Decision Theory

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 tackl...

Suppose that a decision-maker's aim, under certainty, is to maximise some continuous value, such as lifetime income or continuous social welfare. Can such a decision-maker rationally satisfy what has been called "continuity for easy cases" while at the same time satisfying what seems to be a widespread intuition against the full-blown continuity axiom of expected utility theory? In this note I argue that the answer is "no": given transitivity and a weak trade-off principle, continuity for easy cases violates the anti-continuity (...) intuition. I end the note by exploring an even weaker continuity condition that is consistent with the aforementioned intuition. (shrink)

The distinction that Ainslie draws among the triple-phenomena “suppression,” “resolve,” and “habit” is a great advance in decision making theory. But the conceptual machinery “willpower,” and its underpinning distinction between small/soon rewards as opposed to large/later rewards, provides a faulty framework to understand the triple-phenomena.

The main aim of this book is to introduce the topic of limited awareness, and changes in awareness, to those interested in the philosophy of decision-making and uncertain reasoning. (This is for the series Elements of Decision Theory published by Cambridge University Press and edited by Martin Peterson).

Should a scientist rely on methodological triangulation? Heesen et al. (Synthese 196(8):3067–3081, 2019) recently provided a convincing affirmative answer. However, their approach requires belief gambles if the evidence is discordant. We instead propose epistemically modest triangulation (EMT), according to which one should withhold judgement in such cases. We show that for a scientist in a methodologically diffident situation the expected utility of EMT is greater than that of Heesen et al.’s (2019) triangulation or that of using a single method. We (...) also show that EMT is more appropriate for increasing epistemic trust in science. In short: triangulate, but do not gamble with evidence. (shrink)

Why 'social' media 'upsets' us. What is in your 'mind' and, why? The 'unified' background is an uber-simple circle.

In the philosophy of economics, the last fifteen years have witnessed an intense discussion about the epistemological status of economic models of decision making and their theoretical components,...

In the debate about the legal value of naked statistical evidence, Di Bello argues that (1) the likelihood ratio of such evidence is unknown, (2) the decision-theoretic considerations indicate that a conviction based on such evidence is unacceptable when expected utility maximization is combined with fairness constraints, and (3) the risk of mistaken conviction based on such evidence cannot be evaluated and is potentially too high. We argue that Di Bello’s argument for (1) works in a rather narrow context, and (...) that (1) is not exactly in line with the way expert witnesses are required to formulate their opinions. Consequently, Di Bello’s argument for (2), which assumes (1), does not apply uniformly to all convictions based on naked evidence. Moreover, if Di Bello’s analysis is correct, it applies also to eyewitness testimony, given empirical results about its quality, and so the distinctions drawn by DiBello cut across the distinction between naked statistical evidence and other types of evidence. Finally, if we weaken the rather strong requirement of precise measurability of the risk of mistaken conviction, to the availability of reasonable but imprecise and fallible estimates, many field and empirical studies show that often the risk of mistaken conviction based on naked statistical evidence can be estimated to a similar extent as the risk of mistaken conviction based on any other sort of evidence. (shrink)

The paper investigates what type of motivation can be given for adopting a knowledge-based decision theory (hereafter, KBDT). KBDT seems to have several advantages over competing theories of rationality. It is commonly argued that this theory would naturally fit with the intuitive idea that being rational is doing what we take to be best given what we know, an idea often supported by appeal to ordinary folk appraisals. Moreover, KBDT seems to strike a perfect balance between the problematic extremes of (...) subjectivist and objectivist decision theory. We argue that these alleged advantages do not stand up to a closer scrutiny: KBDT inherits the same kinds of problems as alternative decision theoretic frameworks but doesn’t retain any of the respective advantages. Moreover, differently from other knowledge-action principles advanced in the literature, KBDT cannot fully explain the intuitive connections between knowledge and rational action. We conclude that the most serious challenge for knowledge-based decision theorists is to provide a substantive rationale for the adoption of such a view. (shrink)

In a well-known paper, Nick Bostrom presents a confrontation between a fictionalised Blaise Pascal and a mysterious mugger. The mugger persuades Pascal to hand over his wallet by exploiting Pascal's commitment to expected utility maximisation. He does so by offering Pascal an astronomically high reward such that, despite Pascal's low credence in the mugger's truthfulness, the expected utility of accepting the mugging is higher than rejecting it. In this article, I present another sort of high value, low credence mugging. This (...) time, the mugger utilises research on existential risk and the long-term potential of humanity to exploit Pascal's expected-utility-maximising descendant. This mugging is more insidious than Bostrom's original as it relies on plausible facts about the long-term future, as well as realistic credences about how our everyday actions could, albeit with infinitesimally low likelihood, affect the future of humanity. (shrink)

