This is a very short textbook on probabilistic reasoning, expected utility decision-making, cognitive biases, and self-correction, especially in application to medical examples. It also includes a chapter on concepts of health.

While ordinary decision theory focuses on empirical uncertainty, real decision-makers also face normative uncertainty: uncertainty about value itself. From a purely formal perspective, normative uncertainty is comparable to (Harsanyian or Rawlsian) identity uncertainty in the 'original position', where one's future values are unknown. A comprehensive decision theory must address twofold uncertainty -- normative and empirical. We present a simple model of twofold uncertainty, and show that the most popular decision principle -- maximising expected (...) value (`Expectationalism') -- has different formulations, namely Ex-Ante Expectationalism, Ex-Post Expectationalism, and hybrid theories. These alternative theories recommend different decisions, reasoning modes, and attitudes to risk. But they converge under an interesting (necessary and sufficient) condition. (shrink)

Innovative research on decision making under ‘deep uncertainty’ is underway in applied fields such as engineering and operational research, largely outside the view of normative theorists grounded in decision theory. Applied methods and tools for decision support under deep uncertainty go beyond standard decision theory in the attention that they give to the structuring of decisions. Decision structuring is an important part of a broader philosophy of managing uncertainty in decision making, and normative decision (...) theorists can both learn from, and contribute to, the growing deep uncertainty decision support literature. (shrink)

I analyze recent discussions about making moral decisions under normative uncertainty. I discuss whether this kind of uncertainty should have practical consequences for decisions and whether there are reliable methods of reasoning that deal with the possibility that we are wrong about some moral issues. I defend a limited use of the decision theory model of reasoning in cases of normative uncertainty.

Social decisions are often made under great uncertainty – in situations where political principles, and even standard subjective expected utility, do not apply smoothly. In the first section, we argue that the core of this problem lies in decision theory itself – it is about how to act when we do not have an adequate representation of the context of the action and of its possible consequences. Thus, we distinguish two criteria to complement decision theory under (...) ignorance – Laplace’s principle of insufficient reason and Wald’s maximin criterion. After that, we apply this analysis to political philosophy, by contrasting Harsanyi’s and Rawls’s theories of justice, respectively based on Laplace’s principle of insufficient reason and Wald’s maximin rule – and we end up highlighting the virtues of Rawls’s principle on practical grounds (it is intuitively attractive because of its computational simplicity, so providing a salient point for convergence) – and connect this argument to our moral intuitions and social norms requiring prudence in the case of decisions made for the sake of others. (shrink)

In some severely uncertain situations, exemplified by climate change and novel pandemics, policymakers lack a reasoned basis for assigning probabilities to the possible outcomes of the policies they must choose between. I outline and defend an uncertainty averse, egalitarian approach to policy evaluation in these contexts. The upshot is a theory of distributive justice which offers especially strong reasons to guard against individual and collective misfortune.

We typically have to act under uncertainty. We can be uncertain about the relevant descriptive facts, but also about the relevant normative facts. However, the search for a theory of decision-making under normative uncertainty is doomed to failure. First, the most natural proposal for what to do given normative uncertainty faces two devastating problems. Second, the motivations for wanting a theory of what to do given descriptive uncertainty do not carry over to normative (...) class='Hi'>uncertainty. Descriptive facts may be inaccessible even in principle, and ignorance of them excuses one from blame, but normative facts are in principle accessible, and ignorance of them arguably is no excuse. Normative facts differ from descriptive facts: normative facts affect what we ought to do no matter what, while descriptive facts affect what we ought to do only insofar as we are aware of them. (shrink)

Decisions are made under uncertainty when there are distinct outcomes of a given action, and one is uncertain to which the act will lead. Decisions are made under indeterminacy when there are distinct outcomes of a given action, and it is indeterminate to which the act will lead. This paper develops a theory of (synchronic and diachronic) decision-making under indeterminacy that portrays the rational response to such situations as inconstant. Rational agents have to capriciously (...) and randomly choose how to resolve the indeterminacy relevant to a given choice-situation, but such capricious choices once made constrain how they will choose in the future. The account is illustrated by the case of self-interested action in situations where it is indeterminate whether you yourself will survive to benefit or suffer the consequences. The conclusion emphasizes some distinctive anti-hedging predictions of the account. (shrink)

