Results for ' probability agreement theorem'

977 found
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  1.  61
    A Generalization of Aumann's Agreement Theorem.Matthias Hild & Mathias Risse - unknown
    The scope of Aumann’s (1976) Agreement Theorem is needlessly limited by its restriction to Conditioning as the update rule. Here we prove the theorem in a more comprehensive framework, in which the evolution of probabilities is represented directly, without deriving new probabilities from new certainties. The framework allows arbitrary update rules subject only to Goldstein’s (1983) requirement that current expectations agree with current expectations of future expectations.
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  2. Agreement and Equilibrium with Minimal Introspection.Harvey Lederman - 2014 - Dissertation, Oxford University
    Standard models in epistemic game theory make strong assumptions about agents’ knowledge of their own beliefs. Agents are typically assumed to be introspectively omniscient: if an agent believes an event with probability p, she is certain that she believes it with probability p. This paper investigates the extent to which this assumption can be relaxed while preserving some standard epistemic results. Geanakoplos (1989) claims to provide an Agreement Theorem using the “truth” axiom, together with the property (...)
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  3.  8
    Coherence Against the Pareto Principle.John Broome - 2017 - In Weighing Goods. Oxford, UK: Wiley. pp. 151–164.
    The coherence of general good turns out to conflict with the widely accepted Pareto principle. This chapter explains the conflict and resolves it in favour of coherence. It also presents an example of a head‐on collision between coherence and the Pareto principle. The example relies on an auxiliary assumption, but one that is very plausible. The principle of personal good is immune to the difficulty raised by the probability agreement theorem. The theorem presents welfare economics with (...)
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  4. 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 (...)
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  5.  76
    Agreement Theorems in Dynamic-Epistemic Logic.Cédric Dégremont & Oliver Roy - 2012 - Journal of Philosophical Logic 41 (4):735-764.
    This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility models. The (...)
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  6.  80
    Mechanistic Slumber vs. Statistical Insomnia: The Early Phase of Boltzmann’s H-theorem (1868-1877).Massimiliano Badino - 2011 - European Physical Journal - H 36 (3):353-378.
    An intricate, long, and occasionally heated debate surrounds Boltzmann’s H-theorem (1872) and his combinatorial interpretation of the second law (1877). After almost a century of devoted and knowledgeable scholarship, there is still no agreement as to whether Boltzmann changed his view of the second law after Loschmidt’s 1876 reversibility argument or whether he had already been holding a probabilistic conception for some years at that point. In this paper, I argue that there was no abrupt statistical turn. In (...)
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  7. Does chance hide necessity ? A reevaluation of the debate ‘determinism - indeterminism’ in the light of quantum mechanics and probability theory.Louis Vervoort - 2013 - Dissertation, University of Montreal
    In this text the ancient philosophical question of determinism (“Does every event have a cause ?”) will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic: quantum events would have no causes but happen by irreducible chance. Arguably the clearest theorem that leads to this conclusion is Bell’s theorem. The commonly accepted ‘solution’ to the theorem is ‘indeterminism’, in agreement with the Copenhagen interpretation. Here it (...)
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  8. Agreement theorems for self-locating belief.Michael Caie - 2016 - Review of Symbolic Logic 9 (2):380-407.
  9.  25
    Aumann's “No AgreementTheorem Generalized.Matthias Hild, Richard Jeffrey & Mathias Risse - 1999 - In Cristina Bicchieri, Richard C. Jeffrey & Brian Skyrms (eds.), The Logic of Strategy. Oxford University Press. pp. 92--100.
  10.  78
    Comparing the axiomatic and ecological approaches to rationality: fundamental agreement theorems in SCOP.Patricia Rich - 2018 - Synthese 195 (2):529-547.
    There are two prominent viewpoints regarding the nature of rationality and how it should be evaluated in situations of interest: the traditional axiomatic approach and the newer ecological rationality. An obstacle to comparing and evaluating these seemingly opposite approaches is that they employ different language and formalisms, ask different questions, and are at different stages of development. I adapt a formal framework known as SCOP to address this problem by providing a comprehensive common framework in which both approaches may be (...)
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  11. Bell’s Theorem, Quantum Probabilities, and Superdeterminism.Eddy Keming Chen - 2022 - In Eleanor Knox & Alastair Wilson (eds.), The Routledge Companion to Philosophy of Physics. London, UK: Routledge.
