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On Indeterminate Probabilities

Journal of Philosophy 71 (13):233--261 (1978)

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  1. Comparative Expectations.Arthur Paul Pedersen - 2014 - Studia Logica 102 (4):811-848.
    I introduce a mathematical account of expectation based on a qualitative criterion of coherence for qualitative comparisons between gambles (or random quantities). The qualitative comparisons may be interpreted as an agent’s comparative preference judgments over options or more directly as an agent’s comparative expectation judgments over random quantities. The criterion of coherence is reminiscent of de Finetti’s quantitative criterion of coherence for betting, yet it does not impose an Archimedean condition on an agent’s comparative judgments, it does not require the (...)
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  • Dutch Books, Coherence, and Logical Consistency.Anna Mahtani - 2014 - Noûs 49 (3):522-537.
    In this paper I present a new way of understanding Dutch Book Arguments: the idea is that an agent is shown to be incoherent iff he would accept as fair a set of bets that would result in a loss under any interpretation of the claims involved. This draws on a standard definition of logical inconsistency. On this new understanding, the Dutch Book Arguments for the probability axioms go through, but the Dutch Book Argument for Reflection fails. The question of (...)
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  • Perception as Input and as Reason for Action.Isaac Levi - 1995 - Canadian Journal of Philosophy 25 (sup1):135-154.
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  • Credal Dilemmas.Sarah Moss - 2014 - Noûs 48 (3):665-683.
    Recently many have argued that agents must sometimes have credences that are imprecise, represented by a set of probability measures. But opponents claim that fans of imprecise credences cannot provide a decision theory that protects agents who follow it from foregoing sure money. In particular, agents with imprecise credences appear doomed to act irrationally in diachronic cases, where they are called to make decisions at earlier and later times. I respond to this claim on behalf of imprecise credence fans. Once (...)
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  • What are the minimal requirements of rational choice? Arguments from the sequential-decision setting.Katie Siobhan Steele - 2010 - Theory and Decision 68 (4):463-487.
    There are at least two plausible generalisations of subjective expected utility (SEU) theory: cumulative prospect theory (which relaxes the independence axiom) and Levi’s decision theory (which relaxes at least ordering). These theories call for a re-assessment of the minimal requirements of rational choice. Here, I consider how an analysis of sequential decision making contributes to this assessment. I criticise Hammond’s (Economica 44(176):337–350, 1977; Econ Philos 4:292–297, 1988a; Risk, decision and rationality, 1988b; Theory Decis 25:25–78, 1988c) ‘consequentialist’ argument for the SEU (...)
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  • Demystifying Dilation.Arthur Paul Pedersen & Gregory Wheeler - 2014 - Erkenntnis 79 (6):1305-1342.
    Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...)
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  • A challenge to the compound lottery axiom: A two-stage normative structure and comparison to other theories.Donald B. Davis - 1994 - Theory and Decision 37 (3):267-309.
    This paper examines preferences among uncertain prospects when the decision maker is uneasy about his assignment of subjective probabilities. It proposes a two-stage lottery framework for the analysis of such prospects, where the first stage represents an assessment of the vagueness (ambiguity) in defining the problem's randomness and the second stage represents an assessment of the problem for each hypothesized randomness condition. Standard axioms of rationality are prescribed for each stage, including weak ordering, continuity, and strong independence. The ‘Reduction of (...)
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  • Rationality and uncertainty.Amartya Sen - 1985 - Theory and Decision 18 (2):109-127.
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  • (1 other version)Permission to Believe: Why Permissivism Is True and What It Tells Us About Irrelevant Influences on Belief.Miriam Schoenfield - 2012 - Noûs 48 (2):193-218.
    In this paper, I begin by defending permissivism: the claim that, sometimes, there is more than one way to rationally respond to a given body of evidence. Then I argue that, if we accept permissivism, certain worries that arise as a result of learning that our beliefs were caused by the communities we grew up in, the schools we went to, or other irrelevant influences dissipate. The basic strategy is as follows: First, I try to pinpoint what makes irrelevant influences (...)
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  • Why It Is Time To Move Beyond Nagelian Reduction.Marie I. Kaiser - 2012 - In D. Dieks, S. Hartmann, T. Uebel & M. Weber (eds.), Probabilities, Laws and Structure. Springer. pp. 255-272.
