This paper presents a number of apparent anomalies in rational choice scenarios, and their translation into the logic of everyday reasoning. Three classes of examples that have been discussed in the context of probabilistic choice since the 1960s (by Debreu, Tversky and others) are analyzed in a non-probabilistic setting. It is shown how they can at the same time be regarded as logical problems that concern the drawing of defeasible inferences from a given information base. I (...) argue that initial appearances notwithstanding, these cases should not be classed as instances of irrationality in choice or reasoning. One way of explaining away their apparent oddity is to view certain aspects of these examples as making particular options salient. The decision problems in point can then be solved by ‘picking’ these options, although they could not have been ‘chosen’ in a principled way, due to ties or incomparabilities with alternative options. (shrink)

This paper presents a probabilist paraconsistent theory of belief revision. This theory is based on a very general theory of probability, that fits with a wide range of classical and nonclassical logics. The theory incorporates a version of Jeffrey conditionalisation as its method of updating. A Dutch book argument is given, and the theory is applied to the problem of choosing a logical system.

How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a sigma-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain (...) or an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are sigma-algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we compare our results with existing results on binary judgment aggregation and Arrovian preference aggregation. This paper is the first of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of each class of (...) pooling functions (most of them classic, but one new) and argue that linear pooling can be justified procedurally, but not epistemically, while the other two pooling methods can be justified epistemically. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. We conclude by mentioning a number of other pooling methods. (shrink)

최근의 과학철학 논의에서 중요한 비중을 차지하는 주제 중 하나가 ‘과학적 실재론(scientific realism)’이다. 과학적 실재론은 토머스 쿤(Thomas Kuhn)의 『과학혁명의 구조』(1962) 속 역사적 연구를 그 논의 배경으로 한다. 대개 실재론자는 “최선의 설명으로의 추론(Inference to the Best Explanation)”을 근거로 실재론적 관점을, 반실재론자는 “비관적 귀납(Pessimistic Induction)”을 근거로 반실재론적 관점을 주장한다. 이때 많은 경우 논리경험주의의 철학적 관점은 ‘반실재론적 관점’에 포함된다고 전제된다. 그런데 최근의 과학철학사 연구에 따르면 논리경험주의 내에서 반실재론이 아닌 ‘실재론적 관점’을 여럿 발견할 수 있다. 그러므로 토머스 쿤의 ‘역사적 전회’ 이전에 등장한 논리경험주의 판본의 실재론이 (...) 갖는 정체를 파악할 필요가 있다. 실재론적 관점을 취한 논리경험주의자로 슐리크(Schlick), 카르납(Carnap), 파이글(Feigl) 등 여럿 있지만, 이 논문에서 나는 논리경험주의 철학자 한스 라이헨바흐(Hans Reichenbach)의 실재론에 초점을 맞춰 논한다. 그것은 그가 『경험과 예측』(1938) 에서 명시적으로 일종의 실재론적 관점을 제시했으며, 그가 이후 발전시킨 인과 이론 역시 강한 실재론적 특성을 갖기 때문이다. 『경험과 예측』에서 라이헨바흐는 그의 실재론을 카르납의 실증주의적 관점에 대비하여 전개했다. 카르납은 『세계의 논리적 구조』(1928)에서 물리적 대상의 개념이 감각 인상 명제들의 집합으로 ‘환원(reduct)’ 된다고 주장했다. 반면 라이헨바흐는 물리적 대상 개념에는 감각 인상 명제들의 집합으로 환원되지 않는 여분의 의미가 있고, 이 개념은 감각 인상 명제보다 덜 확실하나 더 직관적인 일상적 관측 명제로부터 ‘투영(project)’되며, 이때 투영은 ‘확률적 추론(probabilistic inference)’에 기반한다고 주장했다. 확률적 투영에 기반한 이러한 실재론적 관점에 관해 과학철학자 마티아스 노이버(Matthias Neuber)는 라이헨바흐가 이와 동시에 실재론의 문제를 일종의 ‘언어 선택의 문제’로도 취급하려 했다는 점에서 불완전하므로 결국 실패한다고 진단했다. 그러나 내가 볼 때 ‘확률적 실재론’과 ‘언어 선택의 문제로서의 실재론’은 노이버의 주장과 달리 서로 상충하지 않는다. 왜냐하면 실재론적 언어와 실증주의적 언어는 ‘도출된 결정들(entailed decisions)’에 있어 서로 차별화되기 때문이다. 그리고 이러한 차별화는 언어 선택이 ‘의지적 선택(volitional decision)’이 아닌 ‘의지적 분기(volitional bifurcation)’이며，이러한 ‘의지적 분기’는 세계의 객관적인 ‘인과적 효력(causal effect)’에 기반하기 때문에 가능하다. (shrink)