Objective: The objective of this study was to evaluate the psychometric properties of the Chinese version of the decision regret scale. Methods: The data of 704 patients who completed the DRSc were used for the analyses. We evaluated the construct, convergent/discriminant, and known-group validity; internal consistency and test–retest reliability; and the item invariance of the DRSc. A receiver operating characteristic curve was employed to confirm the optimal cutoff point of the scale. Results: A confirmatory factor analysis indicated that a one-factor (...) model fits the data. The internal consistency and test–retest reliability [intraclass correlation coefficient = 0.71] of the DRSc were acceptable. The DRSc demonstrated unidimensionality and invariance for use across the sexes. It was confirmed that an optimal cutoff point of 25 could discriminate between patients with high and low decisional regret during clinical practice. Conclusion: The DRSc is a parsimonious instrument that can be used to measure the uncertainty inherent in medical decisions. It can be employed to provide knowledge, offer support, and elicit patient preferences in an attempt to promote shared decision-making. (shrink)

Those who are risk averse with respect to money, and thus turn down some gambles with positive monetary expectations, are nevertheless often willing to accept bundles involving multiple such gambles. Therefore, it might seem that such people should become more willing to accept a risky but favourable gamble if they put it in context with the collection of gambles that they predict they will be faced with in the future. However, it turns out that when a risk averse person adopts (...) the long-term perspective, she faces a decision-problem that can be analysed as a noncooperative game between different "time-slices" of herself, where it is in the interest of each time-slice (given its prediction about other slices) to turn down the gamble with which it is faced. Hence, even if a risk averse but rational person manages to take the long-term perspective, she will, in the absence of what Hardin called "mutual coercion", end up in a situation analogous to the "tragedy of the commons". (shrink)

It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing that as an agent's (...) attention shifts, successive batches of "obvious" logical information become available to her. A rule of expected utility maximization can then be applied to the decision of what to attend to next during a train of thought. On the resulting theory, rationality requires ordinary agents to be logically competent and to often engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient. (shrink)

I discuss the trilemma that consists of the following three principles being inconsistent: 1. The Common Principle: if one distribution, A, necessarily brings a higher total sum of personal value that is distributed in a more egalitarian way than another distribution, B, A is more valuable than B. 2. (Weak) ex-ante Pareto: if one uncertain distribution, A, is more valuable than another uncertain distribution, B, for each patient, A is more valuable than B. 3. Pluralism about attitudes to risk (Pluralism): (...) the personal value of a prospect is a weighted sum of the values of the prospect’s outcomes, but the weight each outcome gets might be different from the probability the prospect assigns to the outcome. (shrink)

Policymakers who seek to make scientifically informed decisions are constantly confronted by scientific uncertainty and expert disagreement. This thesis asks: how can policymakers rationally respond to expert disagreement and scientific uncertainty? This is a work of non-ideal theory, which applies formal philosophical tools developed by ideal theorists to more realistic cases of policymaking under scientific uncertainty. I start with Bayesian approaches to expert testimony and the problem of expert disagreement, arguing that two popular approaches— supra-Bayesianism and the standard model of (...) expert deference—are insufficient. I develop a novel model of expert deference and show how it can deal with many of these problems raised for them. I then turn to opinion pooling, a popular method for dealing with disagreement. I show that various theoretical motivations for pooling functions are irrelevant to realistic policymaking cases. This leads to a cautious recommendation of linear pooling. However, I then show that any pooling method relies on value judgements, that are hidden in the selection of the scoring rule. My focus then narrows to a more specific case of scientific uncertainty: multiple models of the same system. I introduce a particular case study involving hurricane models developed to support insurance decision-making. I recapitulate my analysis of opinion pooling in the context of model ensembles, confirming that my hesitations apply. This motivates a shift of perspective, to viewing the problem as a decision theoretic one. I rework a recently developed ambiguity theory, called the confidence approach, to take input from model ensembles. I show how it facilitates the resolution of the policymaker’s problem in a way that avoids the issues encountered in previous chapters. This concludes my main study of the problem of expert disagreement. In the final chapter, I turn to methodological reflection. I argue that philosophers who employ the mathematical methods of the prior chapters are modelling. Employing results from the philosophy of scientific models, I develop the theory of normative modelling. I argue that it has important methodological conclusions for the practice of formal epistemology, ruling out popular moves such as searching for counterexamples. (shrink)

