Richard Bradley

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.

Decision theory is the study of how choices are and should be made.in a variety of different contexts. Here we look at the topic from a formal-philosophical point of view with a focus on normative and conceptual issues. After considering the question of how decision problems should be framed, we look at the both the standard theories of chance under conditions of certainty, risk and uncertainty and some of the current debates about how uncertainty should be measured and how agents should respond to it.

Chance Neutrality is the thesis that, conditional on some proposition being true, its chance of being true should be a matter of practical indifference. The aim of this article is to examine whether Chance Neutrality is a requirement of rationality. We prove that given Chance Neutrality, the Principal Principle entails a thesis called Linearity; the centerpiece of von Neumann and Morgenstern’s expected utility theory. With this in mind, we argue that the Principal Principle is a requirement of practical rationality but that Linearity is not and, hence, that Chance Neutrality is not rationally required.

Diversity of opinion both presents problems and aff ords opportunities. Diff erences of opinion can stand in the way of reaching an agreement within a group on what decisions to take. But at the same time, the fact that the differences in question could derive from access to different information or from the exercise of diff erent judgemental skills means that they present individuals with the opportunity to improve their own opinions. This paper explores the implications for solutions to the former (aggregation) problem of supposing that individuals exploit these opportunities. In particular, it argues that rational individual revision of opinion implies that aggregation problems are unstable in a certain sense and that solving them by exploiting the information embedded in individual opinion has profound implications for the conditions that we should impose on aggregation procedures.

Many fine-grained decisions concerning climate change involve significant, even severe, uncertainty. Here, we focus on modelling the decisions of single agents, whether individual persons or groups perceived as corporate entities. We offer a taxonomy of the sources and kinds of uncertainty that arise in framing these decision problems, as well as strategies for making a choice in spite of uncertainty. The aim is to facilitate a more transparent and structured treatment of uncertainty in climate decision making.

The desirability of what actually occurs is often influenced by what could have been. Preferences based on such value dependencies between actual and counterfactual outcomes generate a class of problems for orthodox decision theory, the best-known perhaps being the so-called Allais paradox. In this article we solve these problems by extending Richard Jeffrey’s decision theory to counterfactual prospects, using a multidimensional possible-world semantics for conditionals, and showing that preferences that are sensitive to counterfactual considerations can still be desirability-maximizing. We end the article by investigating the conditions necessary and sufficient for a desirability function to be a standard expected-utility function. It turns out that the additional conditions imply highly implausible epistemic principles. 1Two Paradoxes of Rational Choice2Jeffrey Desirability3Counterfactuals 3.1Probability and desirability of counterfactuals3.2Representations4Counterfactual-Dependent Preferences 4.1Preference actualism and desirability maximization4.2Modelling Allais's and Diamond’s preferences5Ethical Actualism and Separability 5.1Independence and additive separability5.2 Ethical actualism5.3Expected utility, separability, and ethical actualism6Concluding Remarks7Appendix.

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 questions 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.

How should an impartial social observer judge distributions of well-being across different individuals when there is uncertainty regarding the state of the world? I explore this question by imposing very weak conditions of rationality and benevolent sympathy on impartial betterness judgments under uncertainty. Although weak enough to be consistent with all the main theories of rationality, these conditions prove to be sufficient to rule out any heterogeneity in what is good for individuals, to require a neutral attitude to uncertainty on the part of the social observer, and to require that both individual and social betterness be strongly separable.

The UK has been ‘following the science’ in response to the COVID-19 pandemic in line with the national framework for the use of scientific advice in assessment of risk. We argue that the way in which it does so is unsatisfactory in two important respects. Firstly, pandemic policy making is not based on a comprehensive assessment of policy impacts. And secondly, the focus on reasonable worst-case scenarios as a way of managing uncertainty results in a loss of decision-relevant information and does not provide a coherent basis for policy making.