    In this paper I argue that it is finally time to move beyond the Nagelian framework and to break new ground in thinking about epistemic reduction in biology. I will do so, not by simply repeating all the old objections that have been raised against Ernest Nagel’s classical model of theory reduction. Rather, I grant that a proponent of Nagel’s approach can handle several of these problems but that, nevertheless, Nagel’s general way of thinking about epistemic reduction in terms of (...)
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  • Dutch Book Arguments and Imprecise Probabilities.Seamus Bradley - 2012 - In D. Dieks, S. Hartmann, T. Uebel & M. Weber (eds.), Probabilities, Laws and Structure. Springer.
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  • Probabilistic Belief Contraction.Raghav Ramachandran, Arthur Ramer & Abhaya C. Nayak - 2012 - Minds and Machines 22 (4):325-351.
    Probabilistic belief contraction has been a much neglected topic in the field of probabilistic reasoning. This is due to the difficulty in establishing a reasonable reversal of the effect of Bayesian conditionalization on a probabilistic distribution. We show that indifferent contraction, a solution proposed by Ramer to this problem through a judicious use of the principle of maximum entropy, is a probabilistic version of a full meet contraction. We then propose variations of indifferent contraction, using both the Shannon entropy measure (...)
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  • Chilling out on epistemic rationality: A defense of imprecise credences.Miriam Schoenfield - 2012 - Philosophical Studies 158 (2):197-219.
    A defense of imprecise credences (and other imprecise doxastic attitudes).
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  • Options and the subjective ought.Brian Hedden - 2012 - Philosophical Studies 158 (2):343-360.
    Options and the subjective ought Content Type Journal Article Pages 1-18 DOI 10.1007/s11098-012-9880-0 Authors Brian Hedden, Department of Linguistics and Philosophy, Massachusetts Institute of Technology, Cambridge, MA, USA Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116.
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  • Why Rational Agents Should Not Be Liberal Maximizers.Isaac Levi - 2008 - Canadian Journal of Philosophy 38 (S1):1-17.
    Hans Herzberger's 1973 essay 'Ordinal Preference and Rational Choice' is a classic milestone in the erosion of the idea that rational agents are maximizers of utility. By the time Herzberger wrote, many authors had replaced this claim with the thesis that rational agents are maximizers of preference. That is to say, it was assumed that at the moment of choice a rational agent has a weak ordering representing his or her preferences among the options available to the agent for choice (...)
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  • Updating, Undermining, and Independence.Jonathan Weisberg - 2015 - British Journal for the Philosophy of Science 66 (1):121-159.
    Sometimes appearances provide epistemic support that gets undercut later. In an earlier paper I argued that standard Bayesian update rules are at odds with this phenomenon because they are ‘rigid’. Here I generalize and bolster that argument. I first show that the update rules of Dempster–Shafer theory and ranking theory are rigid too, hence also at odds with the defeasibility of appearances. I then rebut three Bayesian attempts to solve the problem. I conclude that defeasible appearances pose a more difficult (...)
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  • Deductive closure.Isaac Levi - 2012 - Synthese 186 (2):493-499.
    This is a brief review of issues over which Henry Kyburg and I differed concerning the requirement that full beliefs should be closed under deductive consequence.
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  • A defense of imprecise credences in inference and decision making1.James Joyce - 2010 - Philosophical Perspectives 24 (1):281-323.
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  • Scotching Dutch Books?Alan Hájek - 2005 - Philosophical Perspectives 19 (1):139-151.
    The Dutch Book argument, like Route 66, is about to turn 80. It is arguably the most celebrated argument for subjective Bayesianism. Start by rejecting the Cartesian idea that doxastic attitudes are ‘all-or-nothing’; rather, they are far more nuanced degrees of belief, for short credences, susceptible to fine-grained numerical measurement. Add a coherentist assumption that the rationality of a doxastic state consists in its internal consistency. The remaining problem is to determine what consistency of credences amounts to. The Dutch Book (...)
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  • Updating as Communication.Sarah Moss - 2012 - Philosophy and Phenomenological Research 85 (2):225-248.
    Traditional procedures for rational updating fail when it comes to self-locating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with self-locating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect information you have genuinely (...)
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  • Belief and contextual acceptance.Eleonora Cresto - 2010 - Synthese 177 (1):41-66.