Moss (2018) argues that rational agents are best thought of not as having degrees of belief in various propositions but as having beliefs in probabilistic contents, or probabilistic beliefs. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, are modeled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Moss’ account of probabilistic (...) knowledge or her semantics for epistemic modals and probability operators. It is an extremely general model of uncertainty. Indeed, it is at least as general and expressively powerful as every other current imprecise probability framework, including lower probabilities, lower previsions, sets of probabilities, sets of desirable gambles, and choice functions. In addition, we partially answer an important question that Moss leaves open, viz., why should rational agents have consistent probabilistic beliefs? We show that an important subclass of Mossean believers avoid Dutch bookability iff they have consistent probabilistic beliefs. (shrink)

Hilary Bowman-Smart et al. (2023) have rightly pointed out that one of the recurring criticisms of the use of noninvasive prenatal testing (NIPT) for non-medical trait prediction is the probabilist...

How can different individuals' probability functions on a given sigma-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'event-wise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize (...) this idea by introducing a 'premise-based' approach to probabilistic opinion pooling, and show that, under a variety of assumptions, it leads to linear or neutral opinion pooling on the 'premises'. This paper is the second of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

Mathematicians only use deductive proofs to establish that mathematical claims are true. They never use inductive evidence, such as probabilistic proofs, for this task. Don Fallis (1997 and 2002) has argued that mathematicians do not have good epistemic grounds for this complete rejection of probabilistic proofs. But Kenny Easwaran (2009) points out that there is a gap in this argument. Fallis only considered how mathematical proofs serve the epistemic goals of individual mathematicians. Easwaran suggests that deductive proofs might (...) be epistemically superior to probabilistic proofs because they are transferable. That is, one mathematician can give such a proof to another mathematician who can then verify for herself that the mathematical claim in question is true without having to rely at all on the testimony of the first mathematician. In this paper, I argue that collective epistemic goals are critical to understanding the methodological choices of mathematicians. But I argue that the collective epistemic goals promoted by transferability do not explain the complete rejection of probabilistic proofs. (shrink)

The postwar welfare state provides social insurance against economic, health, and related risks in an uncertain world. Because everyone can envision themselves to be among the unfortunate, social insurance fuses self-interest and solidarism in a normative principle Friedman (2020) calls probabilistic justice. But there is a competing principle of status defense, where the aim is to erect boundaries between socioeconomic strata and discourage cross-class mobility. We argue that this principle dominates when inequality is high and uncertainty low. The current (...) moment is one of high inequality and high uncertainty, which results in intense status anxiety, yet does not rule out solidaristic solutions. Our contributions are to diagnose the causes of our current malaise, and to theorize the normative bases for the political choice facing contemporary western democracies. (shrink)

There is a generic way to add any new feature to a system. It involves identifying the basic units which build up the system and introducing the new feature to each of these basic units. In the case where the system is argumentation and the feature is probabilistic we have the following. The basic units are: the nature of the arguments involved; the membership relation in the set S of arguments; the attack relation; and the choice of extensions. (...) Generically to add a new aspect to an argumentation network \ can be done by adding this feature to each component. This is a brute-force method and may yield a non-intuitive or meaningful result. A better way is to meaningfully translate the object system into another target system which does have the aspect required and then let the target system endow the aspect on the initial system. In our case we translate argumentation into classical propositional logic and get probabilistic argumentation from the translation. Of course what we get depends on how we translate. In fact, in this paper we introduce probabilistic semantics to abstract argumentation theory based on the equational approach to argumentation networks. We then compare our semantics with existing proposals in the literature including the approaches by M. Thimm and by A. Hunter. Our methodology in general is discussed in the conclusion. (shrink)

