Decision Theory

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity. There is always a halo of indeterminism, since in the end it is chance itself—the random variations of what we call reality, although we do not quite know what it is—that becomes the cause of causes. From (...) an interpretation not devoid of a certain nihilism. (shrink)

This paper presents an analysis of Rescher’s conception of the mode of structuring and operation of human rationality, which Rescher approaches from a historical-philosophical, logical, and semantic matrix. The aim of this research is to explore the specific features of Rescher’s analysis of rationality through the lens of the instability of optimality and the calculus of risk, which emerge as essential presuppositions of his research. Rationality, understood in this context, has a threefold manifestation: as a procedural matrix, as a modus (...) operandi, and as potential and materialization. This paper, drawing on Rescher’s original works and other relevant sources from the tradition of pragmatism, will explore his approach to this topic with a focus on what Rescher terms the instability of optimality and the calculus of risk. (shrink)

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity.

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity.

Introduction to Impossible Probability, Statistics of Probability or Probabilistic Statistics is one of those works in which a deep bond between mathematics and philosophy can be found. It always asks about the ultimate purpose of science, wrapped in a veil of uncertainty and relativity.

On one plausible story about how we rationally acquire reasons for action, an individual rationally acquires a new reason to φ only if there is something that individual learns about the world. It can also be said without much of a doubt that, in talking to each other, we sometimes rationally acquire reasons for action. This combination of claims is easy to square with declarative sentences, which we clearly use to provide each other with information when we make assertions. But (...) it is much harder to square with imperative sentences, which are standardly taken not to be used in this way. How is it that in attempting to change someone’s behavior by giving them an instruction, we manage to acquaint them with reasons to act? Here, I offer a novel way out of this puzzle: instructions, I argue, are much more like assertions than we ordinarily take them to be, including in their being used to provide each other with information. Whereas assertions provide us with information about any arbitrary aspect of the world, instructions provide us with information specifically about what it is rational to conclude in the course of some practical inquiry, given our goals and the available evidence. (shrink)

We propose a probabilistic algorithm for multiple-choice exams with negative marking that combines deterministic knowledge and data-driven guessing. The algorithm leverages the portion of questions a student knows for certain, alongside historical exam data, to optimize guesses on unknown questions. Recursive iterations and goodness-of-fit analysis enhance the expected score, providing a principled method to maximize the probability of passing, even when only a fraction of questions are fully understood.

We analyze deterministic search algorithms where selection paths are entirely determined by a seed. By studying the cumulative distribution function (CDF) and tail behavior of the search steps, we show that for most seeds, the search completes in constant-time O(1). We discuss applications in hash cracking, black-box optimization, and cognitive modeling, emphasizing the predictive power of tail analysis for worst-case seeds. We also examine the effect of conscious choice, showing that when agents systematically select problem-causing seeds, failure becomes the dominant (...) outcome. (shrink)

This paper investigates the concept of decidability in the context of natural numbers, prime numbers, and Chaitin's Omega. While prime and composite numbers are algorithmically decidable, Chaitin's Omega demonstrates the structural nature of undecidability. We analyze the effects of sorting and aggregating Omega's bits, illustrating how undecidability can be transformed into a decidable summary without retaining the fine-grained structure. Philosophical and mathematical implications of pure and unpure undecidability are discussed.

Probabilidad Imposible Vol 1 reúne los fundamentos de una investigación desarrollada entre 2001 y 2018, cuyo propósito es replantear las bases del conocimiento racional y su relación con la probabilidad empírica y teórica. La obra introduce conceptos como el Impacto del Defecto y el Segundo Método, proponiendo un marco alternativo frente a la epistemología de Karl Popper y orientado hacia la búsqueda del conocimiento puro. Este proyecto, originado en el cruce entre matemáticas, inteligencia artificial y psicología, constituye una semilla teórica (...) para el desarrollo de la Inteligencia Artificial Global y para la construcción de una sociedad tecnológica basada en un nuevo paradigma del saber. (shrink)

Particular Application System is a groundbreaking exploration into one of the most critical operational layers of the Global Artificial Intelligence framework. This book unveils, in precise and accessible detail, how instructions—born from complex decision-making processes—are matched, classified, and executed with flawless precision by robotic systems.