    I develop a strategy for representing epistemic states and epistemic changes that seeks to be sensitive to the difference between voluntary and involuntary aspects of our epistemic life, as well as to the role of pragmatic factors in epistemology. The model relies on a particular understanding of the distinction between full belief and acceptance , which makes room for the idea that our reasoning on both practical and theoretical matters typically proceeds in a contextual way. Within this framework, I discuss (...)
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  • Revising incomplete attitudes.Richard Bradley - 2009 - Synthese 171 (2):235 - 256.
    Bayesian models typically assume that agents are rational, logically omniscient and opinionated. The last of these has little descriptive or normative appeal, however, and limits our ability to describe how agents make up their minds (as opposed to changing them) or how they can suspend or withdraw their opinions. To address these limitations this paper represents the attitudinal states of non-opinionated agents by sets of (permissible) probability and desirability functions. Several basic ways in which such states of mind can be (...)
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  • (1 other version)Epistemic humility, arguments from evil, and moral skepticism.Daniel Howard-Snyder - 2009 - Oxford Studies in Philosophy of Religion 2:17-57.
    Reprinted in Philosophy of Religion: An Anthology, Wadsworth, 2013, 6th edition, eds. Michael Rea and Louis Pojman. In this essay, I argue that the moral skepticism objection to what is badly named "skeptical theism" fails.
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  • Decision making with imprecise probabilities.Brian Weatherson - 1998
    Orthodox Bayesian decision theory requires an agent’s beliefs representable by a real-valued function, ideally a probability function. Many theorists have argued this is too restrictive; it can be perfectly reasonable to have indeterminate degrees of belief. So doxastic states are ideally representable by a set of probability functions. One consequence of this is that the expected value of a gamble will be imprecise. This paper looks at the attempts to extend Bayesian decision theory to deal with such cases, and concludes (...)
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  • Should we respond to evil with indifference?Brian Weatherson - 2005 - Philosophy and Phenomenological Research 70 (3):613–635.
    In a recent article, Adam Elga outlines a strategy for “Defeating Dr Evil with Self-Locating Belief”. The strategy relies on an indifference principle that is not up to the task. In general, there are two things to dislike about indifference principles: adopting one normally means confusing risk for uncertainty, and they tend to lead to incoherent views in some ‘paradoxical’ situations. I argue that both kinds of objection can be levelled against Elga’s indifference principle. There are also some difficulties with (...)
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  • Consensus as shared agreement and outcome of inquiry.Isaac Levi - 1985 - Synthese 62 (1):3 - 11.
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  • Probabilism and induction.Richard Jeffrey - 1986 - Topoi 5 (1):51-58.
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  • (1 other version)Unreliable probabilities, risk taking, and decision making.Peter Gärdenfors & Nils-Eric Sahlin - 1982 - Synthese 53 (3):361-386.
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  • Distinguishing indeterminate belief from “risk-averse” preferences.Katie Steele - 2007 - Synthese 158 (2):189-205.
    I focus my discussion on the well-known Ellsberg paradox. I find good normative reasons for incorporating non-precise belief, as represented by sets of probabilities, in an Ellsberg decision model. This amounts to forgoing the completeness axiom of expected utility theory. Provided that probability sets are interpreted as genuinely indeterminate belief, such a model can moreover make the “Ellsberg choices” rationally permissible. Without some further element to the story, however, the model does not explain how an agent may come to have (...)
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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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  • (2 other versions)Decision theory as philosophy.Mark Kaplan - 1983 - Philosophy of Science 50 (4):549-577.
    Is Bayesian decision theory a panacea for many of the problems in epistemology and the philosophy of science, or is it philosophical snake-oil? For years a debate had been waged amongst specialists regarding the import and legitimacy of this body of theory. Mark Kaplan had written the first accessible and non-technical book to address this controversy. Introducing a new variant on Bayesian decision theory the author offers a compelling case that, while no panacea, decision theory does in fact have the (...)
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  • Varieties of Bayesianism.Jonathan Weisberg - 2011
    Handbook of the History of Logic, vol. 10, eds. Dov Gabbay, Stephan Hartmann, and John Woods, forthcoming.
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  • On Uncertainty.Brian Weatherson - 1998 - Dissertation, Monash University
    This dissertation looks at a set of interconnected questions concerning the foundations of probability, and gives a series of interconnected answers. At its core is a piece of old-fashioned philosophical analysis, working out what probability is. Or equivalently, investigating the semantic question of what is the meaning of ‘probability’? Like Keynes and Carnap, I say that probability is degree of reasonable belief. This immediately raises an epistemological question, which degrees count as reasonable? To solve that in its full generality would (...)