If the influence of libertarian free will on human behaviour is real, the frequency of certain freely chosen actions will differ from the probability of their occurrences deduced from the statistical calculations and neuroscientific observations and laws. According to D. Pereboom, contemporary science does not prove the efficacy of libertarian free will. According to P. van Inwagen, there is always a random element in free decisions, and hence the effect of the free will remains unknown. Swinburne observes that it is (...) not correct to conclude that libertarian free will has no causal effect in the physical world. One can only conclude that these choices are not neurologically real. People sometimes choose to act on abstract principles, and they can do so on a regular and long-term basis. Consequently, human behaviour can be predicted and explained in terms of personal agency and the reasons upon which the people have chosen to act. Probabilistic calculations strengthen the argument that the best way to explain and predict such rational behaviour is to affirm the efficacy of the libertarian free will, which can overcome neurophysiological motivational states of the body and which guarantees a kind of long-term rational determinism. (shrink)

The idea that good explanations come with strong changes in probabilities has been very common. This criterion is called probabilistic difference-making. Since it is an intuitive criterion and has a long tradition in the literature on scientific explanation, it comes as a surprise that probabilistic difference-making is rarely discussed in the context of interventionist causal explanation. Specificity, proportionality, and stability are usually employed to measure explanatory power instead. This paper is a first step into the larger project of (...) connecting difference-making to the interventionist debate, and it starts by investigating whether probabilistic difference-making is contained in the notion of specificity. The choice of specificity is motivated by the observation that both probabilistic difference-making and specificity build on similar underlying intuitions. When comparing measures for both specificity and probabilistic difference-making, it turns out that the measures are not strictly correlated, and so the thesis that probabilistic difference-making is encoded within specificity has to be rejected. Some consequences of this result are discussed as well. (shrink)

Debreu (American Economic Review 50:186–188, 1960) famously criticized Luce (Individual choice behavior, Wiley, New York, 1959) choice model with what became known as the red-bus blue-bus example: if a choice set contains two distinct alternatives C (car) and B (blue bus) then adding a third alternative A (red bus) that is essentially identical to B does not affect the choice probability of C but reduces the choice probability of B by half. Debreu’s critique highlights the (...) existence of substitution effects violating the principle of independence from irrelevant alternatives—the cornerstone of Luce (Individual choice behavior, Wiley, New York, 1959) choice model. This paper weakens this principle to construct a model of probabilistic choice satisfying Debreu’s critique. (shrink)

Several philosophers have used the framework of means/ends reasoning to explain the methodological choices made by scientists and mathematicians (see, e.g., Goldman 1999, Levi 1962, Maddy 1997). In particular, they have tried to identify the epistemic objectives of scientists and mathematicians that will explain these choices. In this paper, the framework of means/ends reasoning is used to study an important methodological choice made by mathematicians. Namely, mathematicians will only use deductive proofs to establish the truth of mathematical claims. In (...) this paper, I argue that none of the epistemic objectives of mathematicians that are currently on the table provide a satisfactory explanation of this rejection of probabilistic proofs. (shrink)

“Everyone knows that language is variable.” This is the bald sentence with which Sapir (1921:147) begins his chapter on language as an historical product. He goes on to emphasize how two speakers’ usage is bound to differ “in choice of words, in sentence structure, in the relative frequency with which particular forms or combinations of words are used”. I should add that much sociolinguistic and historical linguistic research has shown that the same speaker’s usage is also variable (Labov 1966, (...) Kroch 2001:722). However, the tradition of most syntacticians has been to ignore this thing that everyone knows. (shrink)

The Monty Hall Dilemma (MHD) is a two-step decision problem involving counterintuitive conditional probabilities. The first choice is made among three equally probable options, whereas the second choice takes place after the elimination of one of the non-selected options which does not hide the prize. Differing from most Bayesian problems, statistical information in the MHD has to be inferred, either by learning outcome probabilities or by reasoning from the presented sequence of events. This often leads to suboptimal decisions (...) and erroneous probability judgments. Specifically, decision makers commonly develop a wrong intuition that final probabilities are equally distributed, together with a preference for their first choice. Several studies have shown that repeated practice enhances sensitivity to the different reward probabilities, but does not facilitate correct Bayesian reasoning. However, modest improvements in probability judgments have been observed after guided explanations. To explain these dissociations, the present review focuses on two types of causes producing the observed biases: Emotional-based choice biases and cognitive limitations in understanding probabilistic information. Among the latter, we identify a crucial cause for the universal difficulty in overcoming the equiprobability illusion: Incomplete representation of prior and conditional probabilities. We conclude that repeated practice and/or high incentives can be effective for overcoming choice biases, but promoting an adequate partitioning of possibilities seems to be necessary for overcoming cognitive illusions and improving Bayesian reasoning. (shrink)

