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The Foundations of Statistics

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

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  1. Conditional probabilities and probabilities given knowledge of a condition.Paul Weirich - 1983 - Philosophy of Science 50 (1):82-95.
    The conditional probability of h given e is commonly claimed to be equal to the probability that h would have if e were learned. Here I contend that this general claim about conditional probabilities is false. I present a counter-example that involves probabilities of probabilities, a second that involves probabilities of possible future actions, and a third that involves probabilities of indicative conditionals. In addition, I briefly defend these counter-examples against charges that the probabilities they involve are illegitimate.
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  • A decision maker's options.Paul Weirich - 1983 - Philosophical Studies 44 (2):175 - 186.
    An agent's options in a decision problem are best understood as the decisions that the agent might make. Taking options this way eliminates the gap between an option's adoption and its execution.
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  • Gandalf’s solution to the Newcomb problem.Ralph Wedgwood - 2013 - Synthese 190 (14):2643–2675.
    This article proposes a new theory of rational decision, distinct from both causal decision theory (CDT) and evidential decision theory (EDT). First, some intuitive counterexamples to CDT and EDT are presented. Then the motivation for the new theory is given: the correct theory of rational decision will resemble CDT in that it will not be sensitive to any comparisons of absolute levels of value across different states of nature, but only to comparisons of the differences in value between the available (...)
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  • “Tough-Minded” Theories in Ethics.Michael Weber - 2006 - Dialogue 45 (4):747-754.
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  • A robust resolution of Newcomb’s paradox.Thomas A. Weber - 2016 - Theory and Decision 81 (3):339-356.
    Newcomb’s problem is viewed as a dynamic game with an agent and a superior being as players. Depending on whether or not a risk-neutral agent’s confidence in the superior being, as measured by a subjective probability assigned to the move order, exceeds a threshold or not, one obtains the one-box outcome or the two-box outcome, respectively. The findings are extended to an agent with arbitrary increasing utility, featuring in general two thresholds. All solutions require only minimal assumptions about the being’s (...)
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  • Local Explanations via Necessity and Sufficiency: Unifying Theory and Practice.David S. Watson, Limor Gultchin, Ankur Taly & Luciano Floridi - 2022 - Minds and Machines 32 (1):185-218.
    Necessity and sufficiency are the building blocks of all successful explanations. Yet despite their importance, these notions have been conceptually underdeveloped and inconsistently applied in explainable artificial intelligence, a fast-growing research area that is so far lacking in firm theoretical foundations. In this article, an expanded version of a paper originally presented at the 37th Conference on Uncertainty in Artificial Intelligence, we attempt to fill this gap. Building on work in logic, probability, and causality, we establish the central role of (...)
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  • Beliefs, Actions, and Rationality in Strategical Decisions.Zheng Wang, Jerome R. Busemeyer & Brahm deBuys - 2022 - Topics in Cognitive Science 14 (3):492-507.
    Topics in Cognitive Science, Volume 14, Issue 3, Page 492-507, July 2022.
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  • Beliefs, Actions, and Rationality in Strategical Decisions.Zheng Wang, Jerome R. Busemeyer & Brahm deBuys - 2022 - Topics in Cognitive Science 14 (3):492-507.
    A puzzling finding from research on strategic decision making concerns the effect that predictions have on future actions. Simply stating a prediction about an opponent changes the total probability (pooled over predictions) of a player taking a future action as compared to not stating any prediction. These interference effects are difficult to explain using traditional economic models, and instead these results suggest turning to a quantum cognition approach to strategic decision making.
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  • Varieties of modal (classificatory) and comparative probability.Peter Walley & Terrence L. Fine - 1979 - Synthese 41 (3):321 - 374.
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  • Quantum probability from subjective likelihood: Improving on Deutsch's proof of the probability rule.David Wallace - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):311-332.
    I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but the proof is simpler and proceeds from weaker decision-theoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible.
