As a compact representation of joint probability distributions over a dependence graph of random variables, and a tool for modelling and reasoning in the presence of uncertainty, Bayesian networks are of great importance for artificial intelligence to combine domain knowledge, capture causal relationships, or learn from incomplete datasets. Known as a NP-hard problem in a classical setting, Bayesian inference pops up as a class of algorithms worth to explore in a quantum framework. This paper explores such a research (...) direction and improves on previous proposals by a judicious use of the utility function in an entangled configuration. It proposes a completely quantum mechanical decision-making process with a proven computational advantage. A prototype implementation in Qiskit (a Python-based program development kit for the IBM Q machine) is discussed as a proof-of-concept. (shrink)

Reasoning by jurors concerning whether an accused person should be convicted of committing a crime is a kind of casual inference. Jurors need to decide whether the evidence in the case was caused by the accused’s criminal action or by some other cause. This paper compares two computational models of casual inference: explanatory coherence and Bayesian networks. Both models can be applied to legal episodes such as the von Bu¨low trials. There are psychological and computational reasons for preferring the (...) explanatory coherence account of legal inference. (shrink)

Bayesianism is the predominant philosophy of science in North-America, the most important school of statistics world-wide, and the general version of the rational-choice approach in the social sciences. Although often rejected as a theory of actual behavior, it is still the benchmark case of perfect rationality. The paper reviews the development of Bayesianism in philosophy, statistics and decision making and questions its status as an account of perfect rationality. Bayesians, who otherwise are squarely in the empiricist camp, invoke (...) a priori reasoning when they recommend Bayesian methods - a recommendation that is not justified by their own standards. (shrink)

We consider human performance on an optimal stopping problem where people are presented with a list of numbers independently chosen from a uniform distribution. People are told how many numbers are in the list, and how they were chosen. People are then shown the numbers one at a time, and are instructed to choose the maximum, subject to the constraint that they must choose a number at the time it is presented, and any choice below the maximum is incorrect. We (...) present empirical evidence that suggests people use threshold-based models to make decisions, choosing the first currently maximal number that exceeds a fixed threshold for that position in the list. We then develop a hierarchical generative account of this model family, and use Bayesian methods to learn about the parameters of the generative process, making inferences about the threshold decision models people use. We discuss the interesting aspects of human performance on the task, including the lack of learning, and the presence of large individual differences, and consider the possibility of extending the modeling framework to account for individual differences. We also use the modeling results to discuss the merits of hierarchical, generative and Bayesian models of cognitive processes more generally. (shrink)

Orthodox Bayesian decision theory requires an agent’s beliefs representable by a real-valued function, ideally a probability function. Many theorists have argued this is too restrictive; it can be perfectly reasonable to have indeterminate degrees of belief. So doxastic states are ideally representable by a set of probability functions. One consequence of this is that the expected value of a gamble will be imprecise. This paper looks at the attempts to extend Bayesian decision theory to deal with (...) such cases, and concludes that all proposals advanced thus far have been incoherent. A more modest, but coherent, alternative is proposed. Keywords: Imprecise probabilities, Arrow’s theorem. (shrink)

In recent years, somatosensory interaction technology, represented by Microsoft’s Kinect hardware platform, has been widely used in various fields, such as entertainment, education, and medicine. Kinect technology can easily capture and record behavioral data, which provides new opportunities for behavioral and psychological correlation analysis research. In this paper, an automatic decision-style recognition method is proposed. Experiments involving 240 subjects were conducted to obtain face data and individual decision-making style score. The face data was obtained using the Kinect (...) camera, and the decision-style score were obtained via a questionnaire. To realize automatic recognition of an individual decision-making style, machine learning was employed to establish the mapping relationship between the face data and a scaled evaluation of the decision-making style score. This study adopts a variety of classical machine learning algorithms, including Linear regression, Support vector machine regression, Ridge regression, and Bayesian ridge regression. The experimental results show that the linear regression model returns the best results. The correlation coefficient between the linear regression model evaluation results and the scale evaluation results was 0.6, which represents a medium and higher correlation. The results verify the feasibility of automatic decision-making style recognition method based on facial analysis. (shrink)