Experimental studies suggest that individuals exhibit more risk aversion in choices among prospects when the payment and resolution of uncertainty are immediate relative to when it is delayed. This leads to preference reversals that cannot be attributed to discounting. When data suggest that utility is time-independent, probability weighting functions, such as those used to model prospect theory preferences, can accommodate such reversals. We propose a simple descriptive model with a two-parameter probability weighting function where one of these parameters depends on (...) the time at which a prospect is resolved. The time-dependent parameter is responsible for the curvature of the probability weighting function and is regarded as an index of sensitivity towards changes in probabilities. We provide conditions that characterize increased sensitivity towards more distant probabilities; this can account for the observed relatively less risk aversion towards delayed prospects. In our framework, the discount function is unrestricted, such that the model is compatible with empirical findings of non-constant discounting. In a simple application to bargaining we illustrate when it is advantageous for an individual to advance or delay the bargaining resolution time if an opponent displays increased sensitivity towards probability changes with delay. (shrink)

While speakers have been shown to adapt to the knowledge state of their addressee in choosing referring expressions, they often also show some egocentric tendencies. The current paper aims to provide an explanation for this “mixed” behavior by presenting a model that derives such patterns from the probabilistic combination of both the speaker's and the addressee's perspectives. To test our model, we conducted a language production experiment, in which participants had to refer to objects in a context that also (...) included a visually misleading object whose function was either known to both partners, or known just to the speaker but not the addressee. Modeling results indicate that the experimental findings cannot be explained by assuming that speakers tailor a referring expression solely to their own perspective or to the perspective of their addressee. Instead, accounting for the behavioral pattern requires an approach where both perspectives influence the choice of referring expressions. Nevertheless, in our situation, speakers consider their partner's perspective more than their own. (shrink)

We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one (...) we are aware of, and we show how it implies the independent natural extension for sets of desirable gambles, and therefore also for less informative imprecise-probabilistic models. Once this is in place, we compare this concept of epistemic independence to another independence concept for choice functions proposed by Seidenfeld [22], which De Bock and De Cooman [1] have called S-independence. We show that neither is more general than the other. (shrink)

A key challenge for probabilistic causal models is to distinguish non-causal probabilistic dependencies from true causal relations. To accomplish this task, causal models are usually required to satisfy several constraints. Two prominent constraints are the causal Markov condition and the faithfulness condition. However, other constraints are also needed. One of these additional constraints is the causal sufficiency condition, which states that models must not omit any direct common causes of the variables they contain. In this paper, I argue (...) that the causal sufficiency condition is problematic: (1) it is incompatible with the requirement that the variables in a model must not stand in non-causal necessary dependence relations, such as mathematical or conceptual relations, or relations described in terms of supervenience or grounding, (2) it presupposes more causal knowledge as primitive than is actually needed to create adequate causal models, and (3) if models are only required to be causally sufficient, they cannot deal with cases where variables are probabilistically related by accident, such as Sober’s example of the relationship between bread prices in England and the sea level in Venice. I show that these problems can be avoided if causal models are required to be monotonic in the following sense: the causal relations occurring in a model M would not disappear if further variables were added to M. I give a definition of this monotonicity condition and conclude that causal models should be required to be monotonic rather than causally sufficient. (shrink)

The aim of the present paper is to give a purely probabilistic account for the approach to equilibrium of classical and quantum gas. The probability function used is classical. The probabilistic dynamics describes the evolution of the state of the gas due to unary and binary collisions. A state change amounts to a destruction in a state and the creation in another state. Transitions probabilities are splittled into destructions terms, denoting the random choice of the colliding particle(s), (...) and creation terms, describing the allocation of the same particle(s) on the final state(s). While the destruction term is the same for all types of particles, the creation one depends upon a parameter bound to the interpraticle correlation. The transition probabilities give rise to a homogeneous Markov chain. The equilibrium distributions satisfy the principle of detailed balance. Relaxation times depend upon the interparticle correlation. Relationships with the Ehrenfest urn model, Brillouin unified method, ensemble interpretation, and quantum H-theorem are considered too. (shrink)

Given a choice between two sealed envelopes, one of which contains twice as much money as the other (and in any case some), you don't know which contains the larger sum and so choose one at random. You are then given the option of taking the other envelope instead. Is it rational to do so? Surely not. but a specious line of reasoning suggests otherwise.