I explain the shutdown problem: the problem of designing artificial agents that (1) shut down when a shutdown button is pressed, (2) don’t try to prevent or cause the pressing of the shutdown button, and (3) otherwise pursue goals competently. I prove three theorems that make the difficulty precise. These theorems show that agents satisfying some innocuous-seeming conditions will often try to prevent or cause the pressing of the shutdown button, even in cases where it’s costly to do so. And (...) patience trades off against shutdownability: the more patient an agent, the greater the costs that agent is willing to incur to manipulate the shutdown button. I end by noting that these theorems can guide our search for solutions. (shrink)

There are myriad techniques industry actors use to shape the public understanding of science. While a naive view might assume these techniques typically involve fraud or outright deception, the truth is more nuanced. This paper analyzes industrial distraction, a common technique where industry actors fund and share research that is accurate, often high-quality, but nonetheless misleading on important matters of fact. This involves reshaping causal understanding of phenomena with distracting information. Using case studies and causal models, we illustrate how this (...) impacts belief and decision making even for rational learners, informing science policy and debates about misleading content. (shrink)

In light of the problem of logical omniscience, some scholars have argued that belief is question-sensitive: agents don’t simply believe propositions but rather believe answers to questions. Hoek (2022) has recently developed a version of this approach on which a belief state is a “web” of questions and answers. Here, we present several challenges to Hoek’s question-sensitive account of belief. First, Hoek’s account is prone to very similar logical omniscience problems as those he claims to address. Second, the link between (...) belief and action he proposes is too rigid. We close by sketching a generalization of the account that can meet these challenges. (shrink)

The causal explanation of human action has received increasing attention in social studies since the latter half of the twentieth century. A key question in this context is whether Aristotle’s framework of the four causes originally applied to natural phenomena, can also be extended to human actions. Concerning a compatible perspective between free will and causality, we contend that the Scholastic contributions offer a significant advancement in addressing this question. They demonstrate that the four causes, as interpreted by Scholastic thinkers, (...) provide a robust explanatory tool for analyzing human affairs and their dynamics. Moreover, we argue that their contributions go beyond theoretical analysis, offering a comprehensive framework for understanding how causal principles can be applied to various aspects of human experience. (shrink)

This book motivates and systematically develops the view that knowledge should be at the centre of our theory of practical rationality. Only act on what you know -- the book offers the first comprehensive defence of this slogan in the form of a knowledge-based decision theory. The proposed view is shown to be the most straightforward explanation of emerging bodies of evidence for a link between knowledge and rational action. The book provides novel solutions to well-known challenges that invoke high-stakes (...) scenarios, seemingly rational actions based on reasonable but false beliefs, and decision-making under risk and uncertainty. The emerging view brings together traditional and formal approaches to epistemology and the study of practical rationality. The resulting knowledge-based decision theory is embedded in a rich normative landscape, encompassing innovative accounts of excuses, rational acceptance, and the simplification of reasoning. Knowledge and Rational Action will be of great interest to researchers and graduate students interested in epistemology, practical rationality, and decision theory. (shrink)

The developing human brain, far from a tabula rasa, is defined by a spectacular set of characteristics that enable robust and accelerated learning in a dirty and out-of-control world. The article proposes a novel theoretical framework, "Decentralized Frequentist Black Swan Antifragile Predictive Coding," to capture the young brain's unique cognitive structure. We suggest that the baby brain is essentially a frequentist predictive coder, which forms and constantly updates internal models based on statistical patterns in the world. Importantly, this apparatus is (...) extremely sensitive to Black Swans, surprising events that, rather than causing turmoil, are strong signals for adaptation and learning, triggering an inherent antifragility. Furthermore, the decentralized network structure of the developing brain, particularly the emergent prefrontal cortex, is conducive to a non-hierarchical, adaptive style of processing. We integrate this approach with George Lakoff's theory of embodied cognition, contending that predictive coding by the infant is deeply sensorimotor-based. We further contend that mother-child dyad is a symbiotic learning environment that shapes such native capacities. Comparing this to David Graeber's reflections on play and bureaucracy and the notion of having a koan-like mind, we propose that the child has a "philosopher in the flesh" mind, engaging constructively with paradox and ambiguity. This integrative model has deep implications for cognitive development, for shaping educational models, and for motivating the creation of more adaptive and resilient artificial intelligence systems. (shrink)