Savage denied that Bayesian decision theory applies in large worlds. This paper proposes a minimal extension of Bayesian decision theory to a large-world context that evaluates an event E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document} by assigning it a number π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} that reduces to an orthodox probability for a class of measurable events. The Hurwicz criterion evaluates π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} as a weighted arithmetic mean of its upper and lower probabilities, which we derive from the measurable supersets and subsets of E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E$$\end{document}. The ambiguity aversion reported in experiments on the Ellsberg paradox is then explained by assigning a larger weight to the lower probability of winning than to the upper probability. However, arguments are given here that would make anything but equal weights irrational when using the Hurwicz criterion. The paper continues by embedding the Hurwicz criterion in an extension of expected utility theory that we call expectant utility. (shrink)

Consumers can have difficulty expressing their buying intentions on an explicit level. The most common explanation for this intention-action gap is that consumers have many cognitive biases that interfere with decision making. The current resource-rational approach to understanding human cognition, however, suggests that brain environment interactions lead consumers to minimize the expenditure of cognitive energy. This means that the consumer seeks as simple of a solution as possible for a problem requiring decision making. In addition, this (...) resource-rational approach to decision making emphasizes the role of the principle of Occam’s Razor, inductive inference, and Bayesian reasoning by illuminating the human-environment relationship. This paper introduces the Consumer Contextual Decision-Making Model (CCDMM). Based on the CCDMM, two hypothetical strategies of consumer decision making will be presented. First, the SIMilarity-Strategy (SIMS) is one in which most of a consumer’s decisions in a real-life context are based on prior beliefs about the role of a commodities specific to real-life situation being encountered. Because beliefs are based on previous experiences, consumers are already aware of the most likely consequences of their actions. At the same time, they do not waste time on developing contingencies for what, based on previous experience, is unlikely to happen. Second, the What-is-Out-there-in-the-World-Strategy (WOWS) is one in which prior beliefs do not work in a real-life situation, requiring consumers to update their beliefs. The principle argument being made is that most experimental consumer research describes decision making based on the WOWS, when participants cannot apply their previous knowledge and situation-based strategy to problems. The article analyses sensory and cognitive biases described by behavioral economists from a CCDMM perspective, followed by a description and explanation of the typical intention-action gap based on the model. Prior to a section dedicated to discussion, the neuroeconomic approach will be described along with the valuation network of the brain, which has evolved to solve problems that the human has previously encountered in an information-rich environment. The principles of brain functions will also be compared to CCDMM. Finally, different approaches and the future direction of consumer research from a contextual point of view will be presented. (shrink)

For decisions between many alternatives, the benchmark result is Hick's Law: that response time increases log-linearly with the number of choice alternatives. Even when Hick's Law is observed for response times, divergent results have been observed for error rates—sometimes error rates increase with the number of choice alternatives, and sometimes they are constant. We provide evidence from two experiments that error rates are mostly independent of the number of choice alternatives, unless context effects induce participants to trade speed for accuracy (...) across conditions. Error rate data have previously been used to discriminate between competing theoretical accounts of Hick's Law, and our results question the validity of those conclusions. We show that a previously dismissed optimal observer model might provide a parsimonious account of both response time and error rate data. The model suggests that people approximate Bayesian inference in multi-alternative choice, except for some perceptual limitations. (shrink)

While Conviction Narrative Theory correctly criticizes utility-based accounts of decision-making, it unfairly reduces probabilistic models to point estimates and treats affect and narrative as mechanistically opaque yet explanatorily sufficient modules. Hierarchically nested Bayesian accounts offer a mechanistically explicit and parsimonious alternative incorporating affect into a single biologically plausible precision-weighted mechanism that tunes decision-making toward narrative versus sensory dependence under varying uncertainty levels.

