner forcefully challenges the continued dominance of the expected utility model based on subjective probability in macroeconomic analysis and offers in its place a simple yet elegant model of decision making inspired by the pioneering work of G.L.S. Shackle. In doing so, Katzner lends support to a research program to identify a more coherent and empirically grounded theory of decision making under uncertainty. Our paper makes three contributions (...) to this program. First, we argue that the appropriate choice of a model of individual behavior under uncertainty cannot be adjudicated merely on logical, a priori grounds, but must ultimately be based on consistency with observed behavior. There are many internally consistent models and their external conditions of validity hardly ever rely on inconceivable scenarios. Second, while Katzner’s model certainly provides a plausible foundation for understanding choice under uncertainty, we suggest that it is somewhat underdetermined. It requires further theoretical articulation to yield testable predictions which differentiate it from competing approaches. Third, we discuss recent experimental findings that may need to be addressed by any satisfactory theoretical account of decision making under uncertainty. (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)

What is risk? How do we assess risk? What are the ethical implications of risk? The concept of risk is important – sometimes even crucial – for many philosophical domains, from philosophy of science and technology to ethics and sustainability. Philosophy and Science of Risk is a clear, wide-ranging introduction to this urgent and fast-growing subject. It covers the following key topics: -/- • The philosophical and historical background to understanding and interpreting risk -/- • The meaning of risk and (...) how it differs from closely related concepts, such as uncertainty or dangers -/- • The social construction of risk -/- • Risk perception and risk as an object of scientific study -/- • The measurement of risk, its probability and severity -/- • Risk and scientific modeling -/- • Risk, value judgments, and expertise -/- • Risk management, including cost-benefit analysis and the precautionary approach -/- • Risk communication, including deliberative models -/- • Ethics of risk, including duties toward nonhuman animals and future generations -/- • Risk and sustainability -/- • Decision-making under risk -/- Including helpful additional features such as text boxes, chapter summaries, review, and discussion questions, Philosophy and Science of Risk: An Introduction is an ideal textbook for students of the philosophy of risk. It is also suitable for students studying the conceptual questions surrounding risk in related subjects, such as sociology, psychology, economics, politics, geography, sustainability, and environmental studies. (shrink)

Incommensurability is the impossibility to determine how two options relate to each other in terms of conventional comparative relations. This book features new research on incommensurability from philosophers who have shaped the field into what it is today, including John Broome, Ruth Chang and Wlodek Rabinowicz. The book covers four aspects relating to incommensurability. In the first part, the contributors synthesize research on the competing views of how to best explain incommensurability. Part II illustrates how incommensurability can help us deal (...) with seemingly insurmountable problems in ethical theory and population ethics. The contributors address the Repugnant Conclusion, the Mere Addition Paradox and so-called Spectrum Arguments. The chapters in Part III outline and summarize problems caused by incommensurability for decision theory. Finally, Part IV tackles topics related to risk, uncertainty and incommensurability. Value Incommensurability: Ethics, Risk, and Decision-Making will be of interest to researchers and advanced students working in ethical theory, decision theory, action theory, and philosophy of economics. (shrink)

How should you evaluate your choices when you’re unsure what their outcomes will be? One popular answer is to rank your options in terms of their expected utilities. But what should you do when you think that the value of their respective outcomes might be incommensurable? In the face of incommensurable values, it no longer makes sense to speak of ranking your options according to expected utility. Are there any general principles to guide us when facing decisions of this kind? (...) If only! This chapter develops an impossibility result: it holds that there are a handful of independently plausible constraints that no such decision theory can jointly satisfy. The result, while depressing, can be used to helpfully classify extant approaches based on which of the constraints they violate. (shrink)

Do unknown and unrealized risks of harm diminish an individual’s well-being? The traditional answer is no: that the security of prudential goods benefits an individual only instrumentally or by virtue of their subjective sense of security. Recent work has argued, however, that the security of prudential goods non-instrumentally benefits an individual regardless of whether or not they enjoy subjective security. In this paper, I critically examine three claims about the way in which unknown and unrealized risks of harm might diminish (...) individual well-being: it frustrates a desire to be secure, it frustrates the enjoyment of modally-robust goods, and it undermines the ability to make reasonable plans. Ultimately, I argue that all three of these hypotheses are mistaken, but that they deepen our understanding of the ways in which subjective security is an important constituent of individual well-being. (shrink)

For the purpose of this analysis, risk assessment becomes the primary term and risk management the secondary term. The concept of risk management as a primary term is based upon a false ontology. Risk management implies that risk is already there, not created by the decision, but lies already inherent in the situation that the decision sets into motion. The risk that already exists in the objective situation simply needs to be “managed”. By considering risk assessment as the primary term, (...) the ethics of responsibility for risking the lives of others, the environment and future generations in the first place comes into the forefront. The issue of risk heeding is especially important as it highlights the need to pay attention to warnings of danger and to take action to redress problems before disasters occur. In this paper, the decision making that led to the choice of technology utilized and the implementation of such technology in the case of the space shuttle Challenger disaster will be used as a model to illustrate the need to take ethical factors into account when making decisions regarding the safety of technological systems and the heeding of danger warnings. While twenty-five years separates the decision to launch the Challenger and the Fukushima Daiichi nuclear plant disaster, the lessons of the Challenger disaster are still to be learned. (shrink)