Some of our judgments under uncertainty are clear and reliable—how likely do you think this fair coin is to land heads? Others are ambiguous and noisy—how likely do you think I am to own a dozen spoons? I propose that ambiguity is higher-order uncertainty: probabilistic uncertainty about our own subjective probabilities. Such higher-order probabilities are mathematically coherent. But why can’t we resolve our higher-order uncertainty simply by acting? Because cognitive noise makes the link between our subjective probabilities and our behavior (...) stochastic. I summarize the empirical evidence for this, describe a popular model of it, and argue that reasonable agents should be expected to exhibit cognitive noise when and only when they have higher-order uncertainty. I report on an experiment supporting this prediction, and conclude that cognitive scientists modeling noisy uncertainty have been using the wrong (implicitly, higher-order certain) Bayesian models. (shrink)

ABSTRACT What norm governs how an agent should change their beliefs when they encounter a completely new possibility? Orthodox Bayesianism has no answer, as it takes all learning to involve updating prior beliefs. A partial proposal is Reverse Bayesianism, which mandates the preservation of ratios of prior probabilities, but it faces counterexamples introduced by Mahtani (2021). I propose to separate awareness growth into two stages: awareness revision and belief extension. I argue that Mahtani’s cases highlight that we need to theorize (...) awareness revision before we can define a proposal for belief extension, such as Reverse Bayesianism. I provide a formal model of awareness revision which makes explicit how propositions are distinguished within awareness states and identified across them. Reformulating Reverse Bayesianism to take input from my model allows it to navigate Mahtani-style cases. My model leaves open how agents choose to identify propositions across awareness states, and I propose that they ought to do so conservatively: preserving undisturbed prior reasoning about the structure of their awareness. I then spell out this proposal in a special case. This is a partial proposal, and I close with a discussion of how to elaborate on it and how to advance research into awareness revision. (shrink)

Risk is inherent to many, if not all, transformative decisions. The risk of regret, of turning into a person you presently consider to be morally objectionable, or of value change are all risks of choosing to transform. This aspect of transformative decision-making has thus far been ignored, but carries important consequences to those wishing to defend decision theory from the challenge posed by transformative decision-making. I contend that a problem lies in a common method used to cardinalise utilities – the (...) von Neumann and Morgenstern (vNM) method – which measures an agent's utility function over sure outcomes. I argue that the risks involved in transformative experiences are constitutively valuable, and hence their value cannot be accurately measured by the vNM method. In Section 1, I outline what transformative experiences are and the problem they pose to decision theory. In Section 2, I outline Pettigrew's (2019, Choosing for Changing Selves) decision-theoretic response, and in Section 3, I present the case for thinking that risks can carry value. In Section 4, I argue for the claim that at least some transformative experiences involve constitutive risk. I argue that this causes a problem for decision-theoretic responses within the vNM framework in Section 5. (shrink)

By late 20th century, the rationality wars had launched debates about the nature and norms of intuitive and reflective thinking. Those debates drew from mid-20th century ideas such as bounded rationality, which challenged more idealized notions of rationality observed since the 19th century. Now that 21st century cognitive scientists are applying the resulting dual process theories to artificial intelligence, it is time to dust off some lessons from this history. So this paper synthesizes old ideas with recent results from experiments (...) on humans and machines. The result is Strategic Reflectivism, which takes the position that one key to intelligent systems (human or artificial) is pragmatic switching between intuitive and reflective inference to optimally fulfill competing goals. Strategic Reflectivism builds on American Pragmatism, transcends superficial indicators of reflective thinking such as model size or chains of thought, and becomes increasingly actionable as we learn more about the value of intuition and reflection. (shrink)

Many fear that future artificial agents will resist shutdown. I present an idea – the POST-Agents Proposal – for ensuring that doesn’t happen. I propose that we train agents to satisfy Preferences Only Between Same-Length Trajectories (POST). I then prove that POST – together with other conditions – implies Neutrality+: the agent maximizes expected utility, ignoring the probability distribution over trajectory-lengths. I argue that Neutrality+ keeps agents shutdownable and allows them to be useful.