Calibration inductive logics are based on accepting estimates of relative frequencies, which are used to generate imprecise probabilities. In turn, these imprecise probabilities are intended to guide beliefs and decisions — a process called “calibration”. Two prominent examples are Henry E. Kyburg's system of Evidential Probability and Jon Williamson's version of Objective Bayesianism. There are many unexplored questions about these logics. How well do they perform in the short-run? Under what circumstances do they do better or worse? What is their (...) performance relative to traditional Bayesianism? -/- In this article, we develop an agent-based model of a classic binomial decision problem, including players based on variations of Evidential Probability and Objective Bayesianism. We compare the performances of these players, including against a benchmark player who uses standard Bayesian inductive logic. We find that the calibrated players can match the performance of the Bayesian player, but only with particular acceptance thresholds and decision rules. Among other points, our discussion raises some challenges for characterising “cautious” reasoning using imprecise probabilities. Thus, we demonstrate a new way of systematically comparing imprecise probability systems, and we conclude that calibration inductive logics are surprisingly promising for making decisions. (shrink)

Evidence accumulation has been the core component in recent development of perceptual and value-based decision-making theories. Most studies have focused on the evaluation of evidence between alternative options. What remains largely unknown is the process that prepares evidence: how may the decision-maker sample different sources of information sequentially, if they can only sample one source at a time? Here we propose a normative framework in prescribing how different sources of information should be sampled proactively to facilitate the (...) decision process: beliefs for different noisy sources are updated in a Bayesian manner and participants can proactively allocate resource for sampling (i.e. saccades) among different sources to maximize the information gain in such process. We show that our framework can account for human participants’ actual choice and saccade behaviors in a two-alternative value-based decision-making task. Moreover, our framework makes novel predictions about the empirical eye movement patterns. (shrink)

The main purpose of this thesis is to explore de Finetti's ideas and contributions to decision theory. Such ideas are not as well-known as his work on probability. ;The first part of the work is placed in a unisubjective decision-making context. It starts by including a discussion on predictivism, an approach to statistics which de Finetti insisted on and which has only recently been rediscovered and advocated. ;The second part is placed in the context of group, or (...) multisubjective, decision-making. This area is well-known for its negative results, starting with Arrow's impossibility theorem. While being aware of such difficulties, de Finetti made important contributions to this field, which he saw as the appropriate context to approach basic concepts such as "objectivity" and Wald's admissibility theorem. Such concepts, together with exchangeability, illuminate the Bayesian position by also making connection with the non-Bayesian approach. ;The last part of the work starts with a critical discussion of classical methods which are unacceptable for Bayesians. Finally, an important application problem--environmental stress screening--is solved from a Bayesian predictivist point of view. (shrink)

Though individual categorization or decision processes have been studied separately in many previous investigations, few studies have investigated how they interact by using a two-stage task of first categorizing and then deciding. To address this issue, we investigated a categorization-decision task in two experiments. In both, participants were shown six faces varying in width, first asked to categorize the faces, and then decide a course of action for each face. Each experiment was designed to include three groups, and (...) for each group, we manipulated the probabilistic contingencies between stimulus, category assignments, and decision consequences. For each group, each participant received three different sequences of category response, category feedback, decision response, and decision feedback. We found that participants were only partially responsive in the appropriate directions to the contingencies assigned to each group. Comparisons of results from different sequences provided evidence for empirical interference effects of categorization on decisions. The empirical interference effect is defined as the difference between the probability of taking a hostile action in decision-alone conditions and the total probability of taking a hostile action in categorization-decision conditions. To test competing accounts for multiple empirical results, including two-stage choice probabilities and empirical interference effects, we compared a quantum cognition model versus a two-stage exemplar categorization model at both aggregate and individual levels. Using a Bayesian information criterion, we found that the quantum model provided an overall better model fit than the exemplar model. Although both models predicted empirical interference effects, the exemplar model was able to generate probabilistic deviation by incorporating category information of the first stage into the feature representation of the subsequent decision stage, while the quantum model produced interference effect by superposition, measurement, and quantum entanglement. (shrink)

The authors explore the interfaces between different dimensions of moral cognition, bridging economic, Bayesian and reinforcement learning perspectives. The human aversion to harming others cuts across these different interfaces, influencing decisions, judgments, and inferences about morality.