Recent work in judgment and decisionmaking has stressed that institutions, like individuals, often rely on decisionmaking heuristics. But most of the institutional decisionmaking heuristics studied to date are highly firm- and industry-specific. This contrasts to the individual case, in which many heuristics are general-purpose rules suitable for a wide range of decision problems. Are there also general-purpose heuristics for institutional decisionmaking? In this paper, I argue that a number of methods recently developed for decisionmaking under deep uncertainty have (...) a good claim to be understood as general-purpose decisionmaking heuristics suitable for a broad range of institutional decision problems. (shrink)

In this article, I present a new interpretation of the pro-life view on the status of early human embryos. In my understanding, this position is based not on presumptions about the ontological status of embryos and their developmental capabilities but on the specific criteria of rational decisions under uncertainty and on a cautious response to the ambiguous status of embryos. This view, which uses the decision theory model of moral reasoning, promises to reconcile the uncertainty about (...) the ontological status of embryos with the certainty about normative obligations. I will demonstrate that my interpretation of the pro-life view, although seeming to be stronger than the standard one, has limited scope and cannot be used to limit destructive research on human embryos. (shrink)

At the centenary of Frank H. Knight’s Risk, Uncertainty, and Profit (1921), we explore the continuing relevance of Knightian uncertainty to the theory and practice of entrepreneurship. There are three challenges facing such assessment. First, RUP is complex and difficult to interpret. The key but neglected element of RUP is that Knight’s account is not solely about risk and uncertainty as states of nature, but about how an agent’s beliefs about uncertain outcomes and confidence in those beliefs (...) guide their choices. Second, RUP is Knight’s only effort in this area. His subsequent career led elsewhere, so he did not engage with subsequent interpretations of this work. Third, much of the current literature emphasizes that decisions must be different under the two states of nature with a consequent misunderstanding of entrepreneurial agency. This paper addresses each challenge in sequence. First, we explicate Knight’s (1921) approach and explain why that approach is murky. Second, as a complement to Knight’s interpretation, we examine Frank P. Ramsey’s approach to subjective probabilities to help clarify Knight’s murky approach. What links Knight and Ramsey is a shared pragmatism about entrepreneurial agency under uncertainty that depends upon the beliefs about, and confidence in, their judgments of possible outcomes. This Knight-Ramsey approach does not require actor’s behaviors to be determined by the class of uncertain environment (whether risk, uncertainty, or ambiguity) they face. We focus on the response by the entrepreneur to the existence of uncertainty in all its forms. We argue that this reductive account provides a foundation to examine common problems in management, including managerial hubris, the interaction between entrepreneurs and venture capitalists, and the need for experimentation (such as prototyping and market research) in advance of new product and venture launches. Third, we critique current literature that favors epistemic purism about the ontology of risk and uncertainty and ignores Knight-Ramsey pragmatism in meeting uncertainty, such as using formal and informal institutions for uncertainty mitigation. Our account locates Frank Knight’s subtleties in entrepreneurial behavior firmly in the literature on entrepreneurial agency a century later. (shrink)

Decision theory requires agents to assign probabilities to states of the world and utilities to the possible outcomes of different actions. When agents commit to having the probabilities and/or utilities in a decision problem defined by objective features of the world, they may find themselves unable to decide which actions maximize expected utility. Decision theory has long recognized that work-around strategies are available in special cases; this is where dominance reasoning, minimax, and maximin play a role. Here we describe a (...) different work around, wherein a rational decision about one decision problem can be reached by ‘interpolating’ information from another problem that the agent believes has already been rationally solved. (shrink)

The topic of this thesis is axiological uncertainty – the question of how you should evaluate your options if you are uncertain about which axiology is true. As an answer, I defend Expected Value Maximisation (EVM), the view that one option is better than another if and only if it has the greater expected value across axiologies. More precisely, I explore the axiomatic foundations of this view. I employ results from state-dependent utility theory, extend them in various ways and (...) interpret them accordingly, and thus provide axiomatisations of EVM as a theory of axiological uncertainty. (shrink)

In this paper we introduce the nascent literature on Moral Uncertainty Theory and explore its application to the criminal law. Moral Uncertainty Theory seeks to address the question of what we ought to do when we are uncertain about what to do because we are torn between rival moral theories. For instance, we may have some credence in one theory that tells us to do A but also in another that tells us to do B. We examine how (...) we might decide whether or not to criminalize some conduct when we are unsure as to whether or not the conduct is morally permitted, and whether or not it is permissible to criminalize the conduct. We also look at how we might make sentencing decisions under moral uncertainty. We argue that Moral Uncertainty Theory can be an illuminating way to address these questions, but find that doing so is a lot more complicated than applying Moral Uncertainty Theory to individual conduct. (shrink)

