Decision-Theoretic Frameworks

Savage famously contravened his own theory when first confronting the Allais Paradox, but then convinced himself that he had made an error. We examine the formal structure of Savage’s ‘error-correcting’ reasoning in the light of (i) behavioural economists’ claims to identify the latent preferences of individuals who violate conventional rationality requirements and (ii) Broome’s critique of arguments which presuppose that rationality requirements can be achieved through reasoning. We argue that Savage’s reasoning is not vulnerable to Broome’s critique, but does not (...) provide support for the view that behavioural scientists can identify and counteract errors in people’s choices or preferences. (shrink)

This paper takes issue with an influential interpretationist argument for physicalism about intentionality based on the possibility of radical interpretation. The interpretationist defends the physicalist thesis that the intentional truths supervene on the physical truths by arguing that it is possible for a radical interpreter, who knows all of the physical truths, to work out the intentional truths about what an arbitrary agent believes, desires, and means without recourse to any further empirical information. One of the most compelling arguments for (...) the possibility of radical interpretation, associated most closely with David Lewis and Donald Davidson, gives a central role to decision theoretic representation theorems, which demonstrate that if an agent’s preferences satisfy certain constraints, it is possible to deduce probability and utility functions that represent her beliefs and desires. We argue that an interpretationist who wants to rely on existing representation theorems in defence of the possibility of radical interpretation faces a trilemma, each horn of which is incompatible with the possibility of radical interpretation. (shrink)

The critics of rational choice theory (henceforth, RCT) frequently claim that RCT is self-defeating in the sense that agents who abide by RCT’s prescriptions are less successful in satisfying their preferences than they would be if they abided by some normative theory of choice other than RCT. In this paper, I combine insights from philosophy of action, philosophy of mind and the normative foundations of RCT to rebut this often-made criticism. I then explicate the implications of my thesis for the (...) wider philosophical debate concerning the normativity of RCT for both ideal agents who can form and revise their intentions instantly without cognitive costs and real-life agents who have limited control over the formation and the dynamics of their own intentions. (shrink)

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but achieves only static (...) rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs. (shrink)

This paper argues that instrumental rationality is more permissive than expected utility theory. The most compelling instrumentalist argument in favour of separability, its core requirement, is that agents with non-separable preferences end up badly off by their own lights in some dynamic choice problems. I argue that once we focus on the question of whether agents’ attitudes to uncertain prospects help define their ends in their own right, or instead only assign instrumental value in virtue of the outcomes they may (...) lead to, we see that the argument must fail. Either attitudes to prospects assign non-instrumental value in their own right, in which case we cannot establish the irrationality of the dynamic choice behaviour of agents with non-separable preferences. Or they don’t, in which case agents with non-separable preferences can avoid the problematic choice behaviour without adopting separable preferences. (shrink)

Maximising expected value is the classic doctrine in choice theory under empirical uncertainty, and a prominent proposal in the emerging philosophical literature on normative uncertainty, i.e., uncertainty about values. But how should Expectationalism be stated in general, when we can face both uncertainties simultaneously, as is common in life? Surprisingly, different possibilities arise, ranging from Ex-Ante to Ex-Post Expectationalism, with several hybrid versions. Expectationalism thus faces the classic dilemma between ex-ante and ex-post approaches. Different expectational theories reach diverging evaluations, use (...) different modes of reasoning, and take different attitudes to risk; but they converge under an interesting (necessary and sufficient) condition. We relate choice under normative uncertainty to choice by Harsany's 'impartial observer' and Rawls's person behind the 'veil of ignorance', who are uncertain about their own identity and values; and we relate Expectationalism to Harsanyi's linear approach to aggregating values of different individuals or identities. (shrink)

