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The Foundations of Statistics

Synthese 11 (1):86-89 (1954)

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  1. Why scientists gather evidence.Patrick Maher - 1990 - British Journal for the Philosophy of Science 41 (1):103-119.
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  • Symptomatic acts and the value of evidence in causal decision theory.Patrick Maher - 1990 - Philosophy of Science 57 (3):479-498.
    A "symptomatic act" is an act that is evidence for a state that it has no tendency to cause. In this paper I show that when the evidential value of a symptomatic act might influence subsequent choices, causal decision theory may initially recommend against its own use for those subsequent choices. And if one knows that one will nevertheless use causal decision theory to make those subsequent choices, causal decision theory may favor the one-box solution in Newcomb's problem, and may (...)
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  • On the consistency of choice.Ola Mahmoud - 2017 - Theory and Decision 83 (4):547-572.
    Consistency of choice is a fundamental and recurring theme in decision theory, social choice theory, behavioral economics, and psychological sciences. The purpose of this paper is to study the consistency of choice independent of the particular decision model at hand. Consistency is viewed as an inherently logical concept that is fundamentally void of connotation and is thus disentangled from traditional rationality or consistency conditions imposed on decision models. The proposed formalization of consistency takes two forms: internal consistency, which refers to (...)
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  • Diachronic rationality.Patrick Maher - 1992 - Philosophy of Science 59 (1):120-141.
    This is an essay in the Bayesian theory of how opinions should be revised over time. It begins with a discussion of the principle that van Fraassen has dubbed "Reflection". This principle is not a requirement of rationality; a diachronic Dutch argument, that purports to show the contrary, is fallacious. But under suitable conditions, it is irrational to actually implement shifts in probability that violate Reflection. Conditionalization and probability kinematics are special cases of the principle not to implement shifts that (...)
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  • Acceptance Without Belief.Patrick Maher - 1990 - PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990 (1):380-392.
    Bas van Fraassen (1980) maintained that acceptance of a scientific theory does not involve belief that the theory is true, though it does involve belief that the theory is empirically adequate. This provoked a large literature attempting to refute van Fraassen’s position. For the most part, the critics attempted to show that van Fraassen’s position violates principles of inductive inference, or of rationality.2 Such criticisms do not question the possibility of conforming to van Fraassen’s conception of science; they merely argue (...)
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  • Basic‐Know And Super‐Know.Anna Mahtani - 2019 - Philosophy and Phenomenological Research 98 (2):375-391.
    Sometimes a proposition is ‘opaque’ to an agent: he doesn't know it, but he does know something about how coming to know it should affect his or her credence function. It is tempting to assume that a rational agent's credence function coheres in a certain way with his or her knowledge of these opaque propositions, and I call this the ‘Opaque Proposition Principle’. The principle is compelling but demonstrably false. I explain this incongruity by showing that the principle is ambiguous: (...)
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  • Bayesian probability.Patrick Maher - 2010 - Synthese 172 (1):119 - 127.
    Bayesian decision theory is here construed as explicating a particular concept of rational choice and Bayesian probability is taken to be the concept of probability used in that theory. Bayesian probability is usually identified with the agent’s degrees of belief but that interpretation makes Bayesian decision theory a poor explication of the relevant concept of rational choice. A satisfactory conception of Bayesian decision theory is obtained by taking Bayesian probability to be an explicatum for inductive probability given the agent’s evidence.
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  • Do Trade Union Leaders Violate Subjective Expected Utility? Some Insights From Experimental Data.Anna Maffioletti & Michele Santoni - 2005 - Theory and Decision 59 (3):207-253.
    This paper presents the results of two experiments designed to test violations of Subjective Expected Utility Theory (SEUT) within a sample of Italian trade union delegates and leaders. Subjects priced risky and ambiguous prospects in the domain of gains. Risky prospects were based on games of chance, while ambiguous prospects were built on the standard Ellsberg paradox and on event lotteries whose outcomes were based either on the results of a fictional election or on the future results of the 1999 (...)
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  • Knowledge, behaviour, and policy: questioning the epistemic presuppositions of applying behavioural science in public policymaking.Magdalena Małecka - 2021 - Synthese 199 (1-2):5311-5338.
    The aim of this article is to question the epistemic presuppositions of applying behavioural science in public policymaking. Philosophers of science who have examined the recent applications of the behavioural sciences to policy have contributed to discussions on causation, evidence, and randomised controlled trials. These have focused on epistemological and methodological questions about the reliability of scientific evidence and the conditions under which we can predict that a policy informed by behavioural research will achieve the policymakers’ goals. This paper argues (...)