How strongly an agent beliefs in a proposition can be represented by her degree of belief in that proposition. According to the orthodox Bayesian picture, an agent's degree of belief is best represented by a single probability function. On an alternative account, an agent’s beliefs are modeled based on a set of probability functions, called imprecise probabilities. Recently, however, imprecise probabilities have come under attack. Adam Elga claims that there is no adequate account of the way they can be (...) manifested in decision-making. In response to Elga, more elaborate accounts of the imprecise framework have been developed. One of them is based on supervaluationism, originally, a semantic approach to vague predicates. Still, Seamus Bradley shows that some of those accounts that solve Elga’s problem, have a more severe defect: they undermine a central motivation for introducing imprecise probabilities in the first place. In this paper, I modify the supervaluationist approach in such a way that it accounts for both Elga’s and Bradley’s challenges to the imprecise framework. (shrink)

Abstract:The standard, Bayesian account of rational belief and decision is often argued to be unable to cope properly with severe uncertainty, of the sort ubiquitous in some areas of policy making. This paper tackles the question of what should replace it as a guide for rational decision making. It defends a recent proposal, which reserves a role for the decision maker’s confidence in beliefs. Beyond being able to cope with severe uncertainty, the account has (...) strong normative credentials on the main fronts typically evoked as relevant for rational belief and decision. It fares particularly well, we argue, in comparison to other prominent non-Bayesian models in the literature. (shrink)

How can the forensic scientist rationally justify performing a sequence of tests and analyses in a particular case? When is it worth performing a test or analysis on an item? Currently, there is a large void in logical frameworks for making rational decisions in forensic science. The aim of this paper is to fill this void by presenting a step-by-step guide on how to apply Bayesian decision theory to routine decision problems encountered by forensic scientists on (...) performing or not performing a particular laboratory test or analysis. A decision-theoretic framework, composed of actions, states of nature, and utilities, models this problem, and an influence diagram translates its notions into a probabilistic graphical network. Within this framework, the expected value of information (EVOI) for the submission of an item to a particular test or analysis addresses the above questions. The development of a classical case example on whether to perform presumptive tests for blood before submitting the item for a DNA analysis illustrates the use of this model for source level questions in forensic biology (i.e., questions that ask whether a crime stain consisting of a particular body fluid comes from a particular person). We show how to construct an influence diagram for this example, and how sensitivity analyses lead to an optimal analytical sequence. The key idea is to show that such a Bayesian decisional approach provides a coherent framework for justifying the optimal analytical sequence for a particular case in forensic science. (shrink)

We study the wisdom of the crowd in three sequential decision‐making tasks: the Balloon Analogue Risk Task (BART), optimal stopping problems, and bandit problems. We consider a behavior‐based approach, using majority decisions to determine crowd behavior and show that this approach performs poorly in the BART and bandit tasks. The key problem is that the crowd becomes progressively more extreme as the decision sequence progresses, because the diversity of opinion that underlies the wisdom of the crowd is (...) lost. We also consider model‐based approaches to each task. This involves inferring cognitive models for each individual based on their observed behavior, and using these models to predict what each individual would do in any possible task situation. We show that this approach performs robustly well for all three tasks and has the additional advantage of being able to generalize to new problems for which there are no behavioral data. We discuss potential applications of the model‐based approach to real‐world sequential decision problems and discuss how our approach contributes to the understanding of collective intelligence. (shrink)

In this article, I explore a Bayesian approach to avalanche decision-making. I motivate this perspective by highlighting a version of the base-rate fallacy and show that a similar pattern applies to decision-making in avalanche-terrain. I then draw out three theoretical lessons from adopting a Bayesian approach and discuss these lessons critically. Lastly, I highlight a number of challenges for avalanche educators when incorporating the Bayesian perspective in their curriculum.