The past century has witnessed numerous methodological innovations in probabilistic and statistical methods of causal inference (e.g., the graphical modelling and the potential outcomes frameworks, as introduced in Chapter 1). These innovations have not only enhanced the methodologies by which scientists across diverse domains make causal inference, but they have also made a profound impact on the way philosophers think about causation. The philosophical issues discussed in this thesis are stimulated and inspired by these methodological innovations. Chapter 2 addresses (...) the question of how the holding of screening-off conditions for a causal model depends on the choice of variables. As bridge principles between probability and causation, screening-off conditions (especially the Causal Markov Condition) play a key role in causal inference. However, it has been known that these conditions may fail due to poor variable choice. My aim in this chapter is to further examine those constraints on variable choice that are deemed necessary for the satisfaction of screening-off conditions. The idea of a well-defined (hypothetical) intervention is also crucial for reliable causal inference. Chapter 3 explores the question of when interventions invoked in causal inference are “well-defined” or unambiguous, and how this requirement constrains the choice of cause-variables. I propose that an intervention is well-defined just in case the effect of interest is well-defined (under ideal interventions), and that the intervention can serve as a suitable means to identify that effect. Based on this proposal, several distinct types of ambiguous interventions are identified. Methodological progress in causal inference also poses the following question: Can such progress shed light on the ontology of causation? My answer is yes. In Chapter 4, I develop a Carnapian-pragmatist approach to the ontology of causation as an alternative to existing metaphysical approaches. I argue that, compared to traditional metaphysics, the pragmatist approach provides a superior picture of how the ontology and methodology of causation interact with each other in scientific practice. I conclude in Chapter 5 that the thing we call “causation” consists in both the right worldly infrastructure (e.g., screening-off patterns and possibilities for interventions) and appropriate ways of framing this infrastructure. (shrink)

In his paper, ‘Patients, doctors and risk attitudes’, Makins argues that doctors, when choosing a treatment for their patient, need to follow their risk profile.1 He presents a pair of fictitious diseases facing a patient who either has ‘exemplitis’, which requires no treatment or ‘caseopathy’, which is severe and disabling and for which there is a treatment with unpleasant side effects. The doctor needs to decide whether the patient should pursue the unpleasant treatment, just in case he has caseopathy. Makins (...) believes that rational-choice theory is a productive way to approach this problem. This theory frames all decisions as gambles. Each possible gamble (eg, not to pursue treatment) leads, probabilistically, to a set of outcomes (life with no disease and no side effects, but also, possibly, life with a disabling disease, since no treatment is taken). Utilities of these outcomes and probabilities that they will happen are combined to yield a number—expected utility. One is supposed to gamble—to make a choice—in a way that maximises this expected utility. Makins takes this framework for granted and is focused on an additional complication, the patient’s risk preference. He believes that, in his hypothetical example, even if expected utility were exactly the same, withholding treatment …. (shrink)

It is sometimes thought that if we treat decision-theoretic options as interventions, then we can use evidential decision theory to vindicate causal dominance reasoning. This is supposed to be guaranteed by a causal modeling axiom that implies that interventions are probabilistically independent of their non-effects—namely, the Causal Markov Condition. But there are two concerns for this line of reasoning. First, the Causal Markov Condition doesn’t imply that an agent should regard their intervention as probabilistically independent from its non-effects when the (...) agent has “exotic evidence”—i.e., evidence about some variable that they regard as causally downstream from their intervention. Second, the Causal Markov Condition is not plausible when we interpret it as implying constraints on subjective probability distributions, because there are cases where it is rational for an agent to regard variables as causally independent but subjectively probabilistically dependent. In this paper, I argue that interventionists can answer these challenges by adopting a conception of choice according to which there are significant constraints on the objective probabilities for decision-theoretic options. (shrink)

We introduce a set of biologically and computationally motivated design choices for modeling the learning of language, or of other types of sequential, hierarchically structured experience and behavior, and describe an implemented system that conforms to these choices and is capable of unsupervised learning from raw natural-language corpora. Given a stream of linguistic input, our model incrementally learns a grammar that captures its statistical patterns, which can then be used to parse or generate new data. The grammar constructed in this (...) manner takes the form of a directed weighted graph, whose nodes are recursively (hierarchically) defined patterns over the elements of the input stream. We evaluated the model in seventeen experiments, grouped into five studies, which examined, respectively, (a) the generative ability of grammar learned from a corpus of natural language, (b) the characteristics of the learned representation, (c) sequence segmentation and chunking, (d) artificial grammar learning, and (e) certain types of structure dependence. The model's performance largely vindicates our design choices, suggesting that progress in modeling language acquisition can be made on a broad front—ranging from issues of generativity to the replication of human experimental findings—by bringing biological and computational considerations, as well as lessons from prior efforts, to bear on the modeling approach. (shrink)

‘Predictive Processing’ is an emerging paradigm in cognitive neuroscience that depicts the human mind as an uncertainty management system that constructs probabilistic predictions of sensory s...