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  • Decision theory with complex uncertainties.Dilip B. Madan & J. C. Owings - 1988 - Synthese 75 (1):25 - 44.
    A case is made for supposing that the total probability accounted for in a decision analysis is less than unity. This is done by constructing a measure on the set of all codes for computable functions in such a way that the measure of every effectively accountable subset is bounded by a number <1. The consistency of these measures with the Savage axioms for rational preference is established. Implications for applied decision theory are outlined.
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  • Null hypothesis testing ≠ Scientific inference: A critique of the shaky premise at the heart of the science and values debate, and a defense of value‐neutral risk assessment.Brian H. MacGillivray - forthcoming - Risk Analysis.
    Many philosophers and statisticians argue that risk assessors are morally obligated to evaluate the probabilities and consequences of methodological error, and to base their decisions of whether to adopt a given parameter value, model, or hypothesis on those considerations. This argument is couched within the rubric of null hypothesis testing, which I suggest is a poor descriptive and normative model for risk assessment. Risk regulation is not primarily concerned with evaluating the probability of data conditional upon the null hypothesis, but (...)
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  • Book review. [REVIEW]Mark J. Machina - 1992 - Theory and Decision 33 (3):265-271.
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  • A No-Trade Theorem under Knightian Uncertainty with General Preferences.Chenghu Ma - 2001 - Theory and Decision 51 (2/4):173-181.
    This paper derives a no-trade theorem under Knightian uncertainty, which generalizes the theorem of Milgrom and Stokey by allowing general preference relations. It is shown that the no-trade theorem holds true as long as agents' preferences are dynamically consistent in the sense of Machina and Schmeidler, and satisfies the so-called piece-wise monotonicity axiom. A preference satisfying the piece-wise monotonicity axiom does not necessarily imply the additive utility representation, nor is necessarily based on beliefs.
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  • Rational beliefs in rationalizability.Xiao Luo - 2016 - Theory and Decision 81 (2):189-198.
    In this paper I scrutinize the “rational beliefs” in the concept of rationalizability in strategic games [Bernheim, Pearce ]. I illustrate through an example that a rationalizable strategy may not be supported by a “rational belief”, at least under one plausible interpretation of “rational belief”. I offer an alternative formulation of “rational belief” in the concept of rationalizability, which yields a novel epistemic interpretation of the notion of point-rationalizability.
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  • Qualitative independence in probability theory.R. Duncan Luce & Louis Narens - 1978 - Theory and Decision 9 (3):225-239.
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  • Decisions with indeterminate probabilities.Ronald P. Loui - 1986 - Theory and Decision 21 (3):283-309.
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  • Comments on Joseph Agassi.Barry Loewer - 1975 - Synthese 30 (1-2):25 - 30.
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  • Two Tales of Epistemic Models.Yang Liu - 2019 - Thought: A Journal of Philosophy 8 (4):291-302.
    This short paper has two parts. First,we prove a generalisation of Aumann’s surprising impossibility result in the context of rational decision making. We then move, in the second part, to discuss the interpretational meaning of some formal setups of epistemic models, and we do so by means of presenting an interesting puzzle in epistemic logic. The aim is to highlight certain problematic aspects of these epistemic systems concerning first/third-person asymmetry which underlies both parts of the story. This asymmetry, we argue, (...)
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  • Incomplete Preference and Indeterminate Comparative Probabilities.Yang Liu - 2022 - British Journal for the Philosophy of Science 73 (3):795-810.
    The notion of comparative probability defined in Bayesian subjectivist theory stems from an intuitive idea that, for a given pair of events, one event may be considered “more probable” than the other. Yet it is conceivable that there are cases where it is indeterminate as to which event is more probable, due to, e.g., lack of robust statistical information. We take that these cases involve indeterminate comparative probabilities. This paper provides a Savage-style decision-theoretic foundation for indeterminate comparative probabilities.
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  • Countable Additivity, Idealization, and Conceptual Realism.Yang Liu - 2020 - Economics and Philosophy 36 (1):127-147.
    This paper addresses the issue of finite versus countable additivity in Bayesian probability and decision theory -- in particular, Savage's theory of subjective expected utility and personal probability. I show that Savage's reason for not requiring countable additivity in his theory is inconclusive. The assessment leads to an analysis of various highly idealised assumptions commonly adopted in Bayesian theory, where I argue that a healthy dose of, what I call, conceptual realism is often helpful in understanding the interpretational value of (...)
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  • Advances in belief dynamics: Introduction.F. Liu & O. Roy - 2010 - Synthese 173 (2):123-126.