    In this short survey article, I discuss Bell’s theorem and some strategies that attempt to avoid the conclusion of non-locality. I focus on two that intersect with the philosophy of probability: (1) quantum probabilities and (2) superdeterminism. The issues they raised not only apply to a wide class of no-go theorems about quantum mechanics but are also of general philosophical interest.
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  12.  16
    Small probability space formulation of Bell's theorem.Tomasz Placek & Marton Gomori - unknown
    A small probability space representation of quantum mechanical probabilities is defined as a collection of Kolmogorovian probability spaces, each of which is associated with a context of a maximal set of compatible measurements, that portrays quantum probabilities as Kolmogorovian probabilities of classical events. Bell's theorem is stated and analyzed in terms of the small probability space formalism.
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  13. Range theorems for quantum probability and entanglement.Itamar Pitowsky - unknown
    We consider the set of all matrices of the form pij = tr[W (Ei ⊗ Fj)] where Ei, Fj are projections on a Hilbert space H, and W is some state on H ⊗ H. We derive the basic properties of this set, compare it with the classical range of probability, and note how its properties may be related to a geometric measures of entanglement.
     
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  14.  22
    Some theorems on the algorithmic approach to probability theory and information theory:(1971 dissertation directed by AN Kolmogorov).Leonid A. Levin - 2010 - Annals of Pure and Applied Logic 162 (3):224-235.
  15.  21
    Unknown Probabilities, Bayesianism, and de Finetti's Representation Theorem.Jaakko Hintikka - 1970 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1970:325 - 341.
  16. Representation theorems of the de Finetti type for (partially) symmetric probability measures.Godehard Link - 1971 - In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability. Berkeley: University of California Press. pp. 2--207.
     
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  17.  20
    Definability theorems in normal extensions of the probability logic.Larisa L. Maksimova - 1989 - Studia Logica 48 (4):495-507.
    Three variants of Beth's definability theorem are considered. Let L be any normal extension of the provability logic G. It is proved that the first variant B1 holds in L iff L possesses Craig's interpolation property. If L is consistent, then the statement B2 holds in L iff L = G + {0}. Finally, the variant B3 holds in any normal extension of G.
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  18. Some remarks on the probability of cycles - Appendix 3 to 'Epistemic democracy: generalizing the Condorcet jury theorem'.Christian List - 2001 - Journal of Political Philosophy 9 (3):277-306.
    This item was published as 'Appendix 3: An Implication of the k-option Condorcet jury mechanism for the probability of cycles' in List and Goodin (2001) http://eprints.lse.ac.uk/705/. Standard results suggest that the probability of cycles should increase as the number of options increases and also as the number of individuals increases. These results are, however, premised on a so-called "impartial culture" assumption: any logically possible preference ordering is assumed to be as likely to be held by an individual as (...)
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  19.  73
    Probability and the theorem of confirmation.William Todd - 1967 - Mind 76 (302):260-263.
  20.  78
    The total evidence theorem for probability kinematics.Paul R. Graves - 1989 - Philosophy of Science 56 (2):317-324.
    L. J. Savage and I. J. Good have each demonstrated that the expected utility of free information is never negative for a decision maker who updates her degrees of belief by conditionalization on propositions learned for certain. In this paper Good's argument is generalized to show the same result for a decision maker who updates her degrees of belief on the basis of uncertain information by Richard Jeffrey's probability kinematics. The Savage/Good result is shown to be a special case (...)
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  21.  22
    Aggregating subjective probabilities: some limitative theorems.Carl Wagner - 1984 - Notre Dame Journal of Formal Logic 25 (3):233-240.
  22.  51
    Study of Wigner's theorem on joint probabilities.M. Mugur-Schächter - 1979 - Foundations of Physics 9 (5-6):389-404.
    The exact bearing of an important theorem proved by Wigner is established. The study brings out the fact that marginal conditions as well as mean conditions of a form currently required in joint probability attempts are in fact inadequate for the determination of a relevant concept of a joint probability. New vistas are thereby opened up.