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  • Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation.David Wallace - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):415-439.
    An analysis is made of Deutsch's recent claim to have derived the Born rule from decision-theoretic assumptions. It is argued that Deutsch's proof must be understood in the explicit context of the Everett interpretation, and that in this context, it essentially succeeds. Some comments are made about the criticism of Deutsch's proof by Barnum, Caves, Finkelstein, Fuchs, and Schack; it is argued that the flaw which they point out in the proof does not apply if the Everett interpretation is assumed.
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  • Diachronic Rationality and Prediction-Based Games.David Wallace - 2010 - Proceedings of the Aristotelian Society 110 (3pt3):243-266.
    I explore the debate about causal versus evidential decision theory, and its recent developments in the work of Andy Egan, through the method of some simple games based on agents' predictions of each other's actions. My main focus is on the requirement for rational agents to act in a way which is consistent over time and its implications for such games and their more realistic cousins.
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  • Separating marginal utility and probabilistic risk aversion.Peter Wakker - 1994 - Theory and Decision 36 (1):1-44.
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  • Jaffray’s ideas on ambiguity.Peter P. Wakker - 2011 - Theory and Decision 71 (1):11-22.
    This paper discusses Jean-Yves Jaffray’s ideas on ambiguity and the views underlying his ideas. His models, developed 20 years ago, provide the most tractable separation of risk attitudes, ambiguity attitudes, and ambiguity beliefs available in the literature today.
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  • Misadventures in conditional expectation: The two-envelope problem. [REVIEW]Carl G. Wagner - 1999 - Erkenntnis 51 (2-3):233-241.
    Several fallacies of conditionalization are illustrated, using the two-envelope problem as a case in point.
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  • Ultimate and proximate explanations of strong reciprocity.Jack Vromen - 2017 - History and Philosophy of the Life Sciences 39 (3):25.
    Strong reciprocity has recently been subject to heated debate. In this debate, the “West camp” :231–262, 2011), which is critical of the case for SR, and the “Laland camp” :1512–1516, 2011, Biol Philos 28:719–745, 2013), which is sympathetic to the case of SR, seem to take diametrically opposed positions. The West camp criticizes advocates of SR for conflating proximate and ultimate causation. SR is said to be a proximate mechanism that is put forward by its advocates as an ultimate explanation (...)
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  • Transitivity, the Sorites Paradox, and Similarity-Based Decision-making.Alex Voorhoeve & Ken Binmore - 2006 - Erkenntnis 64 (1):101-114.
    A persistent argument against the transitivity assumption of rational choice theory postulates a repeatable action that generates a significant benefit at the expense of a negligible cost. No matter how many times the action has been taken, it therefore seems reasonable for a decision-maker to take the action one more time. However, matters are so fixed that the costs of taking the action some large number of times outweigh the benefits. In taking the action some large number of times on (...)
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  • How Much Ambiguity Aversion? Finding Indifferences between Ellsberg's Risky and Ambiguous Bets.Ken Binmore, Lisa Stewart & Alex Voorhoeve - 2012 - Journal of Risk and Uncertainty 45 (3):215-38.
    Experimental results on the Ellsberg paradox typically reveal behavior that is commonly interpreted as ambiguity aversion. The experiments reported in the current paper find the objective probabilities for drawing a red ball that make subjects indifferent between various risky and uncertain Ellsberg bets. They allow us to examine the predictive power of alternative principles of choice under uncertainty, including the objective maximin and Hurwicz criteria, the sure-thing principle, and the principle of insufficient reason. Contrary to our expectations, the principle of (...)
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  • Ambiguity Attitudes, Framing and Consistency.Alex Voorhoeve, Ken G. Binmore, Arnaldur Stefansson & Lisa Stewart - 2016 - Theory and Decision 81 (3):313-337.