    This is the introduction of the special issue,.
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  • Newcomb’s problem isn’t a choice dilemma.Zhanglyu Li & Frank Zenker - 2021 - Synthese 199 (1-2):5125-5143.
    Newcomb’s problem involves a decision-maker faced with a choice and a predictor forecasting this choice. The agents’ interaction seems to generate a choice dilemma once the decision-maker seeks to apply two basic principles of rational choice theory : maximize expected utility ; adopt the dominant strategy. We review unsuccessful attempts at pacifying the dilemma by excluding Newcomb’s problem as an RCT-application, by restricting MEU and ADS, and by allowing for backward causation. A probability approach shows that Newcomb’s original problem-formulation lacks (...)
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  • On the regress problem of deciding how to decide.Hanti Lin - 2014 - Synthese 191 (4):661-670.
    Any decision is made in some way or another. Which way? (Have I worked out enough alternatives to choose from? Which decision rule to apply?) That is a higher-order decision problem, to be dealt with in some way or other. Which way? That is an even higher-order decision problem. There seems to be a regress of decision problems toward higher and higher orders. But in daily life we stop moving to higher-order decision problems—stop the regress—at some finite point. The regress (...)
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  • Modes of Convergence to the Truth: Steps Toward a Better Epistemology of Induction.L. I. N. Hanti - 2022 - Review of Symbolic Logic 15 (2):277-310.
    Evaluative studies of inductive inferences have been pursued extensively with mathematical rigor in many disciplines, such as statistics, econometrics, computer science, and formal epistemology. Attempts have been made in those disciplines to justify many different kinds of inductive inferences, to varying extents. But somehow those disciplines have said almost nothing to justify a most familiar kind of induction, an example of which is this: “We’ve seen this many ravens and they all are black, so all ravens are black.” This is (...)
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  • Foundations of Everyday Practical Reasoning.Hanti Lin - 2013 - Journal of Philosophical Logic 42 (6):831-862.
    “Since today is Saturday, the grocery store is open today and will be closed tomorrow; so let’s go today”. That is an example of everyday practical reasoning—reasoning directly with the propositions that one believes but may not be fully certain of. Everyday practical reasoning is one of our most familiar kinds of decisions but, unfortunately, some foundational questions about it are largely ignored in the standard decision theory: (Q1) What are the decision rules in everyday practical reasoning that connect qualitative (...)
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  • Betting on Machina’s reflection example: an experiment on ambiguity. [REVIEW]Olivier L’Haridon & Lætitia Placido - 2010 - Theory and Decision 69 (3):375-393.
    In a recent article, Machina (Am Econ Rev forthcoming, 2008) suggested choice problems in the spirit of Ellsberg (Q J Econ 75:643–669, 1961), which challenge tail-separability, an implication of Choquet expected utility (CEU), to a similar extent as the Ellsberg paradox challenged the sure-thing principle implied by subjective expected utility (SEU). We have tested choice behavior for bets on one of Machina’s choice problems, the reflection example. Our results indicate that tail-separability is violated by a large majority of subjects (over (...)
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  • The Logic of Consistency and the Logic of Truth.Isaac Levi - 2004 - Dialectica 58 (4):461-482.
    In “Truth and Probability” Ramsey claimed that the logic of consistency for probability is not a logic of truth. After supporting this claim, he proceeded to explore the possibilities for a logic of truth for probability. An examination of Ramsey's intent reveals that Ramsey was far from being an orthodox Bayesian when it comes to statistical reasoning. The relations between Ramsey's thought and the ideas of Keynes and Peirce are discussed.
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  • On the seriousness of mistakes.Isaac Levi - 1962 - Philosophy of Science 29 (1):47-65.
    Several authors have recently contended that modern statistical theory provides a powerful argument in favor of the view that if scientists accept or reject hypotheses at all they do so only in a behavioral sense--i.e., in a sense which reduces "accepting P" to "acting on the basis of P relative to an objective O". In this paper, the argument from statistics in favor of a behavioral view is outlined; an interpretation of two statistical procedures (Bayes method and signifigance testing) is (...)
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  • Imprecision and indeterminacy in probability judgment.Isaac Levi - 1985 - Philosophy of Science 52 (3):390-409.
    Bayesians often confuse insistence that probability judgment ought to be indeterminate (which is incompatible with Bayesian ideals) with recognition of the presence of imprecision in the determination or measurement of personal probabilities (which is compatible with these ideals). The confusion is discussed and illustrated by remarks in a recent essay by R. C. Jeffrey.
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  • Just Probabilities.Chad Lee-Stronach - forthcoming - Noûs.