This article considers the popular thesis that a more proportional relationship between a cause and its effect yields a more abstract causal explanation of that effect, which in turn produces a deeper explanation. This thesis is taken to have important implications for choosing the optimal granularity of explanation for a given explanandum. In this article, I argue that this thesis is not generally true of probabilistic causal relationships. In light of this finding, I propose a pragmatic, interest-relative measure of (...) explanatory depth. This measure uses a decision-theoretic model of information pricing to determine the optimal granularity of explanation for a given explanandum, agent, and decision problem. (shrink)

In this paper, I challenge the traditional narrative that William James’s arguments against determinism were primarily motivated by his personal struggles with depression. I argue that James presents an alternative argument against determinism that is motivated by his commitment to sound scientific practice. James argues that determinism illegitimately extrapolates from observations of past events to predictions about future events without acknowledging the distinct metaphysical difference between them. This occupation with futurity suggests that James’s true target is better understood as logical (...) determinism rather than causal determinism. This has consequences for James’s proposed alternative, which I call his probabilistic underdeterminism, a conception of the universe that is built on chance, choice, and a local teleology. All of this forms part of a broader criticism of the scientific practices of his day based on their widespread failure to acknowledge the distorting effects of observation on that which is observed. (shrink)

Rationalist models of divine agency typically ascribe perfect freedom to God, where this is understood as a freedom from external causal influences and non-rational influences, including desires or preferences not derived from reason alone. Paul Draper has recently developed a rationalist model of God’s agency on which God faces “hard choices” between options differing in moral and non-moral value. He argues that this model is preferable to rival rationalist models because it is compatible with God’s having significant freedom and being (...) maximally worthy of praise and gratitude. I argue that on an alternative model of divine agency, which rejects perfect freedom and holds that God makes hard choices on the basis of brute preferences, God would be more worthy of praise and gratitude. However, a probabilistic problem for theism which Draper identifies for his model also applies to the brute preference model. (shrink)

This paper considers a puzzling conflict between two positions that are each compelling: it is irrational for an agent to pay to avoid `free' evidence before making a decision, and rational agents may have imprecise beliefs and/or desires. Indeed, we show that Good's theorem concerning the invariable choice-worthiness of free evidence does not generalise to the imprecise realm, given the plausible existing decision theories for handling imprecision. A key ingredient in the analysis, and a potential source of controversy, is (...) the general approach taken for resolving sequential decision problems { we make explicit what the key alternatives are and defend our own approach. Furthermore, we endorse a resolution of the aforementioned puzzle { we privilege decision theories that merely permit avoiding free evidence over decision theories for which avoiding free evidence is uniquely admissible. Finally, we situate this particular result about free evidence within the broader `dynamic-coherence' literature. (shrink)

Conviction Narrative Theory (CNT) is a theory of choice underradical uncertainty– situations where outcomes cannot be enumerated and probabilities cannot be assigned. Whereas most theories of choice assume that people rely on (potentially biased) probabilistic judgments, such theories cannot account for adaptive decision-making when probabilities cannot be assigned. CNT proposes that people usenarratives– structured representations of causal, temporal, analogical, and valence relationships – rather than probabilities, as the currency of thought that unifies our sense-making and decision-making faculties. (...) According to CNT, narratives arise from the interplay between individual cognition and the social environment, with reasoners adopting a narrative that feels “right” to explain the available data; using that narrative to imagine plausible futures; and affectively evaluating those imagined futures to make a choice. Evidence from many areas of the cognitive, behavioral, and social sciences supports this basic model, including lab experiments, interview studies, and econometric analyses. We identify 12 propositions to explain how the mental representations (narratives) interact with four inter-related processes (explanation, simulation, affective evaluation, and communication), examining the theoretical and empirical basis for each. We conclude by discussing how CNT can provide a common vocabulary for researchers studying everyday choices across areas of the decision sciences. (shrink)

We consider random choice rules that, by satisfying a weak form of Luce’s choice axiom, embody a form probabilistic rationality. We show that for this important class of stochastic choices, the law of demand for normal goods—arguably the main result of traditional consumer theory—continues to hold on average when strictly dominated alternatives are dismissed.

