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The Foundations of Statistics

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

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  1. Generalized Learning and Conditional Expectation.Simon M. Huttegger & Michael Nielsen - 2020 - Philosophy of Science 87 (5):868-883.
    Reflection and martingale principles are central to models of rational learning. They can be justified in a variety of ways. In what follows we study martingale and reflection principles in the con...
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  • Bradley Conditionals and Dynamic Choice.Simon M. Huttegger & Gerard J. Rothfus - 2021 - Synthese 199 (3-4):6585-6599.
    One of the main contributions of Richard Bradley’s book is an elegant extension of Jeffrey’s Logic of Decision that countenances the evaluation of conditional prospects. This extension offers a promising new setting in which to model dynamic choice. In Bradley’s framework, plans can be understood as conditionals of an appropriate sort, while dynamic consistency can be viewed as providing a constraint on the evaluation of conditionals across time. In this paper, we study connections between planning conditionals and dynamic consistency.
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  • Who accepts Savage’s axiom now?Steven J. Humphrey & Nadia-Yasmine Kruse - 2023 - Theory and Decision 96 (1):1-17.
    We report the results of an experimental test of whether preaching the normative appeal of the sure-thing principle leads decision-makers to make choices that satisfy it. We use Allais-type decision problems to observe the incentive-compatible choices of 147 subjects, which either violate the sure-thing principle or adhere to it. Subjects are presented with normative arguments that support the counterfactual behaviour and then repeat their decisions. We observe violations of the sure-thing principle are robust to its normative justification. This result replicates (...)
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  • The evolution of group decision support systems to enable collaborative authoring of outcomes.Patrick Humphreys & Garrick Jones - 2006 - World Futures 62 (3):193 – 222.
    This article draws on analysis of a variety of problems emerging from practical applications of Group Decision Support Systems (GDSS) to propose a fundamental evolution of decision support models from the traditional single decision-spine model to the decision-hedgehog. It positions decision making through the construction of narratives making the rhizome that constitutes the body of the hedgehog with the fundamental aim of enriching understanding of the contexts of decision making. Localized processes constructing and exploring prescriptions for action within a plethora (...)
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  • There Is No Pure Empirical Reasoning.Michael Huemer - 2017 - Philosophy and Phenomenological Research 95 (3):592-613.
    The justificatory force of empirical reasoning always depends upon the existence of some synthetic, a priori justification. The reasoner must begin with justified, substantive constraints on both the prior probability of the conclusion and certain conditional probabilities; otherwise, all possible degrees of belief in the conclusion are left open given the premises. Such constraints cannot in general be empirically justified, on pain of infinite regress. Nor does subjective Bayesianism offer a way out for the empiricist. Despite often-cited convergence theorems, subjective (...)
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  • Statistical Approach Involving Bayes' Theorem and the Estimation of the Prior Distribution.Hirosi Hudimoto - 1971 - Annals of the Japan Association for Philosophy of Science 4 (1):35-45.
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  • Theories of probability.Colin Howson - 1995 - British Journal for the Philosophy of Science 46 (1):1-32.
    My title is intended to recall Terence Fine's excellent survey, Theories of Probability [1973]. I shall consider some developments that have occurred in the intervening years, and try to place some of the theories he discussed in what is now a slightly longer perspective. Completeness is not something one can reasonably hope to achieve in a journal article, and any selection is bound to reflect a view of what is salient. In a subject as prone to dispute as this, there (...)
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  • Ramsey's Foundations Extended to Desirabilities.Jordan Howard Sobel - 1998 - Theory and Decision 44 (3):231-278.
    In his Truth and Probability (1926), Frank Ramsey provides foundations for measures of degrees of belief in propositions and preferences for worlds. Nonquantitative conditions on preferences for worlds, and gambles for worlds and certain near-worlds, are formulated which he says insure that a subject's preferences for worlds are represented by numbers, world values. Numbers, for his degrees of belief in propositions, probabilities, are then defined in terms of his world values. Ramsey does not also propose definitions of desirabilities for propositions, (...)