    We use probability-matching variations on Ellsberg’s single-urn experiment to assess three questions: (1) How sensitive are ambiguity attitudes to changes from a gain to a loss frame? (2) How sensitive are ambiguity attitudes to making ambiguity easier to recognize? (3) What is the relation between subjects’ consistency of choice and the ambiguity attitudes their choices display? Contrary to most other studies, we find that a switch from a gain to a loss frame does not lead to a switch from ambiguity (...)
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  • Prudence and extensionality in theories of preference and value.J. M. Vickers - 1995 - Theory and Decision 39 (3):267-299.
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  • On the Reality of Chance.John M. Vickers - 1978 - PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978 (2):563-578.
    In this paper I consider the question of the reality of chance. This is not what divides contemporary probabilists into the objective and subjective schools. That division is accomplished by the question whether there are objective grounds for the correctness of probability judgments. The subjectivists say that there need not be such grounds, and that probability judgments thus need not be empirically meaningful in the verificationist sense, or perhaps that they are not judgments at all, but rather expressions of attitude. (...)
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  • Logic, probability, and coherence.John M. Vickers - 2001 - Philosophy of Science 68 (1):95-110.
    How does deductive logic constrain probability? This question is difficult for subjectivistic approaches, according to which probability is just strength of (prudent) partial belief, for this presumes logical omniscience. This paper proposes that the way in which probability lies always between possibility and necessity can be made precise by exploiting a minor theorem of de Finetti: In any finite set of propositions the expected number of truths is the sum of the probabilities over the set. This is generalized to apply (...)
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  • The normative and descriptive weaknesses of behavioral economics-informed nudge: depowered paternalism and unjustified libertarianism.Riccardo Viale - 2018 - Mind and Society 17 (1):53-69.
    The article aims to demonstrate that the nudge theory suffers from three main weaknesses stemming from its theoretical dependence on behavioural economics. The first two weaknesses endanger the paternalistic goal, whereas the third does not justify the libertarian attribute. The first weakness lies in the incomplete realistic characterisation of behavioural economics theory that is the central theoretical pillar of Nudge theory. The second weakness is even more relevant. The normative model of behavioural economics is neoclassical rationality. It can be applied (...)
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  • The epistemic uncertainty of COVID-19: failures and successes of heuristics in clinical decision-making.Riccardo Viale - 2020 - Mind and Society 20 (1):149-154.
    The brief article deals with the following questions: Was the adaptive toolbox of heuristics ecologically rational and specifically accurate in the initial stages of COVID-19, which was characterized by epistemic uncertainty? In other words, in dealing with COVID-19 did the environmental structural variables allow the success of a given heuristic strategy?
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  • Robust winner determination in positional scoring rules with uncertain weights.Paolo Viappiani - 2020 - Theory and Decision 88 (3):323-367.
    Scoring rules constitute a particularly popular technique for aggregating a set of rankings. However, setting the weights associated with rank positions is a crucial task, as different instantiations of the weights can often lead to different winners. In this work we adopt minimax regret as a robust criterion for determining the winner in the presence of uncertainty over the weights. Focusing on two general settings we provide a characterization of the minimax regret rule in terms of cumulative ranks, allowing a (...)
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  • Goals and the Informativeness of Prior Probabilities.Olav Benjamin Vassend - 2017 - Erkenntnis:1-24.
    I argue that information is a goal-relative concept for Bayesians. More precisely, I argue that how much information is provided by a piece of evidence depends on whether the goal is to learn the truth or to rank actions by their expected utility, and that different confirmation measures should therefore be used in different contexts. I then show how information measures may reasonably be derived from confirmation measures, and I show how to derive goal-relative non-informative and informative priors given background (...)
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  • Biased information and the exchange paradox.Anubav Vasudevan - 2019 - Synthese 196 (6):2455-2485.