We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as an objective and a subjective source respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms (...) of the Pareto principle. After characterizing the ex ante and ex post criteria, we present a first solution to their conflict that extends the former as much possible in the direction of the latter. Then, we present a second solution, which goes in the opposite direction, and is also maximally assertive. Both solutions translate the assumed Pareto conditions into weighted additive utility representations, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of two conceptual arguments, i.e., the by now classic spurious unanimity argument and a novel informational argument labelled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms, but for the sake of completeness, also considers a construal of objective uncertainty based on the assumption of an exogeneously given probability measure. JEL classification: D70; D81. (shrink)

Population axiology concerns how to evaluate populations in terms of their moral goodness, that is, how to order populations by the relations “is better than” and “is as good as”. The task has been to find an adequate theory about the moral value of states of affairs where the number of people, the quality of their lives, and their identities may vary. So far, this field has largely ignored issues about uncertainty and the conditions that have been discussed mostly (...) pertain to the ranking of risk-free outcomes. Most public policy choices, however, are decisions under uncertainty, including policy choices that affect the size of a population. Here, we shall address the question of how to rank population prospects—that is, alternatives that contain uncertainty as to which population they will bring about—by the relations “is better than” and “is as good as”. We start by illustrating how well-known population axiologies can be extended to population prospect axiologies. And we show that new problems arise when extending population axiologies to prospects. In particular, traditional population axiologies lead to prospect-versions of the problems that they praised for avoiding in the risk-free settings. Finally, we identify an intuitive adequacy condition that, we contend, should be satisfied by any population prospect axiology, and show how given this condition, the impossibility theorems in population axiology can be extended to (non-trivial) impossibility theorems for population prospect axiology. (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)

The question of the rationality of conspiratorial belief ¬divides philosophers into mainly two camps. The particularists believe that each conspiracy theory ought to be examined on its own merits. The generalist, by contrast, argues that there is something inherently suspect about conspiracy theories that makes belief in them irrational. Recent empirical findings indicate that conspiratorial thinking is commonplace among ordinary people, which has naturally shifted attention to the particularists. Yet, even the particularist must agree that not all conspiracy belief is (...) rational, in which case she must explain what separates rational from non-rational conspiratorial thinking. In this paper, I contrast three strategies to this end: 1) the probabilistic objectivist, who assesses the objective probability of conspiracies; 2) the subjectivist, who rather focuses on the perspective of the believer, and typically views the decision to believe in a conspiracy as a problem of decision making under risk. Approaches 1) and 2) rely on assessments of the probability of conspiracy which, I argue, limits their applicability. Instead, I explore 3) viewing the problem facing the potential believer as a decision problem under uncertainty about probabilities. I argue, furthermore, that focusing solely on epistemic utilities fails to do justice to the particular character of conspiracy beliefs, which are not exclusively epistemically motivated, and I investigate the rationality of such beliefs under a number of standard decision rules. (shrink)

Current environmental problems and technological risks are a challenge for a new institutional arrangement of the value spheres of Science, Politics and Morality. Distinguished authors from different European countries and America provide a cross-disciplinary perspective on the problems of political decision making under the conditions of scientific uncertainty. cases from biotechnology and the environmental sciences are discussed. The papers collected for this volume address the following themes: (i) controversies about risks and political decision making; (ii) concepts of science (...) for policy; (iii) the use of social science in the policy making process; (iv) ethical problems with developments in science and technology; (v) public and state interests in the development and control of technology. (shrink)

The precautionary principle (PP) aims to anticipate and minimize potentially serious or irreversible risks under conditions of scientific uncertainty. Thus it preserves the potential for future developments. It has been incorporated into many international treaties and pieces of national legislation for environmental protection and sustainable development. In this article, we outline an interpretation of the PP as a framework of orientation for a sustainable information society. Since the risks induced by future information and communication technologies (ICT) are social (...) risks for the most part, we propose to extend the PP from mainly environmental to social subjects of protection. From an ethical point of view, the PP and sustainability share the principle of intergenerational justice, which can be used as an argument to preserve free space for the decisions of future generations. Applied to technical innovation and to ICT issues in particular, the extended PP can serve as a framework of orientation to avoid socio-economically irreversible developments. We conclude that the PP is a useful approach for: (i) policy makers to reconcile information society and sustainability policies and (ii) ICT companies to formulate sustainability strategies. (shrink)