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 has forced a difficult trade-off between limiting the health impacts of the virus and maintaining economic activity. Welfare economics offers tools to conceptualize this trade-off so that policy-makers and the public can see clearly what is at stake. We review four such tools: the Value of Statistical Life (VSL); the Value of Statistical Life Years (VSLYs); Quality-Adjusted Life-Years (QALYs); and social welfare analysis, and argue that the latter are superior. We also discuss how to choose policies that differentially affect people’s wellbeing. We argue in favor of evaluating policies using a Social Welfare Function (SWF), which evaluates the possible distributions of wellbeing across individuals that may result from a policy. Such a function, we argue, should regard increases in the wellbeing of the less well-off as especially valuable. We then use a model to illustrate how such a framework can help evaluate two broad policy types in response to the pandemic: eradication of the virus, and more lenient control of the spread. Our model reveals how such evaluations depend on many empirical facts but also on key value judgments about the relative importance of health and on the extent of special concern for the worse off. The purpose of this brief is not to make precise recommendations, as conditions vary widely across countries and over time, but to provide a methodology.

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.

We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same axioms: responsiveness, which requires that revised beliefs incorporate what has been learnt, and conservativeness, which requires that beliefs on which the learnt input is ‘silent’ do not change. To illustrate the use of non-Bayesian belief revision in economic theory, we sketch a simple decision-theoretic application.

This paper explores some aspects of the relation between aggregation and deliberation as ways of achieving a consensus amongst a group of indviduals on some set of issues. I argue firstly that the framing of an aggregation problem itself generates information about the judgements of others that individuals are rationally obliged to take into account. And secondly that the constraints which aggregation theories typically place on consensual or collective judgements need not be consistent with the outcomes of rational deliberative processes driven by individuals’ attempts to update on this information. The paper focuses on the particular case of allocation problems, for which there are established results both in aggregation theory and deliberation theory, to make this claim.

This dissertation interprets the lack of uniqueness in probability representations of agents' degrees of belief in the decision theory of Richard Jeffrey as a formal statement of an important epistemological problem: the underdetermination of our attributions of belief and desire to agents by the evidence of their observed behaviour. A solution is pursued through investigation of agents' attitudes to information of a conditional nature. ;As a first step, Jeffrey's theory is extended to agents' conditional attitudes of belief and desire by introduction of a definition of conditional desirability. The second step is an analysis of agents' attitudes to conditionals. Following Adams it is argued that the probability of a conditional is the conditional probability of its consequent given the antecedent. Since numerous 'trivialization' results show that no proposition could be such that this were the case, it is proposed that conditionals express a variable proposition as a function of the context in which they are asserted. The consequent technical treatment of conditionals as proposition-valued functions of sets of possible worlds delivers Adams' thesis as a natural consequence without fear of trivialization. ;Conditionals are the underlying objects of the decision theory that is presented in the final chapter. A representation theorem is proven for preferences defined over sets of such conditionals satisfying certain closure conditions, where an agent is understood to prefer one conditional over another just in case she prefers that the former by true rather than the latter. The theorem establishes that a rational preference ranking of conditionals implies the existence of a unique probability function and a desirability function unique up to choice of scale, that agree with the preference ranking, and that these functions satisfy both the axioms of Jeffrey's decision calculus and Adams' thesis. The theorem is interpreted as saying that elicitation of an agent's choices amongst conditional options suffices to determine our attributions of belief and desire to them.

The Desire-as-Belief thesis (DAB) states that any rational person desires a proposition exactly to the degree that she believes or expects the proposition to be good. Many people take David Lewis to have shown the thesis to be inconsistent with Bayesian decision theory. However, as we show, Lewis’s argument was based on an Invariance condition that itself is inconsistent with the (standard formulation of the) version of Bayesian decision theory that he assumed in his arguments against DAB. The aim of this paper is to explore what impact the rejection of Invariance has on the DAB thesis. Without assuming Invariance, we first refute all versions of DAB that entail that there are only two levels of goodness. We next consider two theses according to which rational desires are intimately connected to expectations of (multi-levelled) goodness, and show that these are consistent with Bayesian decision theory as long as we assume that the contents of ‘value propositions’ are not fixed. We explain why this conclusion is independently plausible, and show how to construct such propositions.

Adams' famous thesis that the probabilities of conditionals are conditional probabilities is incompatible with standard probability theory. Indeed it is incompatible with any system of monotonic conditional probability satisfying the usual multiplication rule for conditional probabilities. This paper explores the possibility of accommodating Adams' thesis in systems of non-monotonic probability of varying strength. It shows that such systems impose many familiar lattice theoretic properties on their models as well as yielding interesting logics of conditionals, but that a standard complementation operation cannot be defined within them, on pain of collapsing probability into bivalence.