This paper deeply explores Karl Friston's Free Energy Principle (FEP) as a meta-theory with significant potential for unifying our understanding of individual existence (including survival and adaptation), the emergence of collective order (such as social norms and cultural systems), and the roots of human social value judgments. The paper first systematically outlines the core mechanism of the FEP: organisms continuously optimize their predictive models of the environment and guide adaptive behavior by minimizing variational free energy, which serves as an upper (...) bound on "surprise." Subsequently, this paper elaborates on how the FEP can explain individual-level homeostatic maintenance, emotional motivation, and societal-level phenomena such as shared generative models, communication, coordination, and cultural evolution, viewing them as manifestations of free energy minimization at different scales. A core innovative argument presented is the proposal to link the concept of "free energy gradients" (the trend of free energy change over time) within the FEP to the valuation of social behaviors. It posits that behaviors conforming to social norms and promoting collective well-being tend to decrease expected collective free energy, while contrary behaviors increase it. This perspective offers a novel theoretical pathway for understanding the cognitive and neural foundations of human value judgments. Furthermore, this paper explores the potential of integrating this FEP framework with decision support systems (DSS), particularly by leveraging Large Language Models (LLMs) and their self-attention mechanisms. The aim is to more accurately identify key social factors, optimize resource allocation strategies, and transcend the limitations of traditional economic indicators, thereby constructing decision support tools more aligned with overall and long-term human well-being. Finally, the paper comprehensively summarizes the theoretical advantages of this unifying framework, the practical challenges it faces (such as operationalization, falsifiability, and ethical concerns), and outlines key future research directions. It emphasizes its profound significance in promoting interdisciplinary understanding, advancing computational social science, and building more intelligent, equitable, and sustainable social systems. (shrink)

Bradford (2023) calls attention to the fact that the strength of our reasons to preserve distinctively valuable objects increases as the number of such objects decreases. Bradford develops an account of this phenomenon in terms of ‘irreplaceable value’, and in particular in terms of a notion of the degree of such value, which is distinct from its amount. We present an alternative explanation of this pattern in our reasons, which appeals to the value of diversity: the world is better, other (...) things equal, insofar as it contains more kinds of value. We develop this view in two connected ways: one appeals to evidential probability under conditions of uncertainty, and the other appeals to the value of diversity. We conclude by discussing some explanatory advantages of our view over Bradford’s. (shrink)

Evolutionary psychology claims that human cognition results from adaptations to ancestral environments. We have computational limits that make us myopic because farsighted traits made no sense when humans had limited technologies and chances of interaction. We are biased and tribalistic because in small, closely genetically related tribal groups, limited prosocial traits like kin altruism and in-group reciprocity increased survival and reproduction, while greater inclusivity and cooperation was costly and dangerous. Several scholars argue that shortsightedness and tribalism are rigidly embedded in (...) our genes and hard-wired into our brains: in a world that changed dramatically and rapidly, our Stone Age minds struggle to address problems that are vastly different from those they evolved to meet. This book challenges the view that human psychology is fixed by our evolutionary past, highlighting the fallacies of an adaptationist approach to the moral mind. Human cognition has changed significantly since the Pleistocene, especially over the last few centuries and decades. There is no fixed and universal psychology, and no reason to believe that further shifts toward greater cooperation, inclusivity, and trust cannot occur in the future. (shrink)

The desirable gambles framework provides a rigorous foundation for imprecise probability theory but relies heavily on linear utility via its coherence axioms. In our related work, we introduced function-coherent gambles to accommodate non-linear utility. However, when repeated gambles are played over time---especially in intertemporal choice where rewards compound multiplicatively---the standard additive combination axiom fails to capture the appropriate long-run evaluation. In this paper we extend the framework by relaxing the additive combination axiom and introducing a nonlinear combination operator that effectively (...) aggregates repeated gambles in the log-domain. This operator preserves the time-average (geometric) growth rate and addresses the ergodicity problem. We prove the key algebraic properties of the operator, discuss its impact on coherence, risk assessment, and representation, and provide a series of illustrative examples. Our approach bridges the gap between expectation values and time averages and unifies normative theory with empirically observed non-stationary reward dynamics. (shrink)

This paper presents a unifying diagnosis of a number of important problems facing existing models of rational choice under moral uncertainty and proposes a remedy. I argue that the problems of (i) severely limited scope, (ii) intertheoretic comparisons, and (iii) 'swamping’ all stem from the way in which values are assigned to options in decision rules such as Maximisation of Expected Choiceworthiness. By assigning values to options under a given moral theory by asking something like “how much do I desire (...) this option, supposing this theory is true?” rather than “how much value does this theory assign to this option?” these problems can be avoided, while the appealing features of these accounts can be preserved. This amendment provides a role for the preferences, desires, or goals of rational agents that is curiously absent from the existing discussion of what individuals rationally ought to do when they are uncertain about what they morally ought to do. (shrink)