An agent often does not have precise probabilities or utilities to guide resolution of a decision problem. I advance a principle of rationality for making decisions in such cases. To begin, I represent the doxastic and conative state of an agent with a set of pairs of a probability assignment and a utility assignment. Then I support a decision principle that allows any act that maximizes expected utility according to some pair of assignments in the set. Assuming that computation of (...) an option's expected utility uses comprehensive possible outcomes that include the option's risk, no consideration supports a stricter requirement. (shrink)

The critics of rational choice theory (RCT) frequently build on the contrast between so-called thick and thin applications of RCT to argue that thin RCT lacks the potential to explain the choices of real-world agents. In this paper, I draw on often-cited RCT applications in several decision sciences to demonstrate that despite this prominent critique there are at least two different senses in which thin RCT can explain real-world agents’ choices. I then defend this thesis against the most influential objections (...) put forward by the critics of RCT. In doing so, I explicate the implications of my thesis for the ongoing philosophical debate concerning the explanatory potential of RCT and the comparative merits of widely endorsed accounts of explanation. (shrink)

It is often suggested that when opinions differ among individuals in a group, the opinions should be aggregated to form a compromise. This paper compares two approaches to aggregating opinions, linear pooling and what I call opinion agglomeration. In evaluating both strategies, I propose a pragmatic criterion, No Regrets, entailing that an aggregation strategy should prevent groups from buying and selling bets on events at prices regretted by their members. I show that only opinion agglomeration is able to satisfy the (...) demand. I then proceed to give normative and empirical arguments in support of the pragmatic criterion for opinion aggregation, and that ultimately favor opinion agglomeration. (shrink)

One reasons not just in beliefs, but also in intentions, preferences, and other attitudes. For instance, one forms preferences from preferences, or intentions from beliefs and preferences. Formal logic has proved useful for modelling reasoning in beliefs -- the formation of beliefs from beliefs. Can logic also model reasoning in multiple attitudes? We identify principled obstacles. Logic can model reasoning about attitudes. But this models the discovery of attitudes of (usually) others, not the formation of one's own attitudes. Beliefs are (...) special in that reasoning in beliefs can follow logical entailment between belief contents. This makes beliefs the privileged target of logic, when applying logic to psychology. (shrink)

I describe in section 1 how cyclical preferences can arise. In section 2, I relate preference to judgments of choiceworthiness and distinguish between two kinds of preference cycles, vicious and benign. In section 3, I run through the standard money pump in order to show, in section 4, how this pump can be stopped by foresight, using backward induction. A new money pump that *cannot* be stopped by foresight is presented in section 5. This pump works even for agents with (...) benign cyclical preferences. What makes it work is persistency on the part of the would-be exploiter. In section 6, I compare this pump to a diachronic Dutch book that can be set up against someone whose probability assignments violate Reflection. Even in this case, the book only works if the bookie is assumed to be persistent. I use this comparison between preference cyclicity and violations of Reflection in order to question whether exploitability must be seen as a proof of irrationality. Finally, in section 7, I consider resolute choice as an alternative to the backward-induction procedure. While a resolute chooser cannot be exploited, I argue that resoluteness is not required by rationality. The argument is based on a suggestion that rationality, when it comes to actions, is a local rather than a global requirement. (shrink)

In her second post in this series, Anna Mahtani explores the parallels between philosophy of language and decision theory’s treatment of indexicals and vagueness.

How should we make decisions when we're uncertain about what we ought, morally, to do? Decision-making in the face of fundamental moral uncertainty is underexplored terrain: MacAskill, Bykvist, and Ord argue that there are distinctive norms by which it is governed, and which depend on the nature of one's moral beliefs.

This is an edited transcript of a conversation to be included in the collection "Conversations on Rational Choice". The conversation was conducted in Munich on 7 and 9 February 2016.

Volume 27, Issue 2, June 2020, Page 184-189.