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  • Predicting Short‐Term Remembering as Boundedly Optimal Strategy Choice.Andrew Howes, Geoffrey B. Duggan, Kiran Kalidindi, Yuan-Chi Tseng & Richard L. Lewis - 2016 - Cognitive Science 40 (5):1192-1223.
    It is known that, on average, people adapt their choice of memory strategy to the subjective utility of interaction. What is not known is whether an individual's choices are boundedly optimal. Two experiments are reported that test the hypothesis that an individual's decisions about the distribution of remembering between internal and external resources are boundedly optimal where optimality is defined relative to experience, cognitive constraints, and reward. The theory makes predictions that are tested against data, not fitted to it. The (...)
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  • Putting on the Garber Style? Better Not.Colin Howson - 2017 - Philosophy of Science 84 (4):659-676.
    This article argues that not only are there serious internal difficulties with both Garber’s and later ‘Garber-style’ solutions of the old-evidence problem, including a recent proposal of Hartmann and Fitelson, but Garber-style approaches in general cannot solve the problem. It also follows the earlier lead of Rosenkrantz in pointing out that, despite the appearance to the contrary which inspired Garber’s nonclassical development of the Bayesian theory, there is a straightforward, classically Bayesian, solution.
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  • Popper, prior probabilities, and inductive inference.Colin Howson - 1987 - British Journal for the Philosophy of Science 38 (2):207-224.
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  • Logic with numbers.Colin Howson - 2007 - Synthese 156 (3):491-512.
    Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is (...)
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  • Logic and probability.Colin Howson - 1997 - British Journal for the Philosophy of Science 48 (4):517-531.
    This paper argues that Ramsey's view of the calculus of subjective probabilities as, in effect, logical axioms is the correct view, with powerful heuristic value. This heuristic value is seen particularly in the analysis of the role of conditionalization in the Bayesian theory, where a semantic criterion of synchronic coherence is employed as the test of soundness, which the traditional formulation of conditionalization fails. On the other hand, there is a generally sound rule which supports conditionalization in appropriate contexts, though (...)
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  • De finetti, countable additivity, consistency and coherence.Colin Howson - 2008 - British Journal for the Philosophy of Science 59 (1):1-23.
    Many people believe that there is a Dutch Book argument establishing that the principle of countable additivity is a condition of coherence. De Finetti himself did not, but for reasons that are at first sight perplexing. I show that he rejected countable additivity, and hence the Dutch Book argument for it, because countable additivity conflicted with intuitive principles about the scope of authentic consistency constraints. These he often claimed were logical in nature, but he never attempted to relate this idea (...)
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  • A logic of induction.Colin Howson - 1997 - Philosophy of Science 64 (2):268-290.
    In this paper, I present a simple and straightforward logic of induction: a consequence relation characterized by a proof theory and a semantics. This system will be called LI. The premises will be restricted to, on the one hand, a set of empirical data and, on the other hand, a set of background generalizations. Among the consequences will be generalizations as well as singular statements, some of which may serve as predictions and explanations.
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  • Decision Theory in Light of Newcomb’s Problem.Paul Horwich - 1985 - Philosophy of Science 52 (3):431-450.
    Should we act only for the sake of what we might bring about (causal decision theory); or is it enough for a decent motive that our action is highly correlated with something desirable (evidential decision theory)? The conflict between these points of view is embodied in Newcomb's problem. It is argued here that intuitive evidence from familiar decision contexts does not enable us to settle the issue, since the two theories dictate the same results in normal circumstances. Nevertheless, there are (...)
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  • Carnap's inductive probabilities as a contribution to decision theory.Joachim Hornung - 1980 - Theoretical Medicine and Bioethics 1 (3):325-367.
    Common probability theories only allow the deduction of probabilities by using previously known or presupposed probabilities. They do not, however, allow the derivation of probabilities from observed data alone. The question thus arises as to how probabilities in the empirical sciences, especially in medicine, may be arrived at. Carnap hoped to be able to answer this question byhis theory of inductive probabilities. In the first four sections of the present paper the above mentioned problem is discussed in general. After a (...)