Richard Jeffrey espoused an antifoundationalist variant of Bayesian thinking that he termed ‘Radical Probabilism’. Radical Probabilism denies both the existence of an ideal, unbiased starting point for our attempts to learn about the world and the dogma of classical Bayesianism that the only justified change of belief is one based on the learning of certainties. Probabilistic judgment is basic and irreducible. Bayesian conditioning is appropriate when interaction with the environment yields new certainty of belief in some proposition but leaves one’s conditional beliefs untouched (the ‘Rigidity’ condition). Although Richard Jeffrey denied the general applicability of this condition, one of his main contributions to probabilistic thinking is a form of belief updating—now typically called ‘Jeffrey conditioning’ or ‘probability kinematics’—that is appropriate in circumstances in which Rigidity is satisfied, but where the interaction causes one to reevaluate one’s probability judgments over some partition of the possibility space without conferring certainty on any particular element. The most familiar occasion for Jeffrey conditioning is receipt of uncertain evidence: things partially perceived or remembered. But it also serves to illuminate belief updating occasioned by a change in one’s degrees of conditional belief, a kind of belief change largely ignored by classical Bayesianism. I argue that such changes in conditional belief can also be basic (in the sense of not being analyzable as a consequence of conditioning on factual information) and offer a kinematical model for a particular kind change in conditional belief. Both are applied to changes in preference. Finally, I argue that Rigidity can fail when changes of belief give inferential grounds for changes in conditional belief (and vice versa). These failures show that conditioning methods are properly regarded, not as valid rules of inference, but as tools in the ‘art of judgment’.

This paper examines Becker's thesis that the hypothesis that choices maximise expected utility relative to fixed and universal tastes provides a general framework for the explanation of behaviour. Three different models of preference revision are presented and their scope evaluated. The first, the classical conditioning model, explain all changes in preferences in terms of changes in the information held by the agent, holding fundamental beliefs and desires fixed. The second, the Jeffrey conditioning model, explains them in terms of changes in both the information held by the agent and changes in her prior beliefs, holding her fundamental desires fixed. The final model, that of generalised conditioning, allows for explanations in terms of changes in the values of all three variables.

Adams’ Thesis has much evidence in its favour, but DavidLewis famously showed that it cannot be true, in all but the most trivial of cases, if conditionals are proprositions and their probabilities are classical probabilities of truth. In this paper I show thatsimilar results can be constructed for a much wider class of conditionals. The fact that these results presupposethat the logic of conditionals is Boolean motivates a search for a non-Boolean alternative. It is arguedthat the exact proposition expressed by a conditional depends on the context in which it is uttered. Consequentlyits probability of truth will depend not only on the probabilities of the various propositions it mightexpress, but also on the probabilities of the contexts determining which proposition it does in fact express.The semantic theory developed from this is then shown to explain why agents’ degrees of belief satisfyAdams’ Thesis. Finally the theory is compared with proposals for a three-valued logic of conditionals.

According to the Ramsey Test hypothesis the conditional claim that if A then B is credible just in case it is credible that B, on the supposition that A. If true the hypothesis helps explain the way in which we evaluate and use ordinary language conditionals. But impossibility results for the Ramsey Test hypothesis in its various forms suggest that it is untenable. In this paper, I argue that these results do not in fact have this implication, on the grounds that similar results can be proved without recourse to the Ramsey test hypothesis. Instead they show that a number of well entrenched principles of rational belief and belief revision do not apply to conditionals.

Richard Jeffrey regarded the version of Bayesian decision theory he floated in ‘The Logic of Decision’ and the idea of a probability kinematics—a generalisation of Bayesian conditioning to contexts in which the evidence is ‘uncertain’—as his two most important contributions to philosophy. This paper aims to connect them by developing kinematical models for the study of preference change and practical deliberation. Preference change is treated in a manner analogous to Jeffrey’s handling of belief change: not as mechanical outputs of combinations of intrinsic desires plus information, but as a matter of judgement and of making up one’s mind. In the first section Jeffrey’s probability kinematics is motivated and extended to the treatment of changes in conditional belief. In the second, analogous kinematical models are developed for preference change and in particular belief-induced change that depends on an invariance condition for conditional preference. The two are the brought together in the last section in a tentative model of pratical deliberation.