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  • Rational Polarization.Kevin Dorst - 2023 - Philosophical Review 132 (3):355-458.
    Predictable polarization is everywhere: we can often predict how people’s opinions, including our own, will shift over time. Extant theories either neglect the fact that we can predict our own polarization, or explain it through irrational mechanisms. They needn’t. Empirical studies suggest that polarization is predictable when evidence is ambiguous, that is, when the rational response is not obvious. I show how Bayesians should model such ambiguity and then prove that—assuming rational updates are those which obey the value of evidence—ambiguity (...)
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  • (1 other version)Maximal cluelessness.Andreas Mogensen - manuscript
    I argue that many of the priority rankings that have been proposed by effective altruists seem to be in tension with apparently reasonable assumptions about the rational pursuit of our aims in the face of uncertainty. The particular issue on which I focus arises from recognition of the overwhelming importance and inscrutability of the indirect effects of our actions, conjoined with the plausibility of a permissive decision principle governing cases of deep uncertainty, known as the maximality rule. I conclude that (...)
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  • Unspecific Evidence and Normative Theories of Decision.Rhys Borchert - forthcoming - Episteme:1-23.
    The nature of evidence is a problem for epistemology, but I argue that this problem intersects with normative decision theory in a way that I think is underappreciated. Among some decision theorists, there is a presumption that one can always ignore the nature of evidence while theorizing about principles of rational choice. In slogan form: decision theory only cares about the credences agents actually have, not the credences they should have. I argue against this presumption. In particular, I argue that (...)
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  • Acting on belief functions.Nicholas J. J. Smith - 2023 - Theory and Decision 95 (4):575-621.
    The degrees of belief of rational agents should be guided by the evidence available to them. This paper takes as a starting point the view—argued elsewhere—that the formal model best able to capture this idea is one that represents degrees of belief using Dempster–Shafer belief functions. However degrees of belief should not only respect evidence: they also guide decision and action. Whatever formal model of degrees of belief we adopt, we need a decision theory that works with it: that takes (...)
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  • Philosophical foundations for worst-case arguments.Lara Buchak - 2023 - Politics, Philosophy and Economics 22 (3):215-242.
    Certain ethical views hold that we should pay more attention, even exclusive attention, to the worst-case scenario. Prominent examples include Rawls's Difference Principle and the Precautionary Principle. These views can be anchored in formal principles of decision theory, in two different ways. On the one hand, they can rely on ambiguity-aversion: the idea that we cannot assign sharp probabilities to various scenarios, and that if we cannot assign sharp probabilities, we should decide pessimistically, as if the probabilities are unfavorable. On (...)
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  • Getting Accurate about Knowledge.Sam Carter & Simon Goldstein - 2022 - Mind 132 (525):158-191.
    There is a large literature exploring how accuracy constrains rational degrees of belief. This paper turns to the unexplored question of how accuracy constrains knowledge. We begin by introducing a simple hypothesis: increases in the accuracy of an agent’s evidence never lead to decreases in what the agent knows. We explore various precise formulations of this principle, consider arguments in its favour, and explain how it interacts with different conceptions of evidence and accuracy. As we show, the principle has some (...)
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  • Does Non-Measurability Favour Imprecision?Cian Dorr - 2024 - Mind 133 (530):472-503.
    In a recent paper, Yoaav Isaacs, Alan Hájek, and John Hawthorne argue for the rational permissibility of "credal imprecision" by appealing to certain propositions associated with non-measurable spatial regions: for example, the proposition that the pointer of a spinner will come to rest within a certain non-measurable set of points on its circumference. This paper rebuts their argument by showing that its premises lead to implausible consequences in cases where one is trying to learn, by making multiple observations, whether a (...)
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  • Suspending belief in credal accounts.Andrew del Rio - 2024 - Noûs 58 (1):3-25.
    Traditionally epistemologists have taken doxastic states to come in three varieties—belief, disbelief, and suspension. Recently many epistemologists have taken our doxastic condition to be usefully represented by credences—quantified degrees of belief. Moreover, some have thought that this new credal picture is sufficient to account for everything we want to explain with the old traditional picture. Therefore, belief, disbelief, and suspension must map onto the new picture somehow. In this paper I challenge that possibility. Approaching the question from the angle of (...)