In Richard Bradley's book, Decision Theory with a Human Face (2017), we have selected two themes for discussion. The first is the Bolker-Jeffrey (BJ) theory of decision, which the book uses throughout as a tool to reorganize the whole field of decision theory, and in particular to evaluate the extent to which expected utility (EU) theories may be normatively too demanding. The second theme is the redefinition strategy that can be used to defend EU theories against the Allais and Ellsberg (...) paradoxes, a strategy that the book by and large endorses, and even develops in an original way concerning the Ellsberg paradox. We argue that the BJ theory is too specific to fulfil Bradley’s foundational project and that the redefinition strategy fails in both the Allais and Ellsberg cases. Although we share Bradley’s conclusion that EU theories do not state universal rationality requirements, we reach it not by a comparison with BJ theory, but by a comparison with the non-EU theories that the paradoxes have heuristically suggested. (shrink)

Epistemic decision theory (EDT) employs the mathematical tools of rational choice theory to justify epistemic norms, including probabilism, conditionalization, and the Principal Principle, among others. Practitioners of EDT endorse two theses: (1) epistemic value is distinct from subjective preference, and (2) belief and epistemic value can be numerically quantified. We argue the first thesis, which we call epistemic puritanism, undermines the second.

Good’s theorem is the apparent platitude that it is always rational to ‘look before you leap’: to gather information before making a decision when doing so is free. We argue that Good’s theorem is not platitudinous and may be false. And we argue that the correct advice is rather to ‘make your act depend on the answer to a question’. Looking before you leap is rational when, but only when, it is a way to do this.

This article argues that Lara Buchak’s risk-weighted expected utility 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)

Many moral theories are committed to the idea that some kinds of moral considerations should be respected, whatever the cost to ‘lesser’ types of considerations. A person's life, for instance, should not be sacrificed for the trivial pleasures of others, no matter how many would benefit. However, according to the decision-theoretic critique of lexical priority theories, accepting lexical priorities inevitably leads us to make unacceptable decisions in risky situations. It seems that to operate in a risky world, we must reject (...) lexical priorities altogether. This paper argues that lexical priority theories can, in fact, offer satisfactory guidance in risky situations. It does so by equipping lexical priority theories with overlooked resources from decision theory. (shrink)

Standard decision theory, or rational choice theory, is often interpreted to be a theory of instrumental rationality. This dissertation argues, however, that the core requirements of orthodox decision theory cannot be defended as general requirements of instrumental rationality. Instead, I argue that these requirements can only be instrumentally justified to agents who have a desire to have choice dispositions that are stable over time and across different choice contexts. Past attempts at making instrumentalist arguments for the core requirements of decision (...) theory fail due to a pervasive assumption in decision theory, namely the assumption that the agent’s preferences over the objects of choice – be it outcomes or uncertain prospects – form the standard of instrumental rationality against which the agent’s actions are evaluated. I argue that we should instead take more basic desires to be the standard of instrumental rationality. But unless agents have a desire to have stable choice dispositions, according to this standard, instrumental rationality turns out to be more permissive than orthodox decision theory. (shrink)

This article reviews Herbert Simon's theory of bounded rationality, with a view of deemphasizing his "satisficing" model, and by contrast, of emphasizing his distinction between "procedural" and "substantive" rationality. The article also discusses a possible move from neo-classical economists to respond to Simon's criticisms, i.e., a reduction of bounded rationality to a special case of second-optimization, using Stigler's search theory. This move is eventually dismissed.

Richard Bradley’s written a new book about decision theory. We decided to ask him some questions about it.

The existence of a transitive, complete, and weakly independent relation on the full set of gambles implies the existence of a non-Ramsey set. Therefore, each transitive and weakly independent relation on the set of gambles either is incomplete or does not have an explicit description. Whatever tools decision theory makes available, there will always be decision problems where these tools fail us. In this sense, decision theory remains incomplete.