In most decision-making situations, there is a plethora of information potentially available to people. Deciding what information to gather and what to ignore is no small feat. How do decision makers determine in what sequence to collect information and when to stop? In two experiments, we administered a version of the German cities task developed by Gigerenzer and Goldstein (1996), in which participants had to decide which of two cities had the larger population. Decision makers were (...) not provided with the names of the cities, but they were able to collect different kinds of cues for both response alternatives (e.g., “Does this city have a university?”) before making a decision. Our experiments differed in whether participants were free to determine the number of cues they examined. We demonstrate that a novel model, using hierarchical latent mixtures and Bayesian inference (Lee & Newell, 2011) provides a more complete description of the data from both experiments than simple conventional strategies, such as the take–the–best or the Weighted Additive heuristics. (shrink)

This paper argues that we need to look beyond Bayesian decision theory for an answer to the general problem of making rational decisions under uncertainty. The view that Bayesian decision theory is only genuinely valid in a small world was asserted very firmly by Leonard Savage [18] when laying down the principles of the theory in his path-breaking Foundations of Statistics. He makes the distinction between small and large worlds in a folksy way by quoting (...) the proverbs ”Look before you leap” and ”Cross that bridge when you come to it”. You are in a small world if it is feasible always to look before you leap. You are in a large world if there are some bridges that you cannot cross before you come to them. As Savage comments, when proverbs conflict, it is proverbially true that there is some truth in both—that they apply in different contexts. He then argues that some decision situations are best modeled in terms of a small world, but others are not. He explicitly rejects the idea that all worlds can be treated as small as both ”ridiculous” and ”preposterous”. The first half of his book is then devoted to a very successful development of the set of ideas now known as Bayesian decision theory for use in small worlds. The second half of the book is an attempt to develop a quite different set of ideas for use in large worlds, but this part of the book is usually said to be a failure by those who are aware of its existence.2 Frank Knight [15] draws a similar distinction between making decision under risk or uncertainty.3 The pioneering work of Gilboa and Schmeidler [7] on making.. (shrink)

Bayesian decision theory is here construed as explicating a particular concept of rational choice and Bayesian probability is taken to be the concept of probability used in that theory. Bayesian probability is usually identified with the agent’s degrees of belief but that interpretation makes Bayesian decision theory a poor explication of the relevant concept of rational choice. A satisfactory conception of Bayesian decision theory is obtained by taking Bayesian probability to be (...) an explicatum for inductive probability given the agent’s evidence. (shrink)

It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When (...) is it correct to use Bayesian decision theory--and when does it need to be modified? Using a minimum of mathematics, Rational Decisions clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds. The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies. Written by one of the world's leading game theorists, Rational Decisions is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making. (shrink)

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)

It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When (...) is it correct to use Bayesian decision theory--and when does it need to be modified? Using a minimum of mathematics, Rational Decisions clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds. The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies. Written by one of the world's leading game theorists, Rational Decisions is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making. (shrink)

Most philosophers agree that causal knowledge is essential to decision-making: agents should choose from the available options those that probably cause the outcomes that they want. This book argues against this theory and in favour of evidential or Bayesian decision theory, which emphasises the symptomatic value of options over their causal role. It examines a variety of settings, including economic theory, quantum mechanics and philosophical thought-experiments, where causal knowledge seems to make a practical difference. The arguments (...) make novel use of machinery from other areas of philosophical inquiry, including first-person epistemology and the free will debate. The book also illustrates the applicability of decision theory itself to questions about the direction of time and the special epistemic status of agents. (shrink)