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  • Know Your Way Out of St. Petersburg: An Exploration of "Knowledge-First" Decision Theory.Frank Hong - forthcoming - Erkenntnis:1-20.
    This paper explores the consequences of applying two natural ideas from epistemology to decision theory: (1) that knowledge should guide our actions, and (2) that we know a lot of non-trivial things. In particular, we explore the consequences of these ideas as they are applied to standard decision theoretic puzzles such as the St. Petersburg Paradox. In doing so, we develop a “knowledge-first” decision theory and we will see how it can help us avoid fanaticism with regard to the St. (...)
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  • Economics and the Limits of Optimization: Steps Towards Extending Bernard Hodgson’s Moral Science. [REVIEW]David Geoffrey Holdsworth - 2012 - Journal of Business Ethics 108 (1):37-48.
    In this essay, my point of departure is Bernard Hodgson’s analysis of neo-classical economic theory and his demonstration that neo-classical economic thought is already a branch of normative theory. I undertake to broaden the demonstration by showing that other contemporary conceptions of economics are also irreducibly normative. The essay begins with an overview of Hodgson’s argument strategy, and a discussion of his thesis that economics is a moral science. This illustrates in what way moral presuppositions are at play as core (...)
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  • Chance and the Continuum Hypothesis.Daniel Hoek - 2021 - Philosophy and Phenomenological Research 103 (3):639-60.
    This paper presents and defends an argument that the continuum hypothesis is false, based on considerations about objective chance and an old theorem due to Banach and Kuratowski. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. Since it is possible to randomly pick (...)
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  • Triviality Pursuit.Alan Hájek - 2011 - Topoi 30 (1):3-15.
    The thesis that probabilities of conditionals are conditional probabilities has putatively been refuted many times by so-called ‘triviality results’, although it has also enjoyed a number of resurrections. In this paper I assault it yet again with a new such result. I begin by motivating the thesis and discussing some of the philosophical ramifications of its fluctuating fortunes. I will canvas various reasons, old and new, why the thesis seems plausible, and why we should care about its fate. I will (...)
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  • Risky business.Alan Hájek - 2021 - Philosophical Perspectives 35 (1):189-205.
    Philosophical Perspectives, Volume 35, Issue 1, Page 189-205, December 2021.
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  • Perplexing expectations.Alan Hájek & Harris Nover - 2006 - Mind 115 (459):703 - 720.
    This paper revisits the Pasadena game (Nover and Háyek 2004), a St Petersburg-like game whose expectation is undefined. We discuss serveral respects in which the Pasadena game is even more troublesome for decision theory than the St Petersburg game. Colyvan (2006) argues that the decision problem of whether or not to play the Pasadena game is ‘ill-posed’. He goes on to advocate a ‘pluralism’ regarding decision rules, which embraces dominance reasoning as well as maximizing expected utility. We rebut Colyvan’s argument, (...)
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  • A Tale of Two Epistemologies?Alan Hájek & Hanti Lin - 2017 - Res Philosophica 94 (2):207-232.
    So-called “traditional epistemology” and “Bayesian epistemology” share a word, but it may often seem that the enterprises hardly share a subject matter. They differ in their central concepts. They differ in their main concerns. They differ in their main theoretical moves. And they often differ in their methodology. However, in the last decade or so, there have been a number of attempts to build bridges between the two epistemologies. Indeed, many would say that there is just one branch of philosophy (...)
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  • The coherence argument against conditionalization.Matthias Hild - 1998 - Synthese 115 (2):229-258.
    I re-examine Coherence Arguments (Dutch Book Arguments, No Arbitrage Arguments) for diachronic constraints on Bayesian reasoning. I suggest to replace the usual game–theoretic coherence condition with a new decision–theoretic condition ('Diachronic Sure Thing Principle'). The new condition meets a large part of the standard objections against the Coherence Argument and frees it, in particular, from a commitment to additive utilities. It also facilitates the proof of the Converse Dutch Book Theorem. I first apply the improved Coherence Argument to van Fraassen's (...)