This paper aims to open a dialogue between philosophers working in decision theory and operations researchers and engineers working on decision-making under deep uncertainty. Specifically, we assess the recommendation to follow a norm of robust satisficing when making decisions under deep uncertainty in the context of decision analyses that rely on the tools of Robust Decision-Making developed by Robert Lempert and colleagues at RAND. We discuss two challenges for robust satisficing: whether the norm might derive (...) its plausibility from an implicit appeal to probabilistic representations of uncertainty of the kind that deep uncertainty is supposed to preclude; and whether there is adequate justification for adopting a satisficing norm, as opposed to an optimizing norm that is sensitive to considerations of robustness. We discuss decision-theoretic and voting-theoretic motivations for robust satisficing, and use these motivations to select among candidate formulations of the robust satisficing norm. (shrink)

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given (...) sufficient background uncertainty about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized. (shrink)

How do mushroom foragers make safe and efficient decisions under high degrees of uncertainty, or deal with the genuine risks of misidentification and poisoning? This article is an inquiry into ecological rationality, heuristics, perception, and decision-making in mushroom foraging. By surveying 894 Finnish mushroom foragers with a total of 22,304 years of foraging experience, this article illustrates how socially learned rules of thumb and heuristics are used in mushroom foraging. It illustrates how traditional foraging cultures have evolved (...) precautionary principles to deal with uncertainties and poisonous species, and how foragers leverage both simple heuristics and complex cognitive strategies in their search for, and identification of, mushrooms. Foragers also develop selective attention through experience. The results invite us to consider whether other human foraging cultures might use heuristics similarly, how and why such traditions have culturally evolved, and whether early hunter-gatherers might have used fast and frugal heuristics to deal with uncertainty. (shrink)

This work develops a philosophically credible and psychologically realisable account of control that is necessary for moral responsibility. We live, think, and act in an environment of subjective uncertainty and limited information. As a result, our decisions and actions are influenced by factors beyond our control. Our ability to act freely is restricted by uncertainty, ignorance, and luck. Through three articles, I develop a naturalistic theory of control for action as a process of error minimisation that extends (...) over time. Thus conceived, control can serve to minimise the influence of luck on action and enable freedom in uncertainty. -/- In Article 1, Thor Grünbaum and I argue for a psychologically plausible account of the kind of control that is necessary for moral responsibility. We begin by establishing the relationship between agentive contribution and responsibility-level control. One way to determine whether one the right kind and degree of control to be morally responsible is to track one’s degree of contribution to an action. However, a psychologically plausible account of control in terms of agentive contribution may seem to contradict the types of functional-mechanistic explanations used in cognitive science. In cognitive psychology and cognitive neuroscience, personal-level capacities are explained by a set of sub-personal mechanisms. Often, such explanations leave no room for a contribution by the agent. By integrating insights from theories of cognitive control and incorporating them into a philosophical account of intentions, we propose a way of thinking about the distribution of cognitive control resources as something the agent does. -/- Article 2 argues that a classic argument concerning luck, originally aimed at libertarianism, generalises beyond any specific theory of free will, and regardless of whether determinism or indeterminism is true. I call this mental luck. Because we all make decisions under conditions of relative uncertainty and limited information, it is possible for an agent to make decisions that are contrary to their own motivation. In such situations, it may be a matter of luck whether the agent makes the right decision. Mentally lucky decisions are not rationally governed by attitudes within the agent's perspective, and thus, may be indistinguishable from unlucky ones. From the perspective of the agent, such decisions may resemble the outcome of a lottery. Therefore, mental luck poses a challenge to most prominent theories of free action and moral responsibility. -/- Finally, article 3 engages with the issue of resultant luck, namely luck in how things turn out. Resultant luck raises a challenge for theories of moral responsibility because its existence suggests that one may be responsible for factors beyond one’s control. Prominent responses to resultant luck led to a choice between internalism and scepticism. I argue that familiar cases of resultant luck are based on the assumption that actions are events. Instead, I propose an alternative ontology of action as an ongoing goal-directed process with a many-shots structure. Described this way, cases of resultant luck are not representative of ordinary action. The proposal of action as a many-shots process is consistent with predictive coding, a cognitive architecture which centres around error minimisation. Under this framework, cases of resultant more luck are no longer failures of action, but rather anticipated errors to be settled within the ordinary process of action. (shrink)