Reasons for action is a widely employed methodology in practical philosophy, and especially in moral philosophy. Reasons are facts that explain and justify actions. But, conceptually, if reasons were causes, incontinent actions would be impossible. When an agent ranks an evaluation about what to do as his best judgement, it entails that he has a reason for acting as that judgement prescribes. But when an agent acts incontinently, he acts in accordance to an intention that is not aligned with his (...) best evaluative judgement. Yet, if the agent’s best evaluative judgement provides him a reason for action, this reason should also be his strongest reason, and therefore, the strongest cause. How then can it be possible that an agent incontinently acts according to a reason of inferior causal strength? In this paper, I analyze how Davidson’s argument for the possibility of incontinent actions interacts with his causal theory of actions. I argue that Davidson’s proposal does not fully respect the two principles of intentional rationality, that he himself claims to be compelling. Lastly, I sketch some initial steps that might be helpful to drawing more precise conceptual distinctions in terms of the rationality of incontinent actions. (shrink)

A non-expert who struggles to make good decisions and who turns to decision theory for help, might be more than a little surprised by what they find. If they read a standard treatment of the subject, they will find that they are assumed to be logically omniscient: they know all the logical facts about the propositions whose truth they have considered. Their beliefs are also assumed to be logically closed: if they believe each of a set of propositions S, then (...) they believe everything that can be deduced from S. Finally, they are assumed to be maximally opinionated—they have assigned precise probabilities and cardinal utilities to each possible state of the world that can be formulated via S. The normative core of standard decision theory consists of some very weak axioms for these probabilities and car-dinal utilities, plus the advice to maximize their expected utility, which is a function of the probabil-ities and cardinal utilities for each possible state of the world given each possible choice that they can make. The non-expert might understandably react by saying that this theory is too idealized to be useful for human beings. It is this criticism that Richard Bradley addresses with patience, rigour, and ardour in this book. (shrink)

This article analyses how normative decision theory is understood by economists. The paradigmatic example of normative decision theory, discussed in the article, is the expected utility theory. It...

The notion of comparative probability defined in Bayesian subjectivist theory stems from an intuitive idea that, for a given pair of events, one event may be considered “more probable” than the other. Yet it is conceivable that there are cases where it is indeterminate as to which event is more probable, due to, e.g., lack of robust statistical information. We take that these cases involve indeterminate comparative probabilities. This paper provides a Savage-style decision-theoretic foundation for indeterminate comparative probabilities.

У статті розглянуто ознаки системи, особливості соціально-економічних систем та системного підходу. Враховано вплив аксіоматики, закономірностей та законів на розвиток систем. Досліджено циклічні закономірності у різнорівневих соціально-економічних системах. Визначено проблемно-дискусійні питання та спільні системні ознаки циклічності. Ідентифіковано структуру життєвого циклу соціально-економічної системи із визначенням загальних та конкретних складових елементів повторюваних змін за позасистемними та системними показниками.

John Broome has developed an account of rationality and reasoning which gives philosophical foundations for choice theory and the psychology of rational agents. We formalize his account into a model that differs from ordinary choice-theoretic models through focusing on psychology and the reasoning process. Within that model, we ask Broome’s central question of whether reasoning can make us more rational: whether it allows us to acquire transitive preferences, consistent beliefs, non-akratic intentions, and so on. We identify three structural types of (...) rationality requirements: consistency requirements, completeness requirements, and closedness requirements. Many standard rationality requirements fall under this typology. Based on three theorems, we argue that reasoning is successful in achieving closedness requirements, but not in achieving consistency or completeness requirements. We assess how far our negative results reveal gaps in Broome's theory, or deficiencies in choice theory and behavioral economics. (shrink)

When does it make sense to act randomly? A persuasive argument from Bayesian decision theory legitimizes randomization essentially only in tie-breaking situations. Rational behaviour in humans, non-human animals, and artificial agents, however, often seems indeterminate, even random. Moreover, rationales for randomized acts have been offered in a number of disciplines, including game theory, experimental design, and machine learning. A common way of accommodating some of these observations is by appeal to a decision-maker’s bounded computational resources. Making this suggestion both precise (...) and compelling is surprisingly difficult. Toward this end, I propose two fundamental rationales for randomization, drawing upon diverse ideas and results from the wider theory of computation. The first unifies common intuitions in favour of randomization from the aforementioned disciplines. The second introduces a deep connection between randomization and memory: access to a randomizing device is provably helpful for an agent burdened with a finite memory. Aside from fit with ordinary intuitions about rational action, the two rationales also make sense of empirical observations in the biological world. Indeed, random behaviour emerges more or less where it should, according to the proposal. (shrink)

--- abstract is not requested by the Editor.

One of the possible solutions of the Fermi paradox is that all civilizations go extinct because they hit some Late Great Filter. Such a universal Late Great Filter must be an unpredictable event that all civilizations unexpectedly encounter, even if they try to escape extinction. This is similar to the “Death in Damascus” paradox from decision theory. However, this unpredictable Late Great Filter could be escaped by choosing a random strategy for humanity’s future development. However, if all civilizations act randomly, (...) this could be the actual cause of universal extinction, as no one will choose the most optimal strategy. Using a meta-random strategy, where the decision to start random actions is also made randomly, solves this. (shrink)

Review of Richard Bradley's Decision Theory with a Human Face.