First published in 1982, Ellery Eells' original work on rational decision making had extensive implications for probability theorists, economists, statisticians and psychologists concerned with decision making and the employment of Bayesian principles. His analysis of the philosophical and psychological significance of Bayesian decision theories, causal decision theories and Newcomb's paradox continues to be influential in philosophy of science. His book is now revived for a new generation of readers and presented in a (...) fresh twenty-first-century series livery, including a specially commissioned preface written by Brian Skyrms, illuminating its continuing importance and relevance to philosophical enquiry. (shrink)

In past years, the traditional Bayesian theory of rational decision making, based on subjective calculations of expected utility, has faced powerful attack from philosophers such as David Lewis and Brian Skyrms, who advance an alternative causal decision theory. The test they present for the Bayesian is exemplified in the decision problem known as 'Newcomb's paradox' and in related decision problems and is held to support the prescriptions of the causal theory. As well as (...) his conclusions, the concepts and methods of Professor Eells introduces in the course of his analyses have extensive implications, not solely for probability theorists narrowly conceived, but for economists, statisticians and psychologists concerned with decision making and the employment of Bayesian principles. They and their students will, in addition, find the early chapters of great use as a background and introduction to the subject as a whole. (shrink)

Bayes’ formula is a fundamental statistical method for inference judgments in uncertain situations used by both laymen and professionals. However, since people often fail in situations where Bayes’ formula can be applied, how to improve their performance in Bayesian situations is a crucial question. We based our research on a widely accepted beneficial strategy in Bayesian situations, representing the statistical information in the form of natural frequencies. In addition to this numerical format, we used five visualizations: a 2×2-table, (...) a unit square, an icon array, a tree diagram, and a double-tree diagram. In an experiment with 688 undergraduate students, we empirically investigated the effectiveness of three graphical properties of visualizations: area-proportionality, use of discrete and countable statistical entities, and graphical transparency of the nested-sets structure. We found no additional beneficial effect of area-proportionality. In contrast, the representation of discrete objects seems to be beneficial. Furthermore, our results show a strong facilitating effect of making the nested-sets structure of a Bayesian situation graphically transparent. Our results contribute to answering the questions of how and why a visualization could facilitate judgment and decision making in situations of uncertainty. (shrink)

My dissertation focuses on problems that arise when a group makes decisions that are in reasonable ways connected to the beliefs and values of the group members. These situations are represented by models of decision-theoretic aggregation: Suppose a model of individual rationality in decision-making applies to each of a group of agents. Suppose this model also applies to the group as a whole, and that this group model is aggregated from the individual models. Two questions arise. First, (...) what sets of reasonable conditions can we consistently impose on the aggregation? Second, what can we learn from insights gained in such models, in particular for ethics and political philosophy? The dissertation has three parts, each using a different model of individual rationality. Each part contains essays addressing questions of either the first or the second kind with regard to its underlying model. Part I uses a social-choice-theoretic model, in which agents are only assumed to rank alternatives. Arrow's "Impossibility Theorem" shows that certain conditions that it would be natural to impose on all aggregation cannot be so imposed, on pain of contradiction. I discuss the impact of this result on the evaluation of majority rule and on democratic theory. I also discuss Sen's "Liberal Paradox", which addresses the possibility of incorporating rights into a social-choice theoretic model. Part II uses the von Neumann/Morgenstern theory of expected utility. A result under this model has been regarded as providing an argument for utilitarianism. I locate a place within utilitarianism where the theorem can do some work. To prepare the ground, I interpret the von Neumann/Morgenstern theory as part of a theory of deliberation. Thereby, this version of expected utility theory can be embedded into the philosophy of practical reasoning. The underlying model in Part III is Bayesian decision theory. Whereas the other two inquiries focus on the philosophical assessment of formal results, the third makes a formal contribution. One essay surveys the area, and a second explores a curious phenomenon that occurs in determining outcomes under one type of Bayesian aggregation. (shrink)