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  • Ambiguity aversion under maximum-likelihood updating.Daniel Heyen - 2018 - Theory and Decision 84 (3):373-386.
    Maximum-likelihood updating is a well-known approach for extending static ambiguity sensitive preferences to dynamic set-ups. This paper develops an example in which MLU induces an ambiguity averse maxmin expected utility decision-maker to prefer a bet on an ambiguous over a risky urn and be more willing to bet on the ambiguous urn compared to an subjective expected utility decision-maker. This is challenging, since prior to observing draws from the urns, the MEU decision-maker actually preferred the risky over the ambiguous bet (...)
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  • A Sense of Mission: The Alfred P. Sloan and Russell Sage Foundations' Behavioral Economics Program, 1984–1992.Floris Heukelom - 2012 - Science in Context 25 (2):263-286.
    ArgumentThe main contribution of the Alfred P. Sloan and Russell Sage Foundations' behavioral economics program (1984–1992) was not the resources it provided, which were relatively modest. Instead, the program's contribution lay in catalyzing “a sense of mission” in the collaboration between psychologists Daniel Kahneman and Amos Tversky, economist Richard Thaler, and their associates. Partly this reflected the common strategy of American foundations to pick an individual or small group of scientists and stick with them until scientific success had been achieved. (...)
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  • The psychology and rationality of decisions from experience.Ralph Hertwig - 2012 - Synthese 187 (1):269-292.
    Most investigations into how people make risky choices have employed a simple drosophila: monetary gambles involving stated outcomes and probabilities. People are asked to make decisions from description . When people decide whether to back up their computer hard drive, cross a busy street, or go out on a date, however, they do not enjoy the convenience of stated outcomes and probabilities. People make such decisions either in the void of ignorance or in the twilight of their own often limited (...)
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  • Rational choice as a toolbox for the economist: an interview with Itzhak Gilboa.Catherine Herfeld - 2014 - Erasmus Journal for Philosophy and Economics 7 (2):116-141.
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  • Prediction with expert advice applied to the problem of prediction with expert advice.Daniel A. Herrmann - 2022 - Synthese 200 (4):1-24.
    We often need to have beliefs about things on which we are not experts. Luckily, we often have access to expert judgements on such topics. But how should we form our beliefs on the basis of expert opinion when experts conflict in their judgments? This is the core of the novice/2-expert problem in social epistemology. A closely related question is important in the context of policy making: how should a policy maker use expert judgments when making policy in domains in (...)
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  • Divisive conditioning: Further results on dilation.Timothy Herron, Teddy Seidenfeld & Larry Wasserman - 1997 - Philosophy of Science 64 (3):411-444.
    Conditioning can make imprecise probabilities uniformly more imprecise. We call this effect "dilation". In a previous paper (1993), Seidenfeld and Wasserman established some basic results about dilation. In this paper we further investigate dilation on several models. In particular, we consider conditions under which dilation persists under marginalization and we quantify the degree of dilation. We also show that dilation manifests itself asymptotically in certain robust Bayesian models and we characterize the rate at which dilation occurs.
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  • Variational Free Energy and Economics Optimizing With Biases and Bounded Rationality.Morten Henriksen - 2020 - Frontiers in Psychology 11.
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  • Higher‐order evidence and losing one's conviction.Leah Henderson - 2022 - Noûs 56 (3):513-529.
    There has been considerable puzzlement over how to respond to higher-order evidence. The existing dilemmas can be defused by adopting a ‘two-dimensional’ representation of doxastic attitudes which incorporates not only substantive uncertainty about which first-order state of affairs obtains but also the degree of conviction with which we hold the attitude. This makes it possible that in cases of higher-order evidence the evidence sometimes impacts primarily on our conviction, rather than our substantive uncertainty. I argue that such a two-dimensional representation (...)
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  • Quantum probability and many worlds.Meir Hemmo - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):333-350.