    This paper presents a new solution to the well-known exchange paradox, or what is sometimes referred to as the two-envelope paradox. Many recent commentators have analyzed the paradox in terms of the agent’s biased concern for the contents of his own arbitrarily chosen envelope, claiming that such bias violates the manifest symmetry of the situation. Such analyses, however, fail to make clear exactly how the symmetry of the situation is violated by the agent’s hypothetical conclusion that he ought to switch (...)
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  • Utility, informativity and protocols.Robert van Rooy - 2004 - Journal of Philosophical Logic 33 (4):389-419.
    Recently, natural language pragmatics started to make use of decision-, game-, and information theoretical tools to determine the usefulness of questions and assertions in a quantitative way. In the first part of this paper several of these notions are related with each other. It is shown that under particular natural assumptions the utility of questions and answers reduces to their informativity, and that the ordering relation induced by utility sometimes even reduces to the logical relation of entailment. The second part (...)
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  • Samir Okasha and Ken Binmore's Evolution and rationality: decisions, co-operation, and strategic behaviour. Cambridge: Cambridge University Press, 2012, 281 pp. [REVIEW]Wiljan Van den Berge - 2013 - Erasmus Journal for Philosophy and Economics 6 (1):147.
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  • Questioning to resolve decision problems.Robert van Rooy - 2003 - Linguistics and Philosophy 26 (6):727-763.
    Why do we ask questions? Because we want tohave some information. But why this particular kind ofinformation? Because only information of this particularkind is helpful to resolve the decision problemthat the agent faces. In this paper I argue thatquestions are asked because their answers help toresolve the questioner's decision problem, and that thisassumption helps us to interpret interrogativesentences. Interrogative sentences are claimed to have asemantically underspecified meaning and thisunderspecification is resolved by means of the decisionproblem.
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  • Quality and quantity of information exchange.Robert van Rooy - 2003 - Journal of Logic, Language and Information 12 (4):423-451.
    The paper deals with credible and relevantinformation flow in dialogs: How useful is it for areceiver to get some information, how useful is it fora sender to give this information, and how much credibleinformation can we expect to flow between sender andreceiver? What is the relation between semantics andpragmatics? These Gricean questions will be addressedfrom a decision and game-theoretical point of view.
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  • Logic and the Self: After Certain Crises in Western Thought.Bas C. van Fraassen - 2011 - Diogenes 58 (4):21-29.
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  • Is Economic Rationality in the Head?Kevin Vallier - 2015 - Minds and Machines 25 (4):339-360.
    Many economic theorists hold that social institutions can lead otherwise irrational agents to approximate the predictions of traditional rational choice theory. But there is little consensus on how institutions do so. I defend an economic internalist account of the institution-actor relationship by explaining economic rationality as a feature of individuals whose decision-making is aided by institutional structures. This approach, known as the subjective transaction costs theory, represents apparently irrational behavior as a rational response to high subjective transaction costs of thinking (...)
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  • Rational choice(s)? Rethinking decision-making on breast cancer risk and screening mammography.Mandana Vahabi & Denise Gastaldo - 2003 - Nursing Inquiry 10 (4):245-256.
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  • Bayesian Rationality Revisited: Integrating Order Effects.Pierre Uzan - 2023 - Foundations of Science 28 (2):507-528.
    Bayes’ inference cannot reliably account for uncertainty in mental processes. The reason is that Bayes’ inference is based on the assumption that the order in which the relevant features are evaluated is indifferent, which is not the case in most of mental processes. Instead of Bayes’ rule, a more general, probabilistic rule of inference capable of accounting for these order effects is established. This new rule of inference can be used to improve the current Bayesian models of cognition. Moreover, it (...)
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  • A convention or (tacit) agreement betwixt us: on reliance and its normative consequences.Luca Tummolini, Giulia Andrighetto, Cristiano Castelfranchi & Rosaria Conte - 2013 - Synthese 190 (4):585-618.