Against the background of continuing inadequacy in global efforts to address climate change and apparent social and political inertia, ever greater interest is being generated in the idea that geoengineering may offer some solution to this problem. I do not take a position, here, on whether or not geoengineering could ever be morally justifiable. My goal in this paper is more modest – but also has broader implications. I aim to show that even if some form of geoengineering might be (...) ethically acceptable in certain specific circumstances, lab-based research into such techniques could nevertheless have morally problematic consequences. I support this claim by explaining that our current state of uncertainty regarding how the impacts of geoengineering interventions could be geographically distributed may help to promote international agreement on fair rules for the governance of geoengineering. In these circumstances of scientific uncertainty, international actors also face uncertainty regarding who the winners and losers could be with respect to potential rules of geoengineering governance, thereby obstructing the pursuit of self-interest in the selection of such rules. Instead of a research first approach, then, we have reason to take a governance first approach – ensuring that fair international institutions to regulate geoengineering activities are established before further research is conducted into how the costs and benefits of such interventions could be distributed. (shrink)

The basic axioms or formal conditions of decision theory, especially the ordering condition put on preferences and the axioms underlying the expected utility formula, are subject to a number of counter-examples, some of which can be endowed with normative value and thus fall within the ambit of a philosophical reflection on practical rationality. Against such counter-examples, a defensive strategy has been developed which consists in redescribing the outcomes of the available options in such a way that the threatened axioms or (...) conditions continue to hold. We examine how this strategy performs in three major cases: Sen's counterexamples to the binariness property of preferences, the Allais paradox of EU theory under risk, and the Ellsberg paradox of EU theory under uncertainty. We find that the strategy typically proves to be lacking in several major respects, suffering from logical triviality, incompleteness, and theoretical insularity. To give the strategy more structure, philosophers have developed “principles of individuation”; but we observe that these do not address the aforementioned defects. Instead, we propose the method of checking whether the strategy can overcome its typical defects once it is given a proper theoretical expansion. We find that the strategy passes the test imperfectly in Sen's case and not at all in Allais's. In Ellsberg's case, however, it comes close to meeting our requirement. But even the analysis of this more promising application suggests that the strategy ought to address the decision problem as a whole, rather than just the outcomes, and that it should extend its revision process to the very statements it is meant to protect. Thus, by and large, the same cautionary tale against redescription practices runs through the analysis of all three cases. A more general lesson, simply put, is that there is no easy way out from the paradoxes of decision theory. (shrink)

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)

How ought you to evaluate your options if you're uncertain about what's fundamentally valuable? A prominent response is Expected Value Maximisation (EVM)—the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected value across axiologies. But the expected value of an option depends on quantitative probability and value facts, and in particular on value comparisons across axiologies. We need to explain what it is for such facts to hold. (...) Also, EVM is by no means self-evident. We need an argument to defend that it’s true. This book introduces an axiomatic approach to answer these worries. It provides an explication of what EVM means by use of representation theorems: intertheoretic comparisons can be understood in terms of facts about which options are better than which, and mutatis mutandis for intratheoretic comparisons and axiological probabilities. And it provides a systematic argument to the effect that EVM is true: the theory can be vindicated through simple axioms. The result is a formally cogent and philosophically compelling extension of standard decision theory, and original take on the problem of axiological or normative uncertainty. (shrink)

Many people are worried about the harmful effects of climate change but nevertheless enjoy some activities that contribute to the emission of greenhouse gas (driving, flying, eating meat, etc.), the main cause of climate change. How should such people make choices between engaging in and refraining from enjoyable greenhouse-gas-emitting activities? In this chapter we look at the answer provided by decision theory. Some scholars think that the right answer is given by interactive decision theory, or game theory; and moreover think (...) that since private climate decisions are instances of the prisoner’s dilemma, one rationally should engage in these activities provided that one enjoys them. Others think that the right answer is given by expected utility theory, the best-known version of individual decision theory under risk and uncertainty. In this chapter we review these different answers, with a special focus on the latter answer and the debate it has generated. (shrink)

Many philosophers assume that, when making moral decisions under uncertainty, we should choose the option that has the greatest expected moral value, regardless of how risky it is. But their arguments for maximizing expected moral value do not support it over rival, risk-averse approaches. In this paper, I present a novel argument for maximizing expected value: when we think about larger series of decisions that each decision is a part of, all but the most risk-averse agents (...) would prefer that we consistently choose the option with the highest expected value. To the extent that what we choose on a given occasion should be guided by the entire series of choices we prefer, then on each occasion, we should choose the option with the highest expected moral value. (shrink)