When making decisions, people naturally face uncertainty about the potential consequences of their actions due in part to limits in their capacity to represent, evaluate or deliberate. Nonetheless, they aim to make the best decisions possible. In Decision Theory with a Human Face, Richard Bradley develops new theories of agency and rational decision-making, offering guidance on how 'real' agents who are aware of their bounds should represent the uncertainty they face, how they should revise their opinions (...) as a result of experience and how they should make decisions when lacking full awareness of, or precise opinions on relevant contingencies. He engages with the strengths and flaws of Bayesian reasoning, and presents clear and comprehensive explorations of key issues in decision theory, from belief and desire to semantics and learning. His book draws on philosophy, economics, decision science and psychology, and will appeal to readers in all of these disciplines. (shrink)

Probability theory is important not least because of its relevance for decision making, which also means: its relevance for the single case. The frequency theory of probability on its own is irrelevant in the single case. However, Howson and Urbach argue that Bayesianism can solve the frequentist's problem: frequentist-probability information is relevant to Bayesians. The present paper shows that Howson and Urbach's solution cannot work, and indeed that no Bayesian solution can work. There is no way to (...) make frequentist probability relevant. (shrink)

Collaboration requires agents to coordinate their behavior on the fly, sometimes cooperating to solve a single task together and other times dividing it up into sub‐tasks to work on in parallel. Underlying the human ability to collaborate is theory‐of‐mind (ToM), the ability to infer the hidden mental states that drive others to act. Here, we develop Bayesian Delegation, a decentralized multi‐agent learning mechanism with these abilities. Bayesian Delegation enables agents to rapidly infer the hidden intentions of others by (...) inverse planning. We test Bayesian Delegation in a suite of multi‐agent Markov decision processes inspired by cooking problems. On these tasks, agents with Bayesian Delegation coordinate both their high‐level plans (e.g., what sub‐task they should work on) and their low‐level actions (e.g., avoiding getting in each other's way). When matched with partners that act using the same algorithm, Bayesian Delegation outperforms alternatives. Bayesian Delegation is also a capable ad hoc collaborator and successfully coordinates with other agent types even in the absence of prior experience. Finally, in a behavioral experiment, we show that Bayesian Delegation makes inferences similar to human observers about the intent of others. Together, these results argue for the centrality of ToM for successful decentralized multi‐agent collaboration. (shrink)

Bayesian nets are widely used in artificial intelligence as a calculus for causal reasoning, enabling machines to make predictions, perform diagnoses, take decisions and even to discover causal relationships. This book, aimed at researchers and graduate students in computer science, mathematics and philosophy, brings together two important research topics: how to automate reasoning in artificial intelligence, and the nature of causality and probability in philosophy.

This paper applies Bayesian theories to critically analyse and offer reforms of intelligence analysis, collection, analysis, and decision making on the basis of Human Intelligence, Signals Intelligence, and Communication Intelligence. The article criticises the reliabilities of existing intelligence methodologies to demonstrate the need for Bayesian reforms. The proposed epistemic reform program for intelligence analysis should generate more reliable inferences. It distinguishes the transmission of knowledge from its generation, and consists of Bayesian three stages modular model (...) for the generation of reliable intelligence from multiple coherent and independent testimonial sources, and for the tracing and analysis of intelligence failures. The paper concludes with suggestions for further research, the development of artificial intellignce that may measure coherence and reliability of HUMINT sources and infer intelligence following the outlined general modular model. (shrink)

Bayesian decision theory operates under the fiction that in any decision-making situation the agent is simply given the options from which he is to choose. It thereby sets aside some characteristics of the decision-making situation that are pre-analytically of vital concern to the verdict on the agent's eventual decision. In this paper it is shown that and how these characteristics can be accommodated within a still recognizably Bayesian account of rational agency.