    The aim of this paper is to clarify what kind of normativity characterizes a convention. First, we argue that conventions have normative consequences because they always involve a form of trust and reliance. We contend that it is by reference to a moral principle impinging on these aspects (i.e. the principle of Reliability) that interpersonal obligations and rights originate from conventional regularities. Second, we argue that the system of mutual expectations presupposed by conventions is a source of agreements. Agreements stemming (...)
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  • Uncertainty, Decision Science, and Policy Making: A Manifesto for a Research Agenda.David Tuckett, Antoine Mandel, Diana Mangalagiu, Allen Abramson, Jochen Hinkel, Konstantinos Katsikopoulos, Alan Kirman, Thierry Malleret, Igor Mozetic, Paul Ormerod, Robert Elliot Smith, Tommaso Venturini & Angela Wilkinson - 2015 - Critical Review: A Journal of Politics and Society 27 (2):213-242.
    ABSTRACTThe financial crisis of 2008 was unforeseen partly because the academic theories that underpin policy making do not sufficiently account for uncertainty and complexity or learned and evolved human capabilities for managing them. Mainstream theories of decision making tend to be strongly normative and based on wishfully unrealistic “idealized” modeling. In order to develop theories of actual decision making under uncertainty, we need new methodologies that account for how human actors often manage uncertain situations “well enough.” Some possibly helpful methodologies, (...)
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  • The chain-store paradox revisited.Walter Trockel - 1986 - Theory and Decision 21 (2):163-179.
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  • Fixed-point solutions to the regress problem in normative uncertainty.Philip Trammell - 2019 - Synthese 198 (2):1177-1199.
    When we are faced with a choice among acts, but are uncertain about the true state of the world, we may be uncertain about the acts’ “choiceworthiness”. Decision theories guide our choice by making normative claims about how we should respond to this uncertainty. If we are unsure which decision theory is correct, however, we may remain unsure of what we ought to do. Given this decision-theoretic uncertainty, meta-theories attempt to resolve the conflicts between our decision theories...but we may be (...)
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  • An Integrated Bayesian-Heuristic Semiotic Model for Understanding Human and SARS-CoV-2 Representational Structures.Sergio Torres-Martínez - 2023 - Biosemiotics 16 (3):415-439.
    The aim of this paper is to explore the connections between semiotics and biology by examining the behaviors of both humans and non-cognizant agents, using Bayesian and heuristic inference. The argument is that higher-level organisms use complex predictive reasoning to deal with uncertainty, while non-cognizant species, such as SARS-CoV-2, rely on an economy-driven heuristic to enter host cells. From this viewpoint, the current pandemic is characterized as a clash of representations resulting from the anthropocentric construction of the self, which neglects (...)
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  • Précis of simple heuristics that make us Smart.Peter M. Todd & Gerd Gigerenzer - 2000 - Behavioral and Brain Sciences 23 (5):727-741.
    How can anyone be rational in a world where knowledge is limited, time is pressing, and deep thought is often an unattainable luxury? Traditional models of unbounded rationality and optimization in cognitive science, economics, and animal behavior have tended to view decision-makers as possessing supernatural powers of reason, limitless knowledge, and endless time. But understanding decisions in the real world requires a more psychologically plausible notion of bounded rationality. In Simple heuristics that make us smart (Gigerenzer et al. 1999), we (...)
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  • Risk writ large.Johanna Thoma & Jonathan Weisberg - 2017 - Philosophical Studies 174 (9):2369-2384.
    Risk-weighted expected utility theory is motivated by small-world problems like the Allais paradox, but it is a grand-world theory by nature. And, at the grand-world level, its ability to handle the Allais paradox is dubious. The REU model described in Risk and Rationality turns out to be risk-seeking rather than risk-averse on one natural way of formulating the Allais gambles in the grand-world context. This result illustrates a general problem with the case for REU theory, we argue. There is a (...)
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  • In Defence of Revealed Preference Theory.Johanna Thoma - 2021 - Economics and Philosophy 37 (2):163-187.