    I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many have rejected this thesis because it seems to entail that defendants can be found liable solely on the basis of statistical evidence. I argue that this inference is invalid. I do so by developing a view, called Legal Causalism, that combines Thomson's (1986) causal analysis of evidence with recent work in formal theories of causal inference. On this view, legal standards of proof can be (...)
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  • People with Common Priors Can Agree to Disagree.Harvey Lederman - 2015 - Review of Symbolic Logic 8 (1):11-45.
    Robert Aumann presents his Agreement Theorem as the key conditional: “if two people have the same priors and their posteriors for an event A are common knowledge, then these posteriors are equal” (Aumann, 1976, p. 1236). This paper focuses on four assumptions which are used in Aumann’s proof but are not explicit in the key conditional: (1) that agents commonly know, of some prior μ, that it is the common prior; (2) that agents commonly know that each of them updates (...)
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  • In dubious battle: uncertainty and the ethics of killing.Seth Lazar - 2018 - Philosophical Studies 175 (4):859-883.
    How should deontologists concerned with the ethics of killing apply their moral theory when we don’t know all the facts relevant to the permissibility of our action? Though the stakes couldn’t be higher, and uncertainty is endemic where killing is concerned, few deontologists have an answer to this question. In this paper I canvass two possibilities: that we should apply a threshold standard, equivalent to the ‘beyond a reasonable doubt’ standard applied for criminal punishment; and that we should fit our (...)
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  • Equivalent decision trees and their associated strategy sets.Irving H. Lavalle & Peter C. Fishburn - 1987 - Theory and Decision 23 (1):37-63.
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  • Persuasion with Limited Sight.Alex Lascarides & Markus Guhe - 2019 - Review of Philosophy and Psychology 10 (1):1-33.
    Humans face many game problems that are too large for the whole game tree to be used in their deliberations about action, and very little is understood about how they cope in such scenarios. However, when a human player’s chosen strategy is conditioned on her limited perspective of how the game might progress, then it should be possible to manipulate her into changing her planned move by mentioning a possible outcome of an alternative move. This paper demonstrates that human players (...)
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  • Quantum physical symbol systems.Kathryn Blackmond Laskey - 2006 - Journal of Logic, Language and Information 15 (1-2):109-154.
    Because intelligent agents employ physically embodied cognitive systems to reason about the world, their cognitive abilities are constrained by the laws of physics. Scientists have used digital computers to develop and validate theories of physically embodied cognition. Computational theories of intelligence have advanced our understanding of the nature of intelligence and have yielded practically useful systems exhibiting some degree of intelligence. However, the view of cognition as algorithms running on digital computers rests on implicit assumptions about the physical world that (...)
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  • Mindreading and endogenous beliefs in games.Lauren Larrouy & Guilhem Lecouteux - 2017 - Journal of Economic Methodology 24 (3):318-343.
    We argue that a Bayesian explanation of strategic choices in games requires introducing a psychological theory of belief formation. We highlight that beliefs in epistemic game theory are derived from the actual choice of the players, and cannot therefore explain why Bayesian rational players should play the strategy they actually chose. We introduce the players’ capacity of mindreading in a game theoretical framework with the simulation theory, and characterise the beliefs that Bayes rational players could endogenously form in games. We (...)
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  • Valueless Measures on Pointless Spaces.Tamar Lando - 2022 - Journal of Philosophical Logic 52 (1):1-52.
    On our ordinary representations of space, space is composed of indivisible, dimensionless points; extended regions are understood as infinite sets of points. Region-based theories of space reverse this atomistic picture, by taking as primitive several relations on extended regions, and recovering points as higher-order abstractions from regions. Over the years, such theories have focused almost exclusively on the topological and geometric structure of space. We introduce to region-based theories of space a new primitive binary relation (‘qualitative probability’) that is tied (...)
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  • Probability intervals and rational norms.Henry E. Kyburg - 1985 - Behavioral and Brain Sciences 8 (4):753-754.
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  • Interpreting plural predication: homogeneity and non-maximality.Manuel Križ & Benjamin Spector - 2020 - Linguistics and Philosophy 44 (5):1131-1178.
    Plural definite descriptions across many languages display two well-known properties. First, they can give rise to so-called non-maximal readings, in the sense that they ‘allow for exceptions’. Second, while they tend to have a quasi-universal quantificational force in affirmative sentences, they tend to be interpreted existentially in the scope of negation. Building on previous works, we offer a theory in which sentences containing plural definite expressions trigger a family of possible interpretations, and where general principles of language use account for (...)