This volume brings together philosophers and psychologists to investigate the phenomenon of transformative change and a host of fascinating questions it prompts. Taking their departure from seminal work on transformative choice and experience by L. A. Paul and Edna Ullmann-Margalit, the authors pursue fundamental questions concerning the nature of rationality, the limits of the imagination, and the metaphysics of the self. They also strike out into new areas, including value theory, aesthetics, moral and political philosophy. Several chapters present the results (...) of experimental investigation into the psychology of transformation, self-concept, and moral learning. (shrink)

In his 2018 AJP paper, Shlomo Cohen hints that deception could be a distinct subset of manipulation. We pursue this thought further, but by arguing that Cohen’s accounts of deception and manipulation are incorrect. Deception under uncertainty need not involve adding false premises to the victim’s reasoning but it must involve manipulating her response, and cases of manipulation that do not interfere with the victim’s reasoning, but rather utilize it, also exist. Therefore, deception under uncertainty must be constituted by covert (...) manipulation. (shrink)

In her second post in this series, Anna Mahtani explores the parallels between philosophy of language and decision theory’s treatment of indexicals and vagueness.

Decision theorists and philosophers of language have a lot to learn from one another. In the first of this two-part series, Anna Mahtani looks at the use and interpretation of credences and preferences.

There is currently much discussion about how decision making should proceed when an agent's degrees of belief are imprecise; represented by a set of probability functions. I show that decision rules recently discussed by Sarah Moss, Susanna Rinard and Rohan Sud all suffer from the same defect: they all struggle to rationalize diachronic ambiguity aversion. Since ambiguity aversion is among the motivations for imprecise credence, this suggests that the search for an adequate imprecise decision rule is not yet over.

I present a new argument for the repugnant conclusion. The core of the argument is a risky, intrapersonal analogue of the mere addition paradox. The argument is important for three reasons. First, some solutions to Parfit’s original puzzle do not obviously generalize to the intrapersonal puzzle in a plausible way. Second, it raises independently important questions about how to make decisions under uncertainty for the sake of people whose existence might depend on what we do. And, third, it suggests various (...) difficulties for leading views about the value of a person’s life compared to her nonexistence. (shrink)

The Precautionary Principle (PP) is an influential principle of risk management. It has been widely introduced into environmental legislation, and it plays an important role in most international environmental agreements. Yet, there is little consensus on precisely how to understand and formulate the principle. In this paper I prove some impossibility results for two plausible formulations of the PP as a decision-rule. These results illustrate the difficulty in making the PP consistent with the acceptance of any trade-offs between catastrophic risks (...) and more ordinary goods. (shrink)

In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...) satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems -- without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of “idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent. (shrink)

Can an agent deliberating about an action A hold a meaningful credence that she will do A? 'No', say some authors, for 'Deliberation Crowds Out Prediction' (DCOP). Others disagree, but we argue here that such disagreements are often terminological. We explain why DCOP holds in a Ramseyian operationalist model of credence, but show that it is trivial to extend this model so that DCOP fails. We then discuss a model due to Joyce, and show that Joyce's rejection of DCOP rests (...) on terminological choices about terms such as 'intention', 'prediction', and 'belief'. Once these choices are in view, they reveal underlying agreement between Joyce and the DCOP-favouring tradition that descends from Ramsey. Joyce's Evidential Autonomy Thesis (EAT) is effectively DCOP, in different terminological clothing. Both principles rest on the so-called 'transparency' of first-person present-tensed reflection on one's own mental states. (shrink)

According to Richard Jeffrey’s value-free ideal, scientists should avoid making value judgments about inductive risks by offering explicit representations of scientific uncertainty to decision-makers, who can use these to make decisions according to their own values. Some philosophers have responded by arguing that higher-order inductive risks arise in the process of producing representations of uncertainty. This chapter explores this line of argument and its limits, arguing that the Jeffreyan value-free ideal is achievable in contexts where methodological decisions introduce minimal higher-order (...) uncertainty and where communications of uncertainty are unlikely to be manipulated or misunderstood by scientists or decision-makers. This chapter illustrates the limits of the Jeffreyan ideal with reference to climate science and argues that the context of climate science is not conducive to the Jeffreyan ideal, so the argument that climate modeling is value-laden due to higher-order inductive risks withstands recent criticisms. (shrink)