Investigation of neural and cognitive processes underlying individual variation in moral preferences is underway, with notable similarities emerging between moral- and risk-based decision-making. Here we specifically assessed moral distributive justice preferences and non-moral financial gambling preferences in the same individuals, and report an association between these seemingly disparate forms of decision-making. Moreover, we find this association between distributive justice and risky decision-making exists primarily when the latter is assessed with the Iowa Gambling Task. These findings are consistent with neuroimaging studies (...) of brain function during moral and risky decision-making. This research also constitutes the first replication of a novel experimental measure of distributive justice decision-making, for which individual variation in performance was found. Further examination of decision-making processes across different contexts may lead to an improved understanding of the factors affecting moral behaviour. (shrink)

Unlike other classical arguments for the existence of God, Pascal’s Wager provides a pragmatic rationale for theistic belief. Its most popular version says that it is rationally mandatory to choose a way of life that seeks to cultivate belief in God because this is the option of maximum expected utility. Despite its initial attractiveness, this long-standing argument has been subject to various criticisms by many philosophers. What is less discussed, however, is the rationality of this choice in situations where the (...) decision-makers are confronted with greater uncertainty. In this paper, I examine the imprecise version of Pascal’s Wager: those scenarios where an agent’s credence that God exists is imprecise or vague rather than precise. After introducing some technical background on imprecise probabilities, I apply five different principles for decision-making to two cases of state uncertainty. In the final part of the paper, I argue that it is not rationally permitted to include zero as the lower probability of God’s existence. Although the conditions for what makes an act uniquely optimal vary significantly across those principles, I also show how the option of wagering for God can defeat any mixed strategy under two distinct interpretations of salvation. (shrink)

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency. In this paper, a new approach for multi-attribute group decision making problems is proposed by extending the TOPSIS method under rough neutrosophic environment. Rough neutrosophic set is characterized by the upper and lower approximation (...) operators and the pair of neutrosophic sets that are characterized by truth-membership degree, indeterminacy membership degree, and falsity membership degree. In the decision situation, ratings of alternatives with respect to each attribute are characterized by rough neutrosophic sets that reflect the decision makers’ opinion. Rough neutrosophic weighted averaging operator has been used to aggregate the individual decision maker’s opinion into group opinion for rating the importance of attributes and alternatives. Finally, a numerical example has been provided to demonstrate the applicability and effectiveness of the proposed approach. (shrink)

This fifth volume on Advances and Applications of DSmT for Information Fusion collects theoretical and applied contributions of researchers working in different fields of applications and in mathematics, and is available in open-access. The collected contributions of this volume have either been published or presented after disseminating the fourth volume in 2015 in international conferences, seminars, workshops and journals, or they are new. The contributions of each part of this volume are chronologically ordered. First Part of this book presents some (...) theoretical advances on DSmT, dealing mainly with modified Proportional Conflict Redistribution Rules (PCR) of combination with degree of intersection, coarsening techniques, interval calculus for PCR thanks to set inversion via interval analysis (SIVIA), rough set classifiers, canonical decomposition of dichotomous belief functions, fast PCR fusion, fast inter-criteria analysis with PCR, and improved PCR5 and PCR6 rules preserving the (quasi-)neutrality of (quasi-)vacuous belief assignment in the fusion of sources of evidence with their Matlab codes. Because more applications of DSmT have emerged in the past years since the apparition of the fourth book of DSmT in 2015, the second part of this volume is about selected applications of DSmT mainly in building change detection, object recognition, quality of data association in tracking, perception in robotics, risk assessment for torrent protection and multi-criteria decision-making, multi-modal image fusion, coarsening techniques, recommender system, levee characterization and assessment, human heading perception, trust assessment, robotics, biometrics, failure detection, GPS systems, inter-criteria analysis, group decision, human activity recognition, storm prediction, data association for autonomous vehicles, identification of maritime vessels, fusion of support vector machines (SVM), Silx-Furtif RUST code library for information fusion including PCR rules, and network for ship classification. Finally, the third part presents interesting contributions related to belief functions in general published or presented along the years since 2015. These contributions are related with decision-making under uncertainty, belief approximations, probability transformations, new distances between belief functions, non-classical multi-criteria decision-making problems with belief functions, generalization of Bayes theorem, image processing, data association, entropy and cross-entropy measures, fuzzy evidence numbers, negator of belief mass, human activity recognition, information fusion for breast cancer therapy, imbalanced data classification, and hybrid techniques mixing deep learning with belief functions as well. (shrink)