    This paper defends revealed preference theory against a pervasive line of criticism, according to which revealed preference methodology relies on appealing to some mental states, in particular an agent’s beliefs, rendering the project incoherent or unmotivated. I argue that all that is established by these arguments is that revealed preference theorists must accept a limited mentalism in their account of the options an agent should be modelled as choosing between. This is consistent both with an essentially behavioural interpretation of preference (...)
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  • How Do Social Norms and Expectations About Others Influence Individual Behavior?: A Quantum Model of Self/other-perspective Interaction in Strategic Decision-Making.Jakub Tesar - 2020 - Foundations of Science 25 (1):135-150.
    Social norms can be understood as the grammar of social interaction. Like grammar in speech, they specify what is acceptable in a given context. But what are the specific rules that direct human compliance with the norm? This paper presents a quantitative model of self- and the other-perspective interaction based on a ‘quantum model of decision-making’, which can explain some of the ‘fallacies’ of the classical model of strategic choice. By connecting two fields of social science research—norms compliance, and strategic (...)
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  • A conditional expected utility model for myopic decision makers.Leigh Tesfatsion - 1980 - Theory and Decision 12 (2):185-206.
    An expected utility model of individual choice is formulated which allows the decision maker to specify his available actions in the form of controls (partial contingency plans) and to simultaneously choose goals and controls in end-mean pairs. It is shown that the Savage expected utility model, the Marschak- Radner team model, the Bayesian statistical decision model, and the standard optimal control model can be viewed as special cases of this goal-control expected utility model.
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  • Learning to live with voluntarism.Paul Teller - 2011 - Synthese 178 (1):49-66.
    This paper examines and finds wanting the arguments against van Fraassen’s voluntarism, the view that the only constraint of rationality is consistency. Foundationalists claim that if we have no grounds or rationale for a belief or rule, rationality demands that we suspend it. But that begs the question by assuming that there have to be grounds or a rationale. Instead of asking, why should we hold a basic belief or rule, the question has to be: why should not we be (...)
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  • Uncertainty in Integrated Assessment Modeling of Climate Change.Massimo Tavoni & Giovanni Valente - 2022 - Perspectives on Science 30 (2):321-351.
    Integrated assessment models play a major role in the science and policy of climate change. Similarly to other widely used computational tools for addressing socially relevant problems, IAMs need to account for the key uncertainties characterizing processes and socio-economic responses. In the case of climate change, these are particularly complex given the very long-term nature of climate and the deep uncertainty characterizing technological and human systems. Here we draw from philosophical discussion of mathematical modeling of social problems and review the (...)
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  • Where do Bayesian priors come from?Patrick Suppes - 2007 - Synthese 156 (3):441-471.
    Bayesian prior probabilities have an important place in probabilistic and statistical methods. In spite of this fact, the analysis of where these priors come from and how they are formed has received little attention. It is reasonable to excuse the lack, in the foundational literature, of detailed psychological theory of what are the mechanisms by which prior probabilities are formed. But it is less excusable that there is an almost total absence of a detailed discussion of the highly differentiating nature (...)
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  • Necessary and sufficient conditions for existence of a unique measure strictly agreeing with a qualitative probability ordering.Patrick Suppes & Mario Zanotti - 1976 - Journal of Philosophical Logic 5 (3):431 - 438.
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  • Looking for a Psychology for the Inner Rational Agent.Robert Sugden - 2015 - Social Theory and Practice 41 (4):579-598.
    Research in psychology and behavioral economics shows that individuals’ choices often depend on “irrelevant” contextual factors. This presents problems for normative economics, which has traditionally used preference-satisfaction as its criterion. A common response is to claim that individuals have context-independent latent preferences which are “distorted” by psychological factors, and that latent preferences should be respected. This response implicitly uses a model of human action in which each human being has an “inner rational agent.” I argue that this model is psychologically (...)
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