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  23.  78
    The H-Theorem, Molecular Disorder and Probability: Perspectives from Boltzmann’s Lectures on Gas Theory.Daniel Parker - unknown
    This paper examines Boltzmann’s responses to the Loschmidt reversibility objection to the H-theorem, as presented in his Lectures on Gas Theory. I describe and evaluate two distinct conceptions of the assumption of molecular disorder found in this work, and contrast these notions with the Stosszahlansatz, as well as with the predominant contemporary conception of molecular disorder. Both these conceptions are assessed with respect to the reversibility objection. Finally, I interpret Boltzmann as claiming that a state of molecular disorder serves (...)
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  24.  32
    An analytic completeness theorem for logics with probability quantifiers.Douglas N. Hoover - 1987 - Journal of Symbolic Logic 52 (3):802-816.
    We give a completeness theorem for a logic with probability quantifiers which is equivalent to the logics described in a recent survey paper of Keisler [K]. This result improves on the completeness theorems in [K] in that it works for languages with function symbols and produces a model whose universe is an analytic subset of the real line, and whose relations and functions are Borel relative to this universe.
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  25.  10
    Bernoulli’s golden theorem in retrospect: error probabilities and trustworthy evidence.Aris Spanos - 2021 - Synthese 199 (5-6):13949-13976.
    Bernoulli’s 1713 golden theorem is viewed retrospectively in the context of modern model-based frequentist inference that revolves around the concept of a prespecified statistical model Mθx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{M}}_{{{\varvec{\uptheta}}}} \left( {\mathbf{x}} \right)$$\end{document}, defining the inductive premises of inference. It is argued that several widely-accepted claims relating to the golden theorem and frequentist inference are either misleading or erroneous: (a) Bernoulli solved the problem of inference ‘from probability to frequency’, and thus (b) (...)
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  26.  10
    Subjectivity of pre-test probability value: controversies over the use of Bayes’ Theorem in medical diagnosis.Tomasz Rzepiński - 2023 - Theoretical Medicine and Bioethics 44 (4):301-324.
    This article discusses the use of Bayes’ Theorem in medical diagnosis with a view to examining the epistemological problems of interpreting the concept of pre-test probability value. It is generally maintained that pre-test probability values are determined subjectively. Accordingly, this paper investigates three main philosophical interpretations of probability (the “classic” one, based on the principle of non-sufficient reason, the frequentist one, and the personalistic one). This study argues that using Bayes’ Theorem in medical diagnosis does (...)
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  27.  17
    Imitating Quantum Probabilities: Beyond Bell’s Theorem and Tsirelson Bounds.Marek Czachor & Kamil Nalikowski - 2024 - Foundations of Science 29 (2):281-305.
    Local hidden-variable model of singlet-state correlations discussed in Czachor (Acta Phys Polon A 139:70, 2021a) is shown to be a particular case of an infinite hierarchy of local hidden-variable models based on an infinite hierarchy of calculi. Violation of Bell-type inequalities can be interpreted as a ‘confusion of languages’ problem, a result of mixing different but neighboring levels of the hierarchy. Mixing of non-neighboring levels results in violations beyond the Tsirelson bounds.
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  28.  15
    Conditionals and Conditional Probabilities: Three Triviality Theorems.Hugues Leblanc & Peter Roeper - 1990 - In Kyburg Henry E., Loui Ronald P. & Carlson Greg N. (eds.), Knowledge Representation and Defeasible Reasoning. Kluwer Academic Publishers. pp. 287--306.
  29.  25
    Why propensities cannot be probabilities, Paul Humphreys proposed accounts of probability are usually required to satisfy the standard axioms of the probability calculus. Because of the fundamentally causal nature of propensities, they cannot do this, primarily because in-version formulas such as the multiplication axiom and bayes' theorem do.Ruth Garrett Millikan - 1985 - Philosophical Review 94 (4).
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  30. Choice and chance: an introduction to inductive logic.Brian Skyrms - 1975 - Encino, Calif.: Dickenson Pub. Co..
    Preface. I. BASICS OF LOGIC. Introduction. The Structure of Simple Statements. The Structure of Complex Statements. Simple and Complex Properties. Validity. 2. PROBABILITY AND INDUCTIVE LOGIC. Introduction. Arguments. Logic. Inductive versus Deductive Logic. Epistemic Probability. Probability and the Problems of Inductive Logic. 3. THE TRADITIONAL PROBLEM OF INDUCTION. Introduction. Hume’s Argument. The Inductive Justification of Induction. The Pragmatic Justification of Induction. Summary. IV. THE GOODMAN PARADOX AND THE NEW RIDDLE OF INDUCTION. Introduction. Regularities and Projection. The Goodman (...)
