James M. Joyce

Richard Bradley’s landmark book Decision Theory with a Human Face makes seminal contributions to nearly every major area of decision theory, as well as most areas of formal epistemology and many areas of semantics. In addition to sketching Bradley’s distinctive semantics for conditional beliefs and desires, I will explain his theory of conditional desire, focusing particularly on his claim that we should not desire events, either positively or negatively, under the supposition that they will occur. I shall argue, to the contrary, that permitting non-trivial desirabilities for events whose occurrence is known or assumed is both more intuitively plausible and more theoretically fruitful than Bradley’s approach. In the course of the discussion I will contrast Bradley’s broadly evidentialist picture of decision theory with my own more orthodox causal approach.

Bayesianism claims to provide a unified theory of epistemic and practical rationality based on the principle of mathematical expectation. In its epistemic guise it requires believers to obey the laws of probability. In its practical guise it asks agents to maximize their subjective expected utility. Joyce’s primary concern is Bayesian epistemology, and its five pillars: people have beliefs and conditional beliefs that come in varying gradations of strength; a person believes a proposition strongly to the extent that she presupposes its truth in her practical and theoretical reasoning; rational graded beliefs must conform to the laws of probability; evidential relationships should be analyzed subjectively in terms of relations among a person’s graded beliefs and conditional beliefs; empirical learning is best modeled as probabilistic conditioning. Joyce explains each of these claims and evaluates some of the justifications that have been offered for them, including “Dutch book,” “decision-theoretic,” and “non-pragmatic” arguments for and. He also addresses some common objections to Bayesianism, in particular the “problem of old evidence” and the complaint that the view degenerates into an untenable subjectivism. The essay closes by painting a picture of Bayesianism as an “internalist” theory of reasons for action and belief that can be fruitfully augmented with “externalist” principles of practical and epistemic rationality.

The pragmatic character of the Dutch book argument makes it unsuitable as an "epistemic" justification for the fundamental probabilist dogma that rational partial beliefs must conform to the axioms of probability. To secure an appropriately epistemic justification for this conclusion, one must explain what it means for a system of partial beliefs to accurately represent the state of the world, and then show that partial beliefs that violate the laws of probability are invariably less accurate than they could be otherwise. The first task can be accomplished once we realize that the accuracy of systems of partial beliefs can be measured on a gradational scale that satisfies a small set of formal constraints, each of which has a sound epistemic motivation. When accuracy is measured in this way it can be shown that any system of degrees of belief that violates the axioms of probability can be replaced by an alternative system that obeys the axioms and yet is more accurate in every possible world. Since epistemically rational agents must strive to hold accurate beliefs, this establishes conformity with the axioms of probability as a norm of epistemic rationality whatever its prudential merits or defects might be

Recently several authors have argued that accuracy-first epistemology ends up licensing problematic epistemic bribes. They charge that it is better, given the accuracy-first approach, to deliberately form one false belief if this will lead to forming many other true beliefs. We argue that this is not a consequence of the accuracy-first view. If one forms one false belief and a number of other true beliefs, then one is committed to many other false propositions, e.g., the conjunction of that false belief with any of the true beliefs. Once we properly account for all the falsehoods that are adopted by the person who takes the bribe, it turns out that the bribe does not increase accuracy.

Bayesian decision theorists argue that rational agents should always perform acts that maximize subjective expected utility. To justify this claim, they prove representation theorems which are designed to show that any decision maker whose beliefs and desires satisfy reasonable axiomatic constraints will necessarily behave like an expected utility maximizer. The existence of such a representation result is a prerequisite for any adequate account of rational choice because one is only able to determine what a decision theory says about beliefs and desires by looking at the axioms used in the proof of its representation result. ;I examine a number of versions of decision theory and their representation theorems. Particular attention is paid to so-called causal and evidential decision theories. It is argued that only the latter has an adequate representation which is found in a theorem due to Ethan Bolker which was adapted to the decision theoretic context by R. Jeffrey. I remove the single outstanding problem with Bolker's theorem by reformulating it in a way which yields a unique probability and utility representation. This is possible because, unlike Bolker, I make use of axioms which govern not only preference but comparative probability. ;I show how this reformulated version of Bolker's result can be further generalized to a representation theorem for a generic theory of conditional expected utility whose basic term is a function which measures the strength of an agent's desires when he supposes that various hypotheses are true. Evidential and causal decision theories are show to be special cases of this generic theory. They differ only in the interpretation they give to the notion of supposition. The evidential account interprets it indicatively, while the causal account views it subjunctively. ;Finally, I show how my generic representation theorem for conditional decision theory can serve as a foundation for both causal and evidential decision theories. This provides the first fully adequate representation result for causal decision theory, thereby removing its most serious defect.