State-dependent utility is a problem for the behavioural branch of decision theory under uncertainty. It questions the very possibility that beliefs be revealed by choice data. According to the current literature, all models of beliefs are equally exposed to the problem. Moreover, the problem is solvable only when the decision-maker can influence the resolution of uncertainty. This article gives grounds to reject these two views. The various models of beliefs can be shown to be unequally exposed to (...) the problem of state-dependent utility. The problem can be argued to be solved even when the decision-maker has no influence over the resolution of uncertainty. The implications of such reappraisal for a philosophical appreciation of the revealed preference methodology are discussed. (shrink)

Decision-making under normative uncertainty requires an agent to aggregate the assessments of options given by rival normative theories into a single assessment that tells her what to do in light of her uncertainty. But what if the assessments of rival theories differ not just in their content but in their structure -- e.g., some are merely ordinal while others are cardinal? This paper describes and evaluates three general approaches to this "problem of structural diversity": structural enrichment, structural (...) depletion, and multi-stage aggregation. All three approaches have notable drawbacks, but I tentatively defend multi-stage aggregation as least bad of the three. (shrink)

In situations where we ignore everything but the space of possibilities, we ought to suspend judgment—that is, remain agnostic—about which of these possibilities is the case. This means that we cannot sum our degrees of belief in different possibilities, something that has been formalized as an axiom of non-additivity. Consistent with this way of representing our ignorance, I defend a doxastic norm that recommends that we should nevertheless follow a certain additivity of possibilities: even if we cannot sum degrees of (...) belief in different possibilities, we should be more confident in larger groups of possibilities. It is thus shown that, in the type of situation considered (in so-called ‘classical ignorance’, i.e. “behind a thin veil of ignorance”), it is epistemically rational for advocates of suspending judgment to endorse this comparative confidence; while on the other hand it is shown that, even in classical ignorance, no stronger belief—such as a precise uniform probability distribution—is warranted. (shrink)

The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to a dominance condition; (...) that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe- Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance. (shrink)

Neoclassical economists use expected utility theory to explain, predict, and prescribe choices under risk, that is, choices where the decision-maker knows---or at least deems suitable to act as if she knew---the relevant probabilities. Expected utility theory has been subject to both empirical and conceptual criticism. This chapter reviews expected utility theory and the main criticism it has faced. It ends with a brief discussion of subjective expected utility theory, which is the theory neoclassical economists use to explain, predict, and (...) prescribe choices under uncertainty, that is, choices where the decision-maker cannot act on the basis of objective probabilities but must instead consult her own subjective probabilities. (shrink)

In his early experimental work with Suppes, Davidson adopted rationality assumptions, not as necessary constraints on interpretation, but as practical conceits in addressing methodological problems faced by experimenters studying decision making under uncertainty. Although the content of their theory has since been undermined, their methodological approach—a Galilean form of methodological rationalism—lives on in contemporary psychological research. This article draws on Max Weber’s verstehen to articulate an account of Galilean methodological rationalism; explains how anomalies faced by Davidson’s early experimental (...) work gave rise to his later, canonical claims about rationality and interpretation; and reclaims this Galilean framework for use in contemporary psychological research. (shrink)

In the growing literature on decision-making under moral uncertainty, a number of skeptics have argued that there is an insuperable barrier to rational "hedging" for the risk of moral error, namely the apparent incomparability of moral reasons given by rival theories like Kantianism and utilitarianism. Various general theories of intertheoretic value comparison have been proposed to meet this objection, but each suffers from apparently fatal flaws. In this paper, I propose a more modest approach that aims to identify (...) classes of moral theories that share common principles strong enough to establish bases for intertheoretic comparison. I show that, contra the claims of skeptics, there are often rationally perspicuous grounds for precise, quantitative value comparisons within such classes. In light of this fact, I argue, the existence of some apparent incomparabilities between widely divergent moral theories cannot serve as a general argument against hedging for one's moral uncertainties. (shrink)

Although probabilistic statements are ubiquitous, probability is still poorly understood. This shows itself, for example, in the mere stipulation of policies like expected utility maximisation and in disagreements about the correct interpretation of probability. In this work, we provide an account of probabilistic predictions that explains when, how, and why they can be useful for decision-making. We demonstrate that a calibration criterion on finite sets of predictions allows one to anticipate the distribution of utilities that a given policy will yield. (...) Based on this, we specify assumptions under which expected utility maximisation is a sensible decision criterion. We also introduce the notion of prediction methods and argue that all probabilities are outputs of such prediction methods. This helps to explain how the calibration criterion can be satisfied and to show that also supposedly objective probabilities are model-dependent. We compare our account of probability with common interpretations and show that it recovers key intuitions behind the latter. We, thus, provide a novel account of what probabilities are and how they can enable successful decision-making under uncertainty. (shrink)