In some cases of higher-order defeat, you rationally doubt whether your credence in p is rational without having evidence of how to improve your credence in p. According to the resilience framework proposed by Steglich-Petersen (Higher-order defeat and Doxastic Resilience), such cases require loss of doxastic resilience: retain your credence level but become more disposed to change your mind given future evidence. Henderson (Higher-Order Evidence and Losing One’s Conviction) responds that this allows for irrational decision-making and that we are better (...) off understanding higher-order defeat in terms of imprecise probabilities. We argue first that Henderson’s imprecise probability framework models the wrong kind of thing. Credal imprecision is neither necessary nor sufficient for higher-order doubt. Second, we offer two ways of understanding the practical import of higher-order defeat given loss of doxastic resilience. (shrink)

Recently, Kenneth Himma (2010) argued that salvific exclusivism, some common beliefs about Hell, and a plausible moral principle entailed anti-natalism. Himma is on to something. But given the dialectic between Himma and a staunch critic, Shaun Bawulski (2013), I’ll provide a stronger version of Himma’s argument that allows us to discard a commitment to salvific exclusivism and satisfactorily respond to some of Bawulski’s strongest objections. In this paper, I’ll argue that some common beliefs about Hell, a risk-averse decision principle, and (...) Himma’s moral principle—reworked in light of the risk-averse decision principle—entail anti-natalism. (shrink)

It is argued that that the desire attributed to an agent, X, in sentences of the form ‘X wants to know whether P’, is not X’s overall desire for ‘X knows that P or X knows that “not P”’, but rather X’s expected conditional desire for knowing the truth about P, given the truth. An implication of this account for distributive justice is discussed.

The small improvement argument has been said to establish that the standard weak preference or value relation can be incomplete. We first show that the argument is one of three possible ‘small amendment arguments’, each of which would yield the same conclusion. Generalizing the analysis thus, we subsequently present a strong and a weak version of small amendment arguments and derive the exact rationality conditions under which they reveal incompleteness. The results show that the arguments (in any of their variants) (...) need not reveal a problem for the possibility of rational choice. In fact, it can be argued that they only reveal such a problem if the underlying relation is complete rather than incomplete. (shrink)

This article presents a fragmented account of Bayesianism in its’ most general form. First, it recalls the central theses of orthodox Bayesianism, and provides an overview over the notions of justification that can be for- mulated within orthodox Bayesianism. It presents a very general account of fragmented Bayesianism, and then provides a list of parameters along which the account can be made moderately or very fragmented, depending on which and how many of those parameters one chooses to relativize to fragments. (...) It, furthermore, presents an epistemic risk argument in order to justify fragmen- tation. I first provide a very general version of it, and the provide epistemic risk arguments for the fragmentation of each of the parameters. Lastly, the paper concludes by a brief comparison between the account of fragmented Bayesianism developed here and the qualitative account of fragmented justification developed earlier. (shrink)

In computational cognitive science, a valuationist picture of human agent architecture has become widespread. At the heart of valuationism is a simple and sweeping claim: Every time an agent acts, they do so on the basis of value representations, which are, roughly, representations of the expected value of one’s response options. In this essay, I do three things. First, I give a systematic, philosophically rich account of the valuationist picture of agency. I also highlight the generality of the model in (...) explaining diverse forms of person-level agency. Second, I discuss connections between the valuationist model and two traditional models in philosophy, the belief/desire model and the decision-theoretic model. Third, I canvas the wide-ranging implications of valuationism for philosophical inquiry. Among other things, valuationism illuminates the elusive boundary between activity and passivity; it flips the standard philosophical view of decision around, with decision being a source of, rather than a product of, one’s agency; it understands motivation as, in part, a representational phenomenon; it challenges a philosophical dogma that control over action is more extensive than control over belief; and it highlights an underappreciated connection between deviations from rational agency and inaccurate value representations. (shrink)

(1) Emotions influence decisions in various ways. In particular, they can induce new intrinsic desires. This mechanism is the topic of this paper. (2) After briefly discussing some rival approaches a new theory of such emotional decisions is presented. (3) The general framework into which this theory is integrated is an expectancy-valence or decision-theoretic model of decision, however with a strict distinction between intrinsic and other desires. (4) The specific part of the theory then explains emotional decisions by non-hedonic emotion-induced (...) intrinsic desires that grow and wane with the respective emotion, e.g. when in rage the desire to destroy or hurt the ‘aggressor’. A general approach to the content of these desires is provided, namely that they take up the values inherent in specific satisfying emotions coupled with the present emotion. (5) Finally, some theoretical consequences and advantages of this theory are shown. (shrink)