This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory. The book solves a long-standing problem for Jeffrey's theory by showing for the first time how to obtain a unique utility and probability representation for preferences and judgements of comparative likelihood. The book also contains a major new discussion of what it means to suppose that some event occurs or that some proposition is true. The most complete and robust defence of causal decision theory available.

Andy Egan has recently produced a set of alleged counterexamples to causal decision theory in which agents are forced to decide among causally unratifiable options, thereby making choices they know they will regret. I show that, far from being counterexamples, CDT gets Egan's cases exactly right. Egan thinks otherwise because he has misapplied CDT by requiring agents to make binding choices before they have processed all available information about the causal consequences of their acts. I elucidate CDT in a way that makes it clear where Egan goes wrong, and which explains why his examples pose no threat to the theory. My approach has similarities to a modification of CDT proposed by Frank Arntzenius, but it differs in the significance that it assigns to potential regrets. I maintain, contrary to Arntzenius, that an agent facing Egan's decisions can rationally choose actions that she knows she will later regret. All rationality demands of agents it that they maximize unconditional causal expected utility from an epistemic perspective that accurately reflects all the available evidence about what their acts are likely to cause. This yields correct answers even in outlandish cases in which one is sure to regret whatever one does

Richard Jeffrey long held that decision theory should be formulated without recourse to explicitly causal notions. Newcomb problems stand out as putative counterexamples to this ‘evidential’ decision theory. Jeffrey initially sought to defuse Newcomb problems via recourse to the doctrine of ratificationism, but later came to see this as problematic. We will see that Jeffrey’s worries about ratificationism were not compelling, but that valid ratificationist arguments implicitly presuppose causal decision theory. In later work, Jeffrey argued that Newcomb problems are not decisions at all because agents who face them possess so much evidence about correlations between their actions and states of the world that they are unable to regard their deliberate choices as causes of outcomes, and so cannot see themselves as making free choices. Jeffrey’s reasoning goes wrong because it fails to recognize that an agent’s beliefs about her immediately available acts are so closely tied to the immediate causes of these actions that she can create evidence that outweighs any antecedent correlations between acts and states. Once we recognize that deliberating agents are free to believe what they want about their own actions, it will be clear that Newcomb problems are indeed counterexamples to evidential decision theory.

Colin Howson has recently argued that accuracy arguments for probabilism fail because they assume a privileged ‘coding’ in which TRUE is assigned the value 1 and FALSE is assigned the value 0. I explain why this is wrong by first showing that Howson’s objections are based on a misconception about the way in which degrees of confidence are measured, and then reformulating the accuracy argument in a way that manifestly does not depend on the coding of truth-values. Along the way, I will explain how to formulate the laws of probability and rational expectation in a scale-invariant way, and how to properly understand the values of the credence functions that we use to represent rational degrees of confidence

Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, the Theorem's central insight — that a hypothesis is confirmed by any body of data that its truth renders probable — is the cornerstone of all subjectivist methodology

In The Logic of Decision Richard Jeffrey defends a version of expected utility theory that advises agents to choose acts with an eye to securing evidence for thinking that desirable results will ensue. Proponents of "causal" decision theory have argued that Jeffrey's account is inadequate because it fails to properly discriminate the causal features of acts from their merely evidential properties. Jeffrey's approach has also been criticized on the grounds that it makes it impossible to extract a unique probability/utility representation from a sufficiently rich system of preferences (given a zero and unit for measuring utility). The existence of these problems should not blind us to the fact that Jeffrey's system has advantages that no other decision theory can match: it can be underwritten by a particularly compelling representation theorem proved by Ethan Bolker; and it has a property called partition invariance that every reasonable theory of rational choice must possess. I shall argue that the non-uniqueness problem can be finessed, and that it is impossible to adequately formulate causal decision theory, or any other, without using Jeffrey's theory as one's basic analysis of rational desire