Is Bayesian decision theory a panacea for many of the problems in epistemology and the philosophy of science, or is it philosophical snake-oil? For years a debate had been waged amongst specialists regarding the import and legitimacy of this body of theory. Mark Kaplan had written the first accessible and non-technical book to address this controversy. Introducing a new variant on Bayesian decision theory the author offers a compelling case that, while no panacea, decision theory does in fact have the (...) most profound consequences for the way in which philosophers think about inquiry, criticism and rational belief. The new variant on Bayesian theory is presented in such a way that a non-specialist will be able to understand it. The book also offers new solutions to some classic paradoxes. It focuses on the intuitive motivations of the Bayesian approach to epistemology and addresses the philosophical worries to which it has given rise. (shrink)

We suscribe to an account of framing-effects in decision theory in terms of an inference to a background informationa by the hearer when a speaker uses a certain frame while other equivalent frames were also available. This account was sketched by Craig McKenzie. We embed it in Bolker-Jeffrey decision model - one main reason of this is that this latter model makes preferences bear on propositions. We can deduce a given anomaly or cognitive bias in a formal decision theory. This (...) leads to some philosophical considerations on the relationship between the rationality of preferences and the sensitivity to descriptions or labels of states of affairs in decision-making. (shrink)

This book, first published in 1997, is an introductory overview of decision theory. It is completely non-technical, without a single formula in the book. Written in a crisp and clear style it succinctly covers the full range of philosophical issues of rationality and decision theory, including game theory, social choice theory, prisoner's dilemma and much else. The book aims to expand the scope and enrich the foundations of decision theory. By addressing such issues as ambivalence, inner conflict, and the constraints (...) imposed upon us by our attachments to others, Frederic Schick reveals that our thinking is often more subtle than standard theories of rationality allow. Only a theory that respects that subtlety can illumine what is otherwise puzzling. The book contains many examples drawn from history and literature dealing with subjects such as love, war, friendship, and crime. (shrink)

Theory choice can be approached in at least four ways. One of these calls for the application of decision theory, and this article endorses this approach. But applying standard forms of decision theory imposes an overly demanding standard of numeric information, supposedly satisfied by point-valued utility and probability functions. To ameliorate this difficulty, a version of decision theory that requires merely comparative utilities and plausibilities is proposed. After a brief summary of this alternative, the article illustrates how comparative decision theory (...) affords a rational reconstruction of decisions made by exemplary scientists in two cases of theory choice: Buffon’s law and the luminiferous ether. It also offers a rational reconstruction of two cases of theory diagnosis: Mendeleev’s anomalies and the Pioneer anomaly. (shrink)

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. (shrink)

This paper presents a decision theory which allows subjects to account for the uncertainties of their probability estimates. This is accomplished by modelling beliefs about states of nature by means of a class of probability measures. In order to represent uncertainties of those beliefs a measure of epistemic reliability is introduced. The suggested decision theory is evaluated in the light of empirical evidence on ambiguity and uncertainty in decision making. The theory is also compared to Tversky & Kahneman's prospect theory.

In a widely discussed forthcoming article, “What you can't expect when you're expecting,” L. A. Paul challenges culturally and philosophically traditional views about how to rationally make major life-decisions, most specifically the decision of whether to have children. The present paper argues that because major life-decisions are transformative, the only rational way to approach them is to become resilient people: people who do not “over-plan” their lives or expect their lives to play out “according to plan”—people who understand that beyond (...) a certain limit, life cannot be rationally planned and must be accepted as it comes. I show that this focus on resilience—on self-mastery—stands in direct opposition to culturally dominant attitudes toward decision-making, which focus not on the self-mastery but on control and mastery over one's surroundings. In short, I argue that if Paul's general point about transformative experiences is correct, it follows that we rationally ought to adopt a very different approach to life choices, self-development, and the moral education of our children than currently-dominant cultural norms and practices suggest. (shrink)