The much-debated Reflection principle states that a coherent agent’s credences must match their estimates for their future credences. Defenders claim that there are Dutch-book arguments in its favor, putting it on the same normative footing as probabilistic coherence. Critics claim that those arguments rely on the implicit, implausible assumption that the agent is introspective: that they are certain what their own credences are. In this paper, we clarify this debate by surveying several different conceptions of the book scenario. We show (...) that the crucial disagreement hinges on whether agents who are not introspective are known to reliably act on their credences: if they are, then coherent Reflection failures are (at best) ephemeral; if they aren’t, then Reflection failures can be robust— and perhaps rational and coherent. We argue that the crucial question for future debates is which notion of coherence makes sense for such unreliable agents and sketch a few avenues to explore. (shrink)

The Comprehensive Human Decision-Making Equation presents a robust model for understanding Holistic Free Will (HFW), conceptualizing decision-making as an autonomous, non-deterministic process within a complex network of influences. This model addresses the Infinite Regress issue by portraying free will as an emergent property of interacting layers, including internal beliefs, external contexts, emotional responses, cognitive biases, and habitual tendencies. Departing from traditional linear models, the equation adopts a systemic framework where each choice reflects a cumulative utility, integrating multiple components such as (...) personal, ethical, social, and temporal utilities. This holistic approach emphasizes the probabilistic nature of free will, challenging deterministic interpretations and highlighting the ethical and relational dimensions of autonomy. By situating free will within a structured yet adaptive process, the model supports the notion that true autonomy is ethically aligned, relational, and embedded in a flexible reality, thereby promoting communal and ethical development. (shrink)

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

Do imprecise beliefs lead to worse decisions under uncertainty? This BJPS Short Reads article provides an informal introduction to our use of agent-based modelling to investigate this question. We explain the strengths of imprecise probabilities for modelling evidential states. We explain how we used an agent-based model to investigate the relative performance of Imprecise Bayesian reasoners against a standard Bayesian who has precise credences. We found that the very features of Imprecise Bayesianism which give it representational strengths also cause relative (...) underperformance in this decision problem. We explain the practical relevance of this research to applications of Bayesian reasoning in areas like artificial intelligence. (shrink)

What norm governs how an agent should change their beliefs when they encounter a completely new possibility? Orthodox Bayesianism has no answer, as it takes all learning to involve updating prior beliefs. A partial proposal is Reverse Bayesianism, which mandates the preservation of ratios of prior probabilities, but it faces counterexamples introduced by Mahtani (2021). I propose to separate awareness growth into two stages: awareness revision and belief extension. I argue that Mahtani’s cases highlight that we need to theorize awareness (...) revision before we can define a proposal for belief extension, such as Reverse Bayesianism. I provide a formal model of awareness revision which makes explicit how propositions are distinguished within awareness states and identified across them. Reformulating Reverse Bayesianism to take input from my model allows it to navigate Mahtani-style cases. My model leaves open how agents choose to identify propositions across awareness states, and I propose that they ought to do so conservatively: preserving undisturbed prior reasoning about the structure of their awareness. I then spell out this proposal in a special case. This is a partial proposal, and I close with a discussion of how to elaborate on it and how to advance research into awareness revision. (shrink)

Several philosophers have proposed Knowledge-Based Decision Theories (KDTs)—theories that require agents to maximize expected utility as yielded by utility and probability functions that depend on the agent’s knowledge. Proponents of KDTs argue that such theories are motivated by Knowledge-Reasons norms that require agents to act only on reasons that they know. However, no formal derivation of KDTs from Knowledge-Reasons norms has been suggested, and it is not clear how such norms justify the particular ways in which KDTs relate knowledge and (...) rational action. In this paper, I suggest a new axiomatic method for justifying KDTs and providing them with stronger normative foundations. I argue that such theories may be derived from constraints on the relation between knowledge and preference, and that these constraints may be evaluated relative to intuitions regarding practical reasoning. To demonstrate this, I offer a representation theorem for a KDT proposed by Hawthorne and Stanley (2008) and briefly evaluate it through its underlying axioms. (shrink)