Recent research has begun to investigate sensory processing in relation to nonclinical variation in traits associated with the autism spectrum disorders (ASD). We propose that existing accounts of autistic perception can be augmented by considering a role for individual differences in top-down expectations for the precision of sensory input, related to the processing of state-dependent levels of uncertainty. We therefore examined ASD-like traits in relation to the rubber-hand illusion: an experimental paradigm that typically elicits crossmodal integration of visual, tactile, (...) and proprioceptive information in an unusual illusory context. Individuals with higher ASD-like traits showed reduced effects of the rubber-hand illusion on perceived arm position and reach-to-grasp movements, compared to individuals with lower ASD-like traits. These differences occurred despite both groups reporting the typical subjective experience of the illusion concerning visuotactile integration and ownership for the rubber hand. Together these results suggest that the integration of proprioceptive information with cues for arm position derived from the illusory context differs between individuals partly in relation to traits associated with ASD. We suggest that the observed differences in sensory integration can be best explained in terms of differing expectations regarding the precision of sensory estimates in contexts that suggest uncertainty. (shrink)

Choice often proceeds in two stages: We construct a shortlist on the basis of limited and uncertain information about the options and then reduce this uncertainty by examining the shortlist in greater detail. The goal is to do well when making a final choice from the option set. I argue that we cannot realise this goal by constructing a ranking over the options at shortlisting stage which determines of each option whether it is more or less worthy of being (...) included in a shortlist. This is relevant to the 2010 UK Equality Act. The Act requires that shortlists be constructed on grounds of candidate rankings and affirmative action is only permissible for equally qualified candidates. This is misguided: Shortlisting candidates with lower expected qualifications but higher variance may raise the chance of finding an exceptionally strong candidate. If it does, then shortlisting such candidates would make eminent business sense and there is nothing unfair about it. This observation opens up room for including more underrepresented candidates with protected characteristics, as they are more likely to display greater variance in the selector’s credence functions at shortlisting stage. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. (...) The probability bounds imposed by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

Three challenges to a unified understanding of delusions emerge from Radden's On Delusion (2011). Here, I propose that in order to respond to these challenges, and to work towards a unifying framework for delusions, we should see delusions as arising in inference under uncertainty. This proposal is based on the observation that delusions in key respects are surprisingly like perceptual illusions, and it is developed further by focusing particularly on individual differences in uncertainty expectations.

Accounts of arguments from expert opinion take it for granted that expert judgments count as (defeasible) evidence for propositions, and so an argument that proceeds from premises about what an expert judges to a conclusion that the expert is probably right is a strong argument. In Mizrahi (2013), I consider a potential justification for this assumption, namely, that expert judgments are significantly more likely to be true than novice judgments, and find it wanting because of empirical evidence suggesting that expert (...) judgments under uncertainty are not significantly more likely to be true than novice judgments or even chance. In this paper, I consider another potential justification for this assumption, namely, that expert judgments are not influenced by the cognitive biases novice judgments are influenced by, and find it wanting, too, because of empirical evidence suggesting that experts are vulnerable to pretty much the same cognitive biases that novices are vulnerable to. If this is correct, then the basic assumption at the core of accounts of arguments from expert opinion, namely, that expert judgments count as (defeasible) evidence for propositions, remains unjustified. (shrink)

How do you make decisions under ignorance? That is, how do you decide when you lack subjective probabilities for some of your options’ possible outcomes? One answer is that you follow the Laplace Rule: you assign an equal probability to each state of nature for which you lack a subjective probability (that is, you use the Principle of Indifference) and then you maximize expected utility. The most influential objection to the Laplace Rule is that it is sensitive to (...) the individuation of states of nature. This sensitivity is problematic because the individuation of states seems arbitrary. In this paper, however, I argue that this objection proves too much. I argue that all plausible rules for decisions under ignorance are sensitive to the individuation of states of nature. (shrink)

This paper introduces the axiom of Negative Dominance, stating that if a lottery f is strictly preferred to a lottery g, then some outcome in the support of f is strictly preferred to some outcome in the support of g. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this (...) setting, Negative Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent. (shrink)