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  31. Conditionals and Conditional Probabilities: Three Triviality Theorems.H. E. Kyburg Jr - 1990 - In Kyburg Henry E., Loui Ronald P. & Carlson Greg N. (eds.), Knowledge Representation and Defeasible Reasoning. Kluwer Academic Publishers. pp. 287.
  32.  60
    The Relation between Credence and Chance: Lewis' "Principal Principle" Is a Theorem of Quantum Probability Theory.John Earman - unknown
    David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. Given the generally accepted updating rule for quantum probabilities, there is a straight forward sense in which the Principal Principle (...)
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  33.  30
    Some basic theorems of qualitative probability.Peter Gärdenfors - 1975 - Studia Logica 34 (3):257 - 264.
  34.  20
    Reasoning about conditional probabilities in a higher-order-logic theorem prover.Osman Hasan & Sofiène Tahar - 2011 - Journal of Applied Logic 9 (1):23-40.
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  35.  23
    The Generalization of de Finetti's Representation Theorem to Stationary Probabilities.Jan von Plato - 1982 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1982:137 - 144.
    de Finetti's representation theorem of exchangeable probabilities as unique mixtures of Bernoullian probabilities is a special case of a result known as the ergodic decomposition theorem. It says that stationary probability measures are unique mixtures of ergodic measures. Stationarity implies convergence of relative frequencies, and ergodicity the uniqueness of limits. Ergodicity therefore captures exactly the idea of objective probability as a limit of relative frequency (up to a set of measure zero), without the unnecessary restriction to (...)
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  36. No-Forcing and No-Matching Theorems for Classical Probability Applied to Quantum Mechanics.Ehtibar N. Dzhafarov & Janne V. Kujala - 2014 - Foundations of Physics 44 (3):248-265.
    Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov’s probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice–Bob EPR paradigm, non-contextuality means that the identity of Alice’s spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis $\alpha _{i}$ chosen by Alice, irrespective of Bob’s axis $\beta _{j}$ (and vice versa). Here, we study contextual KPT models, with two properties: (...)
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  37.  8
    L. A. Levin. Some theorems on the algorithmic approach to probability theory and information theory (1971 Dissertation directed by A. N. Kolmogorov). Annals of Pure and Applied Logic, vol. 162 (2010), pp. 224–235. [REVIEW]Jan Reimann - 2013 - Bulletin of Symbolic Logic 19 (3):397-399.
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  38.  35
    Reviewed Work(s): Some theorems on the algorithmic approach to probability theory and information theory (1971 Dissertation directed by A. N. Kolmogorov). Annals of Pure and Applied Logic, vol. 162 by L. A. Levin. [REVIEW]Jan Reimann - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    Review by: Jan Reimann The Bulletin of Symbolic Logic, Volume 19, Issue 3, Page 397-399, September 2013.
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  39.  16
    Reviewed Work(s): Some theorems on the algorithmic approach to probability theory and information theory (1971 Dissertation directed by A. N. Kolmogorov). Annals of Pure and Applied Logic, vol. 162 by L. A. Levin. [REVIEW]Review by: Jan Reimann - 2013 - Bulletin of Symbolic Logic 19 (3):397-399,.
  40. Quantum probability and decision theory, revisited [2002 online-only paper].David Wallace - 2002
    An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented which are based upon different decision theories and upon Gleason's Theorem. It is argued that decision theory gives Everettians most or all of what they need from `probability'. Contact is made with Lewis's Principal Principle linking subjective credence with objective chance: an Everettian (...)
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  41. Experimental Philosophy of Connexivity.Niki Pfeifer & Leon Schöppl - manuscript
    While Classical Logic (CL) used to be the gold standard for evaluating the rationality of human reasoning, certain non-theorems of CL—like Aristotle’s and Boethius’ theses—appear intuitively rational and plausible. Connexive logics have been developed to capture the underlying intuition that conditionals whose antecedents contradict their consequents, should be false. We present results of two experiments (total n = 72), the first to investigate connexive principles and related formulae systematically. Our data suggest that connexive logics provide more plausible rationality frameworks for (...)
