Richard Bradley

Reports of the Intergovernmental Panel on Climate Change (IPCC) employ an evolving framework of calibrated language for assessing and communicating degrees of certainty in findings. A persistent challenge for this framework has been ambiguity in the relationship between multiple degree-of-certainty metrics. We aim to clarify the relationship between the likelihood and confidence metrics used in the Fifth Assessment Report (2013), with benefits for mathematical consistency among multiple findings and for usability in downstream modeling and decision analysis. We discuss how our proposal meshes with current and proposed practice in IPCC uncertainty assessment.

In this reply, we address a comment on our paper “Combining probability with qualitative degree-of-certainty metrics in assessment” (Helgeson et al. Clim Change 149(3):517–525, 2018). Our original paper proposes an incremental systematization of confidence and likelihood language used by the Intergovernmental Panel on Climate Change (IPCC). Our goals were to improve consistency across findings and support use of confidence judgments in decision making. The comment critiques our proposal and recommends against its adoption. We argue that this recommendation is based on two misunderstandings. The first concerns trading off confidence against the precision of a finding (our proposal endorses and systematizes the practice). We defend this practice and attribute opposition to an overzealous Bayesianism inapt for the IPCC context. The second misunderstanding concerns our purported commitment to a specific procedure for producing confidence judgements. We clarify that our proposal makes no such commitment. We also note, contrary to the comment’s claim, that a version of the procedure in question has been used in the IPCC’s Sixth Assessment Report.

In this reply, we address a comment on our paper “Combining probability with qualitative degree-of-certainty metrics in assessment” (Helgeson et al. Clim Change 149(3):517–525, 2018). Our original paper proposes an incremental systematization of confidence and likelihood language used by the Intergovernmental Panel on Climate Change (IPCC). Our goals were to improve consistency across findings and support use of confidence judgments in decision making. The comment critiques our proposal and recommends against its adoption. We argue that this recommendation is based on two misunderstandings. The first concerns trading off confidence against the precision of a finding (our proposal endorses and systematizes the practice). We defend this practice and attribute opposition to an overzealous Bayesianism inapt for the IPCC context. The second misunderstanding concerns our purported commitment to a specific procedure for producing confidence judgements. We clarify that our proposal makes no such commitment. We also note, contrary to the comment’s claim, that a version of the procedure in question has been used in the IPCC’s Sixth Assessment Report.

Reports of the Intergovernmental Panel on Climate Change (IPCC) employ an evolving framework of calibrated language for assessing and communicating degrees of certainty in findings. A persistent challenge for this framework has been ambiguity in the relationship between multiple degree-of-certainty metrics. We aim to clarify the relationship between the likelihood and confidence metrics used in the Fifth Assessment Report (2013), with benefits for mathematical consistency among multiple findings and for usability in downstream modeling and decision analysis. We discuss how our proposal meshes with current and proposed practice in IPCC uncertainty assessment.

Decision making typically requires judgments about causal relations: we need to know both the causal e¤ects of our actions and the causal relevance of various environmental factors. Judgments about the nature and strength of causal relations often differ, even among experts. How to handle such diversity is the topic of this paper. First, we consider the possibility of aggregating causal judgments via the aggregation of probabilistic ones. The broadly negative outcome of this investigation leads us to look at aggregating causal judgments independently of probabilistic ones. We do so by transcribing causal claims into the formal judgment-aggregation framework and applying some recent results in this field. Finally, we look at the implications for probability aggregation when it is constrained by prior aggregation of qualitative causal judgments.

As readers of this journal can attest to, although philosophers and economists are somewhat used to talking to and learning from each other, it tends to be the subset of philosophers working in decision theory, philosophy of science, and particular areas of ethics and political philosophy that contribute to our interdisciplinary field of research. The book that is the subject of this review symposium, Anna Mahtani’s The Objects of Credence (Oxford University Press, 2024), is a wonderful exemplar of what can be learned when a different branch of philosophy is brought to bear on central questions in this field. Both philosophers and economists talk about and work with credences, or degrees of belief, all the time. These are usually modelled as probabilities, which are in turn usually thought of as attaching to propositions. But it has long been argued by philosophers of language that propositions cannot be the objects of credence. Mahtani’s book is an investigation into all that begins to unravel once we accept this insight. The results have profound implications both for rational choice modelling and for welfare economics.