Modeling risk in a prescriptively plausible way represents a major issue in decision theory. The benchmarking procedure, being based on the satisficing principle and providing a probabilistic interpretation of expected utility (EU) theory, is prescriptive. Because it is a target-based language, the benchmarking procedure can be applied naturally to finance. In finance, the centrality of risk is widely recognized, but the risk measures that are commonly used to assess risk are too poor as a decision making tool. In this (...) paper we propose a two-stage decision criterion of choice under risk that provides an application of benchmarking to finance through a risk measure. We will analyze some nonexpected utility theories, in particular lottery dependent utility, as potential frameworks for our criterion. (shrink)

According to the foundations of economic theory, agents have stable and coherent preferences that guide their choices among alternatives. However, people are constrained by information-processing and memory limitations and hence have a propensity to avoid cognitive load. We propose that this in turn will encourage them to respond to preferences and goals influenced by context and memory representations.

The “Asian disease” problem (Tversky & Kahneman, 1981) demonstrated behaviour in contradiction to the invariance axiom of EU theory. However, the risky choice behaviour was simply seen by the equate-to-differentiate model as a choice between the best possible outcomes or a choice between the worst possible outcomes. It was then argued that a way in which frame influences choice is through the perceived difference between possible outcomes. A “judgement” task was designed to examine whether the knowledge (...) of “the value difference between each possible outcome and the certain outcome” will permit prediction of preference in the choice pattern related to the Asian disease problem. Participants were exposed to an anthrax disease problem (the original or probabilistic version of the Asian disease problem) and a SARS problem (the fuzzy version of the Asian disease problem). It was shown that the empirical evidence in relation to the Asian disease problem could be satisfactorily accounted for by the generalised weak dominance strategy revealed by the judgement results. (shrink)

The prominent characteristic of a delayed-choice effect is to make the choice between complementary types of phenomena after the relevant interaction between the system and measuring instrument has already come to an end. In this paper, we first represent a detailed comparative analysis of some early delayed-choice propositions and also most of the experimentally performed delayed-choice proposals in a coherent and unified quantum mechanical formulation. Taking into the account the represented quantum mechanical descriptions and also the (...) rules of probability theory, we discuss that there are two fundamentally different descriptions concerning the physical mechanism of the delayed-choice between the complementary types of phenomena in these experiments. In this regard, we finally conclude that the delayed-choice experiments can be classified into two main groups where the temporal aspect of each group is characterized differently within their probabilistic descriptions. (shrink)

In our daily lives, we continuously evaluate feedback information, update our knowledge, and adapt our behavior in order to reach desired goals. This ability to learn from feedback information, however, declines with age. Previous research has indicated that certain higher-level learning processes, such as feedback evaluation, integration of feedback information, and updating of knowledge, seem to be affected by age, and recent studies have shown how the adaption of choice behavior following feedback can differ with age. The neural mechanisms (...) underlying this age-related change in choice behavior during learning, however, remain unclear. The aim of this study is therefore to investigate the relation between learning-related neural processes and choice behavior during feedback learning in two age groups. Behavioral and fMRI data were collected, while a group of young and older adults performed a probabilistic learning task consisting of 10 blocks of 20 trials each. On each trial, the participants chose between a house and a face, after which they received visual feedback. In each block, either the house or the face image had a higher probability of yielding a reward. Participants were instructed to try to maximize their gains. Our results showed that less successful learning in older adults, as indicated by a lower learning rate, corresponded with a higher tendency to switch to the other stimulus option, and with a reduced adaptation of this switch choice behavior following positive feedback. At the neural level, activation following positive and negative feedback was found to be less distinctive in the older adults, due to a smaller feedback-evaluation response to positive feedback in this group. Furthermore, whereas young adults displayed increased levels of knowledge updating prior to adapting choice behavior, we did not find this effect in older adults. Together, our results suggest that diminished learning performance with age corresponds with diminished evaluation of positive feedback and reduced knowledge updating related to changes in choice behavior, indicating how such differences in feedback processing at the trial level in older adults might lead to reduced learning performance across trials. (shrink)