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  • Extensive measurement in semiorders.David H. Krantz - 1967 - Philosophy of Science 34 (4):348-362.
    In both axiomatic theories and the practice of extensive measurement, it is assumed that a series of replicas of any given object can be found. The replicas give rise to a standard series, the "multiples" of the given object. The numerical value assigned to any object is determined, approximately, by comparisons with members of a suitable standard series. This prescription introduces unspecified errors, if the comparison process is somewhat insensitive, so that "replicas" are not really equivalent. In this paper, it (...)
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  • The interpretation of uncertainty in ecological rationality.Anastasia Kozyreva & Ralph Hertwig - 2019 - Synthese 198 (2):1517-1547.
    Despite the ubiquity of uncertainty, scientific attention has focused primarily on probabilistic approaches, which predominantly rely on the assumption that uncertainty can be measured and expressed numerically. At the same time, the increasing amount of research from a range of areas including psychology, economics, and sociology testify that in the real world, people’s understanding of risky and uncertain situations cannot be satisfactorily explained in probabilistic and decision-theoretical terms. In this article, we offer a theoretical overview of an alternative approach to (...)
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  • The Foundations of Epistemic Decision Theory.Jason Konek & Benjamin A. Levinstein - 2019 - Mind 128 (509):69-107.
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  • How Does Coherence Matter?Niko Kolodny - 2007 - Proceedings of the Aristotelian Society 107 (1pt3):229 - 263.
    Recently, much attention has been paid to ‘rational requirements’ and, especially, to what I call ‘rational requirements of formal coherence as such’. These requirements are satisfied just when our attitudes are formally coherent: for example, when our beliefs do not contradict each other. Nevertheless, these requirements are puzzling. In particular, it is unclear why we should satisfy them. In light of this, I explore the conjecture that there are no requirements of formal coherence. I do so by trying to construct (...)
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  • Risk aversion and elite‐group ignorance.David Kinney & Liam Kofi Bright - 2021 - Philosophy and Phenomenological Research 106 (1):35-57.
    Critical race theorists and standpoint epistemologists argue that agents who are members of dominant social groups are often in a state of ignorance about the extent of their social dominance, where this ignorance is explained by these agents' membership in a socially dominant group (e.g., Mills 2007). To illustrate this claim bluntly, it is argued: 1) that many white men do not know the extent of their social dominance, 2) that they remain ignorant as to the extent of their dominant (...)
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  • On the Explanatory Depth and Pragmatic Value of Coarse-Grained, Probabilistic, Causal Explanations.David Kinney - 2018 - Philosophy of Science (1):145-167.
    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 (...)
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  • The foundations of statistics—are there any?J. Kiefer - 1977 - Synthese 36 (1):161 - 176.
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  • The information inelasticity of habits: Kahneman’s bounded rationality or Simon’s procedural rationality?Elias L. Khalil - 2022 - Synthese 200 (4):1-40.
    Why would decision makers adopt heuristics, priors, or in short “habits” that prevent them from optimally using pertinent information—even when such information is freely-available? One answer, Herbert Simon’s “procedural rationality” regards the question invalid: DMs do not, and in fact cannot, process information in an optimal fashion. For Simon, habits are the primitives, where humans are ready to replace them only when they no longer sustain a pregiven “satisficing” goal. An alternative answer, Daniel Kahneman’s “mental economy” regards the question valid: (...)
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  • Rational preference in transformative experiences.Saira Khan - 2021 - Synthese 199 (3-4):6715-6732.
    L. A. Paul’s Transformative Experience makes the claim that many important life decisions are epistemically and personally transformative in a way that does not allow us to assign subjective values to their outcomes. As a result, we cannot use normative decision theory to make such decisions rationally, or when we modify it to do so, decision theory leads us to choose in a way that is in tension with our authenticity. This paper examines Paul’s version of decision theory, and whether (...)
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  • Conquering Mount Everett: Branch-Counting Versus the Born Rule.Jake Khawaja - forthcoming - British Journal for the Philosophy of Science.
    Abstract: This paper develops and advocates a rule for assigning self-locating credences in quantum branching scenarios, called Indexed Branch-Counting. It is argued that Indexed Branch-Counting can be justified on both accuracy-theoretic grounds and on the grounds that it satisfies a requirement of exchangeability for probability assignments. Since Indexed Branch-Counting diverges from the Born Rule, this poses trouble for Everettian approaches to probability. The paper also addresses a common argument against branch-counting, namely that the rule is incoherent in light of putative (...)
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  • Judged Knowledge and Ambiguity Aversion.Hans-jÜrgen Keppe - 1995 - Theory and Decision 39 (1):51-77.
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