Models of collective deliberation often assume that the chief aim of a deliberative exchange is the sharing of information. In this paper, we argue that an equally important role of deliberation is to draw participants’ attention to pertinent questions, which can aid the assembly and processing of distributed information by drawing deliberators’ attention to new issues. The assumption of logical omniscience renders classical models of agents' informational states unsuitable for modelling this role of deliberation. Building on recent insights from psychology, linguistics and philosophy about the role of questions in speech and thought, we propose a different model in which beliefs are treated as answers directed at specific questions. Here, questions are formally represented as partitions of the space of possibilities and individuals’ information states as sets of and corresponding partial answers to them. The state of conversation is then characterised by individuals’ information together with the questions under discussion, which can be steered by various deliberative inputs. Using this model, deliberation is then shown to shape collective decisions in ways that classical models cannot capture, allowing for novel explanations of how group consensus is achieved.

Climate science is an umbrella term referring to scientific disciplines studying aspects of the Earth’s climate. It includes, among others, parts of atmospheric science, oceanography, and glaciology. In the wake of public discussions about an appropriate reaction to climate change, parts of decision theory and economics have also been brought to bear on issues of climate. The philosophy of climate science is a new sub-discipline of the philosophy of science that began to crystalise at the turn of the twenty-first century when philosophers started having a closer look at climate science. It comprises a reflection on almost all aspects of climate science, including observation and data, methods of detection and attribution, kinds of uncertainties, model ensembles, and decision-making under uncertainty. The philosophy of climate science operates in close contact with science itself and pays careful attention to the scientific details.

Many policy decisions take input from collections of scientific models. Such decisions face significant and often poorly understood uncertainty. We rework the so-called confidence approach to tackle decision-making under severe uncertainty with multiple models, and we illustrate the approach with a case study: insurance pricing using hurricane models. The confidence approach has important consequences for this case and offers a powerful framework for a wide class of problems. We end by discussing different ways in which model ensembles can feed information into the approach, appropriate to different collections of models.

The COVID-19 crisis and the policy responses to it have impacted many different areas of common concern including public health and the economy. This raises difficult questions about how to balance these concerns in making policy decisions. In this chapter, we review a number of tools that welfare economics offers for conceptualizing and studying such trade-offs. We argue that social welfare analysis is the most useful method for doing so. We show how concerns for the distributive and other effects of a policy on individual wellbeing can be evaluated using a Social Welfare Function (SWF) and survey some of the main features of such functions. As an illustration, we then use this approach to model and evaluate the implications for social welfare of the adoption of pandemic policies that vary in terms of the stringency of the controls that they impose on individual behaviour. Our model reveals how such evaluations not only are determined by empirical facts but may also depend on key judgments about the relative importance of the different determinants of individual wellbeing (health, income, longevity, and so on) and about the extent to which special concern should be given to the worse-off. In doing so, it illustrates how critical transparent modelling of these concerns is in developing responses to pandemics of this kind.

How should we revise our beliefs in response to the expressed probabilistic opinions of experts on some proposition when these experts are in disagreement? In this paper I examine the suggestion that in such circumstances we should adopt a linear average of the experts’ opinions and consider whether such a belief revision policy is compatible with Bayesian conditionalisation. By looking at situations in which full or partial deference to the expressed opinions of others is required by Bayesianism I show that only in trivial circumstances are the requirements imposed by linear averaging compatible with it.

An allocation problem is a type of aggregation problem in which the values of individuals' opinions on some set of variables (canonically a set of mutually exclusive and exhaustive possibilities) sum to a constant. This paper shows that for realistic allocation problems, namely ones in which the set of possible opinion values is finite, the only universal aggregation methods that satisfy two commonly invoked conditions are the dictatorial ones. The two conditions are, first, that the aggregate opinion on any variable depends only on the individuals' opinions on that variable and not on their opinions on any other variable and, secondly, that the aggregate opinion minimally preserves unanimous individual opinion. Connections between this result and similar ones in the literature on judgment aggregation are explored and their significance assessed.