    We discuss the meaning of probabilities in the many worlds interpretation of quantum mechanics. We start by presenting very briefly the many worlds theory, how the problem of probability arises, and some unsuccessful attempts to solve it in the past. Then we criticize a recent attempt by Deutsch to derive the quantum mechanical probabilities from the nonprobabilistic parts of quantum mechanics and classical decision theory. We further argue that the Born probability does not make sense even as an additional probability (...)
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  • Truth does not explain predictive success.Carsten Held - 2011 - Analysis 71 (2):232-234.
    Laudan famously argued that neither truth nor approximate truth can be part of an explanation of a scientific theory's predictive success because in the history of science there were theories that enjoyed some limited success but now are considered outright false. The power of his argument lay in the many historic examples he listed . Realists have disputed that all theories on Laudan's list can be regarded as predictively successful but let's suppose momentarily that at least some exist that support (...)
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  • Structuring Decisions Under Deep Uncertainty.Casey Helgeson - 2020 - Topoi 39 (2):257-269.
    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 (...)
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  • Rationalizing two-tiered choice functions through conditional choice.Jeffrey Helzner - 2013 - Synthese 190 (6):929-951.
    Set-valued choice functions provide a framework that is general enough to encompass a wide variety of theories that are significant to the study of rationality but, at the same time, offer enough structure to articulate consistency conditions that can be used to characterize some of the theories within this encompassed variety. Nonetheless, two-tiered choice functions, such as those advocated by Isaac Levi, are not easily characterized within the framework of set-valued choice functions. The present work proposes conditional choice functions as (...)
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  • On the representation of error.Jeffrey Helzner - 2012 - Synthese 186 (2):601-613.
    Though he maintained a significant interest in theoretical aspects of measurement, Henry E. Kyburg, Jr. was critical of the representational theory that in many ways has come to dominate discussions concerning the foundations of measurement. In particular, Kyburg (in Savage and Ehrlich (eds) Philosophical and foundational issues in measurement theory, 1992 ) asserts that the representational theory of measurement, as introduced in (Scott and Suppes, Journal of Symbolic Logic, 23:113–128, 1958 ) and developed in (Krantz et al., Foundations of measurment: (...)
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  • Expected content.Jeffrey Helzner - 2008 - Review of Symbolic Logic 1 (4):424-432.
    We propose an approach to assigning propositional content to deliberate acts of arbitrary type, as opposed to just speech acts. This approach, which is based on the idea that the content of an act is the decision maker's expectation concerning the change that would take place if the act were to be performed, is shown to be related to the concept of expected utility that has played a central role in various accounts of rationality.
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  • Rational Choice with Deontic Constraints.Joseph Heath - 2001 - Canadian Journal of Philosophy 31 (3):361-388.
    Anyone who has ever lived with roommates understands the Hobbesian state of nature implicitly. People sharing accommodations quickly discover that buying groceries, doing the dishes, sweeping the floor, and a thousand other household tasks, are all prisoner's dilemmas waiting to happen. For instance, if food is purchased communally, it gives everyone an incentive to overconsume. Individuals also have an incentive to buy expensive items that the others are unlikely to want. As a result, everyone's food bill will be higher than (...)
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  • Rational Choice with Deontic Constraints.Joseph Heath - 2001 - Canadian Journal of Philosophy 31 (3):361-388.
    Anyone who has ever lived with roommates understands the Hobbesian state of nature implicitly. People sharing accommodations quickly discover that buying groceries, doing the dishes, sweeping the floor, and a thousand other household tasks, are all prisoner's dilemmas waiting to happen. For instance, if food is purchased communally, it gives everyone an incentive to overconsume. Individuals also have an incentive to buy expensive items that the others are unlikely to want. As a result, everyone's food bill will be higher than (...)
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  • No Title available: Reviews.Joseph Heath - 1996 - Economics and Philosophy 12 (2):243-249.
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  • Subjectively weighted linear utility.Gordon B. Hazen - 1987 - Theory and Decision 23 (3):261-282.
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  • On the logic of nonmonotonic conditionals and conditional probabilities.James Hawthorne - 1996 - Journal of Philosophical Logic 25 (2):185-218.