This up-to-date introduction to decision theory offers comprehensive and accessible discussions of decision-making under ignorance and risk, the foundations of utility theory, the debate over subjective and objective probability, Bayesianism, causal decision theory, game theory, and social choice theory. No mathematical skills are assumed, and all concepts and results are explained in non-technical and intuitive as well as more formal ways. There are over 100 exercises with solutions, and a glossary of key terms and concepts. An (...) emphasis on foundational aspects of normative decision theory (rather than descriptive decision theory) makes the book particularly useful for philosophy students, but it will appeal to readers in a range of disciplines including economics, psychology, political science and computer science. • Has over 100 end of chapter review questions and exercises with solutions • Includes a chapter on how to draw a decision matrix • Explains the link between individual decision making, game theory and social choice theory Contents Preface; 1. Introduction; 2. The decision matrix; 3. Decisions under ignorance; 4. Decisions under risk; 5. Utility; 6. The mathematics of probability; 7. The philosophy of probability; 8. Why should we accept the preference axioms; 9. Causal vs. evidential decision theory; 10. Bayesian vs. non-Bayesian decision theory; 11. Game theory I: basic concepts and zero sum games; 12. Game theory II: nonzero sum and co-operative games; 13. Social choice theory; 14. Overview of descriptive decision theory; Appendix A. Glossary; Appendix B. Proof of the von Neumann-Morgenstern theorem; Further reading; Index. (shrink)

Suboptimality of decision making needs no explanation. High level accounts of suboptimality in diverse tasks cannot add up to a mechanistic theory of perceptual decision making. Mental processes operate on the contents of information brought by the experimenter and the participant to the task, not on the amount of information in the stimuli without regard to physical and social context.

Bayesian confirmation theory is a leading theory to decide the confirmation/refutation of a hypothesis based on probability calculus. While it may be much discussed in philosophy of science, is it actually practiced in terms of hypothesis testing by scientists? Since the assignment of some of the probabilities in the theory is open to debate and the risk of making the wrong decision is unknown, many scientists do not use the theory in hypothesis testing. Instead, they use alternative (...) statistical tests that can measure the risk or the reliability in decision making, circumventing some of the theoretical problems in practice. Therefore, the theory is not very popular in hypothesis testing among scientists at present. However, there are some proponents of Bayesian hypothesis testing, and software packages are made available to accelerate utilization by scientists. Time will tell whether Bayesian confirmation theory can become both a leading theory and a widely practiced method. In addition, this theory can be used to model the belief of scientists when testing hypotheses. (shrink)

How should we make decisions when we do not know the relevant physical probabilities? In these ambiguous situations, we cannot use our knowledge to determine expected utilities or payoffs. The traditional Bayesian answer is that we should create a probability distribution using some mix of subjective intuition and objective constraints. Imprecise Bayesians argue that this approach is inadequate for modelling ambiguity. Instead, they represent doxastic states using credal sets. Generally, insofar as we are more uncertain about the physical probability (...) of an event, there is more divergence in the credal set. Hence, their approach can represent these ambiguities via the extent of the divergence. Imprecise Bayesianism has mostly been advocated for its epistemological features. In this article, we examine its properties for decision-making. We develop a model for comparing standard and Imprecise Bayesianism by testing their performances in a classic decision problem. We find that the representational tools of Imprecise Bayesianism also cause it to underperform in our tests. This issue has been overlooked, because previous research on Imprecise Bayesianism has not utilised agent-based modelling to provide information about its performance in the short-run. Overall, we reveal the Ambiguity Dilemma for Imprecise Bayesianism: To what extent should one value representational power or decision-making performance? (shrink)

There is an increasing recognition by friends of personal probability that the standard systems of personal probability do not provide a fully adequate basis for the theories of scientific inference and rational decision making. This recognition has methodological and formal components. On the methodological side, Jeffrey [8] and Spielman [16], [17] have suggested that personal probabilities should be interpreted as judgments about thecredibilityof propositions, i.e., as appraisals of the degrees of confidence that are warranted by the information available (...) to the appraiser. The idea behind this interpretation is that there are criteria for appraising degrees of confidence as rational, plausible, silly or unwarranted. They have not been canonized, with the exception of the traditional informal fallacies of insufficient evidence, and if they were, would be highly vague and subject to revision as knowledge advances. (shrink)