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  42. Representation theorems and realism about degrees of belief.Lyle Zynda - 2000 - Philosophy of Science 67 (1):45-69.
    The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism can be defended on (...)
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  43. Bayes' theorem.James Joyce - 2008 - Stanford Encyclopedia of Philosophy.
    Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of (...)
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  44. Epistemic Probabilities are Degrees of Support, not Degrees of (Rational) Belief.Nevin Climenhaga - 2024 - Philosophy and Phenomenological Research 108 (1):153-176.
    I argue that when we use ‘probability’ language in epistemic contexts—e.g., when we ask how probable some hypothesis is, given the evidence available to us—we are talking about degrees of support, rather than degrees of belief. The epistemic probability of A given B is the mind-independent degree to which B supports A, not the degree to which someone with B as their evidence believes A, or the degree to which someone would or should believe A if they had (...)
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  45.  36
    Naive probability: A mental model theory of extensional reasoning.Philip Johnson-Laird, Paolo Legrenzi, Vittorio Girotto, Maria Sonino Legrenzi & Jean-Paul Caverni - 1999 - Psychological Review 106 (1):62-88.
    This article outlines a theory of naive probability. According to the theory, individuals who are unfamiliar with the probability calculus can infer the probabilities of events in an extensional way: They construct mental models of what is true in the various possibilities. Each model represents an equiprobable alternative unless individuals have beliefs to the contrary, in which case some models will have higher probabilities than others. The probability of an event depends on the proportion of models in (...)
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  46. Better Foundations for Subjective Probability.Sven Neth - forthcoming - Australasian Journal of Philosophy.
    How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used (...)
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  47.  19
    Degradation in Probability Logic : When more Information Leads to Less Precise Conclusions.Christian Wallmann & Gernot Kleiter - unknown
    Probability logic studies the properties resulting from the probabilistic interpretation of logical argument forms. Typical examples are probabilistic Modus Ponens and Modus Tollens. Argument forms with two premises usually lead from precise probabilities of the premises to imprecise or interval probabilities of the conclusion. In the contribution, we study generalized inference forms having three or more premises. Recently, Gilio has shown that these generalized forms ``degrade'' -- more premises lead to more imprecise conclusions, i. e., to wider intervals. We (...)
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  48.  89
    The probability of inconsistencies in complex collective decisions.Christian List - 2005 - Social Choice and Welfare 24 (1):3-32.
    Many groups make decisions over multiple interconnected propositions. The “doctrinal paradox” or “discursive dilemma” shows that propositionwise majority voting can generate inconsistent collective sets of judgments, even when individual sets of judgments are all consistent. I develop a simple model for determining the probability of the paradox, given various assumptions about the probability distribution of individual sets of judgments, including impartial culture and impartial anonymous culture assumptions. I prove several convergence results, identifying when the probability of the (...)
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  49. Witness agreement and the truth-conduciveness of coherentist justification.William Roche - 2012 - Southern Journal of Philosophy 50 (1):151-169.
    Some recent work in formal epistemology shows that “witness agreement” by itself implies neither an increase in the probability of truth nor a high probability of truth—the witnesses need to have some “individual credibility.” It can seem that, from this formal epistemological result, it follows that coherentist justification (i.e., doxastic coherence) is not truth-conducive. I argue that this does not follow. Central to my argument is the thesis that, though coherentists deny that there can be noninferential justification, (...)
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  50. Probability in ethics.David McCarthy - 2016 - In Alan Hájek & Christopher Hitchcock (eds.), The Oxford Handbook of Probability and Philosophy. Oxford: Oxford University Press. pp. 705–737.
    The article is a plea for ethicists to regard probability as one of their most important concerns. It outlines a series of topics of central importance in ethical theory in which probability is implicated, often in a surprisingly deep way, and lists a number of open problems. Topics covered include: interpretations of probability in ethical contexts; the evaluative and normative significance of risk or uncertainty; uses and abuses of expected utility theory; veils of ignorance; Harsanyi’s aggregation (...); population size problems; equality; fairness; giving priority to the worse off; continuity; incommensurability; nonexpected utility theory; evaluative measurement; aggregation; causal and evidential decision theory; act consequentialism; rule consequentialism; and deontology. (shrink)
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