Considerations of dynamic inconsistency have figured prominently in debates over the rationality of preferences that violate the separability conditions characteristic of expected utility theory. These debates have mostly focused on risk- and ambiguity averse preferences, but analogous considerations apply to preferences for fairness. We revisit these debates in the context of a specific hypothesis regarding the violations of separability by such preferences, namely that they are potentially both explained and rationalised by attitudes to the chances of goods that motivate a preference for equality in the distribution of chances across people and possible events. Our main aim is to argue that, first, when these violations of static separability are motivated by such attitudes to chances, then they need not result in dynamically inconsistent behaviour. Second, and more generally, considerations of dynamic consistency do not, we argue, undermine the rationality of such attitudes towards the distribution of chances, despite the fact that such attitudes give rise to violations of the static separability assumptions of expected utility theory.

Insurers draw on sophisticated models for the probability distributions over losses associated with catastrophic events that are required to price insurance policies. But prevailing pricing methods don’t factor in the ambiguity around model-based projections that derive from the relative paucity of data about extreme events. I argue however that most current theories of decision making under ambiguity only partially support a solution to the challenge that insurance decision makers face and propose an alternative approach that allows for decision making that is responsive to both the evidential situation of the insurance decision maker and their attitude to ambiguity.

On Hume’s account of motivation, beliefs and desires are very different kinds of propositional attitudes. Beliefs are cognitive attitudes, desires emotive ones. An agent’s belief in a proposition captures the weight he or she assigns to this proposition in his or her cognitive representation of the world. An agent’s desire for a proposition captures the degree to which he or she prefers its truth, motivating him or her to act accordingly. Although beliefs and desires are sometimes entangled, they play very different roles in rational agency. In two classic papers (Lewis 1988, 1996), David Lewis discusses several challenges to this Humean picture, but ultimately rejects them. We think that his discussion of a central anti-Humean alternative – the desire-as-belief thesis – is in need of refinnement. On this thesis, the desire for proposition p is given by the belief that p is desirable. Lewis claims that ‘[e]xcept in trivial cases, [this thesis] collapses into contradiction’(Lewis 1996, p. 308). The problem, he argues, is that the thesis is inconsistent with the purportedly plausible requirement that one’s desire for a proposition should not change upon learning that the proposition is true; call this the invariance requirement. In this paper, we revisit Lewis’s argument. We show that, if one carefully distinguishes between non-evaluative and evaluative propositions, the desire-asbelief thesis can be rendered consistent with the invariance requirement. Lewis’s conclusion holds only under certain conditions: the desire-as-belief thesis conflicts with the invariance requirement if and only if there are certain correlations between non-evaluative and evaluative propositions. But when there are such correlations, we suggest, the invariance requirement loses its plausibility. Thus Lewis’s argument against the desire-as-belief thesis appears to be valid only in cases in which it is unsound.

As readers of this journal can attest to, although philosophers and economists are somewhat used to talking to and learning from each other, it tends to be the subset of philosophers working in decision theory, philosophy of science, and particular areas of ethics and political philosophy that contribute to our interdisciplinary field of research. The book that is the subject of this review symposium, Anna Mahtani’s The Objects of Credence (Oxford University Press, 2024), is a wonderful exemplar of what can be learned when a different branch of philosophy is brought to bear on central questions in this field. Both philosophers and economists talk about and work with credences, or degrees of belief, all the time. These are usually modelled as probabilities, which are in turn usually thought of as attaching to propositions. But it has long been argued by philosophers of language that propositions cannot be the objects of credence. Mahtani’s book is an investigation into all that begins to unravel once we accept this insight. The results have profound implications both for rational choice modelling and for welfare economics.

Control measures, such as “lockdowns”, have been widely used to suppress the COVID-19 pandemic. Under some conditions, they prevent illness and save lives. But they also exact an economic toll. How should we balance the impact of such policies on individual lives and livelihoods (and other dimensions of concern) to determine which is best? A widely used method of policy evaluation, benefit–cost analysis (BCA), answers these questions by converting all the effects of a policy into monetary equivalents and then summing them up. A different method, social welfare analysis, proceeds by determining the effects of a policy on individual wellbeing and then applying an aggregation formula to them to evaluate the overall effects of a policy. In this chapter, we survey these methods and argue that social welfare analysis has important advantages. One crucial advantage is that it enables ethical considerations relating to the impact of policies on individual wellbeing and its distribution to be incorporated into policy assessments in a transparent way. We illustrate this with a simple numerical model for evaluating pandemic policies that vary in terms of the stringency of the controls that they impose on individual behaviour, showing how the evaluation depends on the ethical significance accorded to their impact on the wellbeing of different age and income groups.