    I will describe the logics of a range of conditionals that behave like conditional probabilities at various levels of probabilistic support. Families of these conditionals will be characterized in terms of the rules that their members obey. I will show that for each conditional, →, in a given family, there is a probabilistic support level r and a conditional probability function P such that, for all sentences C and B, 'C → B' holds just in case P[B | C] ≥ (...)
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  • Radical interpretation and decision theory.Anandi Hattiangadi & H. Orri Stefánsson - 2021 - Synthese 199 (3-4):6473-6494.
    This paper takes issue with an influential interpretationist argument for physicalism about intentionality based on the possibility of radical interpretation. The interpretationist defends the physicalist thesis that the intentional truths supervene on the physical truths by arguing that it is possible for a radical interpreter, who knows all of the physical truths, to work out the intentional truths about what an arbitrary agent believes, desires, and means without recourse to any further empirical information. One of the most compelling arguments for (...)
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  • Varieties of paternalism and the heterogeneity of utility structures.Glenn W. Harrison & Don Ross - 2018 - Journal of Economic Methodology 25 (1):42-67.
    A principal source of interest in behavioral economics has been its advertised contributions to policies aimed at ‘nudging’ people away from allegedly natural but self-defeating behavior toward patterns of response thought more likely to improve their welfare. This has occasioned controversies among economists and philosophers around the normative limits of paternalism, especially by technical policy advisors. One recent suggestion has been that ‘boosting,’ in which interventions aim to enhance people’s general cognitive skills and representational repertoires instead of manipulating their choice (...)
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  • The empirical adequacy of cumulative prospect theory and its implications for normative assessment.Glenn W. Harrison & Don Ross - 2017 - Journal of Economic Methodology 24 (2):150-165.
    Much behavioral welfare economics assumes that expected utility theory does not accurately describe most human choice under risk. A substantial literature instead evaluates welfare consequences by taking cumulative prospect theory as the natural default alternative, at least where description is concerned. We present evidence, based on a review of previous literature and new experimental data, that the most empirically adequate hypothesis about human choice under risk is that it is heterogeneous, and that where EUT does not apply, more choice is (...)
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  • Independent postulates for subjective expected utility.Mikko Harju, Juuso Liesiö & Kai Virtanen - forthcoming - Theory and Decision:1-10.
    Although the subjective expected utility (SEU) theory is more than 60 years old, it was recently discovered by Hartmann (Econometrica 88(1):203–205, 2020, https://doi.org/10.3982/ECTA17428) that one of the original seven postulates is redundant, i.e., it is implied by the other six postulates. In this brief communication, we show that this redundant axiom is the only one that is implied by the other axioms, thereby establishing that the remaining six postulates form an independent axiomatic system. This result further streamlines the preference assumptions (...)
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  • How to play the ultimatum game: An engineering approach to metanormativity.Benoit Hardy-Vallée & Paul Thagard - 2008 - Philosophical Psychology 21 (2):173 – 192.
    The ultimatum game is a simple bargaining situation where the behavior of people frequently contradicts the optimal strategy according to classical game theory. Thus, according to many scholars, the commonly observed behavior should be considered irrational. We argue that this putative irrationality stems from a wrong conception of metanormativity (the study of norms about the establishment of norms). After discussing different metanormative conceptions, we defend a Quinean, naturalistic approach to the evaluation of norms. After reviewing empirical literature on the ultimatum (...)
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  • Full Belief and Probability: Comments on Van Fraassen.William Harper & Alan Hajek - 1997 - Dialogue 36 (1):91 - 100.
    As van Fraassen pointed out in his opening remarks, Henry Kyburg's lottery paradox has long been known to raise difficulties in attempts to represent full belief as a probability greater than or equal to p, where p is some number less than 1. Recently, Patrick Maher has pointed out that to identify full belief with probability equal to 1 presents similar difficulties. In his paper, van Fraassen investigates ways of representing full belief by personal probability which avoid the difficulties raised (...)
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