We introduce a “reason-based” framework for explaining and predicting individual choices. It captures the idea that a decision-maker focuses on some but not all properties of the options and chooses an option whose motivationally salient properties he/she most prefers. Reason-based explanations allow us to distinguish between two kinds of context-dependent choice: the motivationally salient properties may (i) vary across choice contexts, and (ii) include not only “intrinsic” properties of the options, but also “context-related” properties. Our framework can accommodate boundedly rational (...) and sophisticatedly rational choice. Since properties can be recombined in new ways, it also offers resources for predicting choices in unobserved contexts. (shrink)

The puzzle of the absentminded driver combines an unstable decision problem with a version of the Sleeping Beauty problem. Its analysis depends on the choice between “halfing” and “thirding” as well as that between “evidential” and “causal” decision theory. I show that all four combinations lead to interestingly different solutions, and draw some general lessons about the formulation of causal decision theory, the interpretation of mixed strategies and the connection between rational credence and objective chance.

Those who model doxastic states with a set of probability functions, rather than a single function, face a pressing challenge: can they provide a plausible decision theory compatible with their view? Adam Elga and others claim that they cannot, and that the set of functions model should be rejected for this reason. This paper aims to answer this challenge. The key insight is that the set of functions model can be seen as an instance of the supervaluationist approach to vagueness (...) more generally. We can then generate our decision theory by applying the general supervaluationist semantics to decision-theoretic claims. The result: if an action is permissible according to all functions in the set, it’s determinately permissible; if impermissible according to all, determinately impermissible; and – crucially – if permissible according to some, but not all, it’s indeterminate whether it’s permissible. This proposal handles with ease some difficult cases ) on which alternative decision theories falter. One reason this view has been overlooked in the literature thus far is that all parties to the debate presuppose that an acceptable decision theory must classify each action as either permissible or impermissible. But I will argue that this thought is misguided. Seeing the set of functions model as an instance of supervaluationism provides a compelling motivation for the claim that there can be indeterminacy in the rationality of some actions. (shrink)

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. (shrink)

Mark Kaplan proposes amending decision theory to accommodate better cases in which an agent's probability assignment is imprecise. The review describes and evaluates his proposals.

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. (shrink)

For a long while Bayesian techniques in statistics in general, and decision theory in particular, were considered suspect at best, and to be avoided; but now along comes Jeffrey with a system of subjective probability and utility functions determined by the individual's preferences, and a strongly Bayesian approach to decision-making, and by so doing puts the whole matter in a new light and makes it quite important to reassess the prior rejection of Bayesian methods. There are twelve chapters, each with (...) exercises, which begin with the model of deliberation, progress though scaling and ranking desirability, preference and propositional attitudes, thence to probability and measurement of desirability, and finally to induction and confirmation. The author's theory bears some resemblances to that sketched by Ramsey, but it draws somewhat on the later work of Von Neumann and Morgenstern. The author examines probability as viewed both statically—when the agent's attitudes are constant—and dynamically-when desirability and, consequently, probability assignments change. This text is one of the small but growing library of works whose interest is induction and probability theory; in that library, it will occupy an important place.—P. J. M. (shrink)

I explore the prospects for modelling epistemic rationality (in the probabilist setting) via an epistemic decision theory, in a consequentialist spirit. Previous work has focused on cases in which the truth-values of the propositions in which the agent is selecting credences do not depend, either causally or merely evidentially, on the agent’s choice of credences. Relaxing that restriction leads to a proliferation of puzzle cases and theories to deal with them, including epistemic analogues of evidential and causal decision theory, and (...) of the Newcomb Problem and ‘Psychopath Button’ Problem. A variant of causal epistemic decision theory deals well with most cases. However, there is a recalcitrant class of problem cases for which no epistemic decision theory seems able to match our intuitive judgements of epistemic rationality. This lends both precision and credence to the view that there is a fundamental mismatch between epistemic consequentialism and the intuitive notion of epistemic rationality; the implications for understanding the latter are briefly discussed. (shrink)