There are 1,000 of us and one victim. We each increase the level at which a ‘discomfort machine’ operates on the victim – leading to great discomfort. Suppose that consecutive levels of the machine are so similar that the victim cannot distinguish them. Have we acted permissibly? According to the ‘no-difference argument’ the answer is ‘yes’ because each of our actions was guaranteed to make the victim no worse off. This argument is of interest because, if it is sound, similar (...) arguments threaten intuitive moral verdicts about many cases in which a large number of individual choices cumulatively make a great difference, while each choice seems to make no difference on its own. But the argument is not sound, as is shown by a simple objection based on a plausible dominance principle – an objection that avoids challenges that have been brought against previous criticisms of the no-difference argument. (shrink)

Physical translation of a mental content must involve a set of causal antecedents A and a set of causal consequents B which instantiate properties that figure in strict laws as antecedent and consequent conditions respectively. Only if there are double-role events in common between A and B capable of migrating to purely A or to purely B in future depending on the role that the mental content play then, psychological anomalism can be established but without any need to give up (...) the type-identity of mental and physical events. This paper argues that belief and desire are explanatorily inextricable likewise. (shrink)

In response to cases that involve tiny probabilities of huge payoffs, some argue that we ought to discount small probabilities down to zero. However, this paper shows that doing so violates Independence and Continuity, and as a result of these violations, those who discount small probabilities can be exploited by money pumps. Various possible ways of avoiding exploitation will be discussed. This paper concludes that the money pump for Independence undermines the plausibility of discounting small probabilities. Much of the discussion (...) on Independence generalizes to other views that also violate Independence. (shrink)

Stalnaker’s ‘Assertion’ (1978 [1999]) offers a classic account of diagonalization as an approach to the meaning of a declarative sentence in context. Here I explore the relationship between diagonalization and some puzzles in Mahtani’s book The Objects of Credence. Diagonalization can influence how we think about both credence and desirability, so it influences both components of a standard expected utility equation. In that vein, I touch on two of Mahtani’s case-studies, chance and the finite version of the Two Envelope Paradox.

A truism: a name that is essentially associated with a description—so that its description contributes to the psychological explanations in which it figures—refers not to its referent simpliciter but to its referent relative to the information that is mirrored by the description.

This paper argues that decision theory presupposes free will. Although decision theorists seldom acknowledge this, the way decision theory represents, explains, or rationalizes choice behaviour acquires its intended interpretation only under the assumption that decision-makers are agents capable of making free choices between alternative possibilities. Without that assumption, both normative and descriptive decision theory, including the revealed-preference paradigm, would have to be reinterpreted in implausible ways. The hypothesis that decision-makers have free will is therefore explanatorily indispensable for decision theory. If (...) we regard explanatory indispensability as an indicator of reality in science, decision theorists should embrace the idea of free will. (shrink)

In collective action problems, large numbers of contributions together produce a good outcome, but any one contribution often makes no difference. Many philosophers think that act consequentialism implies that individuals should not contribute in these cases, given that their contributions cannot be expected to affect the outcome. Nearly everyone has assumed that the relevant expected effects of an action are those effects that are counterfactually dependent on what a given agent does. This assumption is at the heart of causal decision (...) theory. In contrast, evidential decision theory evaluates actions on the basis of whatever can be expected to happen, given that the agent performs some action, where this includes events that are simply correlated with the action. I show that causal and evidentialist versions of act consequentialism can diverge in collective action problems. Evidential decision theory can require us to do our part even when causal decision theory does not. (shrink)

Where do values live in thought? A straightforward answer is that we (or our brains) make decisions using explicit value representations which are our values. Recent work applying reinforcement learning to decision-making and planning suggests that more specifically, we may represent both the instrumental expected value of actions as well as the intrinsic reward of outcomes. In this paper, I argue that identifying value with either of these representations is incomplete. For agents such as humans and other animals, there is (...) another place where reward can be located in thought: the division of the space of possibilities or ‘state space’. (shrink)

Countenancing unbounded utility in ethics gives rise to deep puzzles in formal decision theory. Here, these puzzles are taken as an invitation to assess the most fundamental principles relating probability and value, with the aim of demonstrating that unbounded utility in ethics is compatible with a desirable decision theory. The resulting theory frames further discussion of Expected Utility Theory and of principles concerning symmetries of utility.