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  • Imprecise Credences and Acceptance.Benjamin Lennertz - 2022 - Ergo: An Open Access Journal of Philosophy 9.
    Elga (2010) argues that no plausible decision rule governs action with imprecise credences. I follow Moss (2015a) in claiming that the solution to Elga’s challenge is found in the philosophy of mind, not in devising a special new decision rule. Moss suggests that in decision situations that involve imprecise credences, we must identify with a precise credence, but she says little about identification. By reflecting on the common conception of identification and on what is necessary for Moss’s solution to succeed, (...)
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  • Meditations on Beliefs Formed Arbitrarily.Miriam Schoenfield - 2022 - In Tamar Szabó Gendler, John Hawthorne & Julianne Chung (eds.), Oxford Studies in Epistemology 7. Oxford, GB: Oxford University Press. pp. 278-305.
    Had we grown up elsewhere or been educated differently, our view of the world would likely be radically different. What to make of this? This paper takes an accuracy-centered first-personal approach to the question of how to respond to the arbitrary nature in which many of our beliefs are formed. I show how considerations of accuracy motivate different responses to this sort of information depending on the type of attitude we take towards the belief in question upon subjecting the belief (...)
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  • Respecting Evidence: Belief Functions not Imprecise Probabilities.Nicholas J. J. Smith - 2022 - Synthese 200 (475):1-30.
    The received model of degrees of belief represents them as probabilities. Over the last half century, many philosophers have been convinced that this model fails because it cannot make room for the idea that an agent’s degrees of belief should respect the available evidence. In its place they have advocated a model that represents degrees of belief using imprecise probabilities (sets of probability functions). This paper presents a model of degrees of belief based on Dempster–Shafer belief functions and then presents (...)
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  • Generalized Immodesty Principles in Epistemic Utility Theory.Alejandro Pérez Carballo - 2023 - Ergo: An Open Access Journal of Philosophy 10 (31):874–907.
    Epistemic rationality is typically taken to be immodest at least in this sense: a rational epistemic state should always take itself to be doing at least as well, epistemically and by its own light, than any alternative epistemic state. If epistemic states are probability functions and their alternatives are other probability functions defined over the same collection of proposition, we can capture the relevant sense of immodesty by claiming that epistemic utility functions are (strictly) proper. In this paper I examine (...)
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  • Pascal’s Wager and Decision-making with Imprecise Probabilities.André Neiva - 2022 - Philosophia 51 (3):1479-1508.
    Unlike other classical arguments for the existence of God, Pascal’s Wager provides a pragmatic rationale for theistic belief. Its most popular version says that it is rationally mandatory to choose a way of life that seeks to cultivate belief in God because this is the option of maximum expected utility. Despite its initial attractiveness, this long-standing argument has been subject to various criticisms by many philosophers. What is less discussed, however, is the rationality of this choice in situations where the (...)
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  • Exposing some points of interest about non-exposed points of desirability.Arthur Van Camp & Teddy Seidenfeld - 2022 - International Journal of Approximate Reasoning 144:129-159.
    We study the representation of sets of desirable gambles by sets of probability mass functions. Sets of desirable gambles are a very general uncertainty model, that may be non-Archimedean, and therefore not representable by a set of probability mass functions. Recently, Cozman (2018) has shown that imposing the additional requirement of even convexity on sets of desirable gambles guarantees that they are representable by a set of probability mass functions. Already more that 20 years earlier, Seidenfeld et al. (1995) gave (...)
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  • Confidence in Beliefs and Rational Decision Making.Brian Hill - 2019 - Economics and Philosophy 35 (2):223-258.
    Abstract:The standard, Bayesian account of rational belief and decision is often argued to be unable to cope properly with severe uncertainty, of the sort ubiquitous in some areas of policy making. This paper tackles the question of what should replace it as a guide for rational decision making. It defends a recent proposal, which reserves a role for the decision maker’s confidence in beliefs. Beyond being able to cope with severe uncertainty, the account has strong normative credentials on the main (...)
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  • Comparative Opinion Loss.Benjamin Eva & Reuben Stern - 2022 - Philosophy and Phenomenological Research 107 (3):613-637.
    It is a consequence of the theory of imprecise credences that there exist situations in which rational agents inevitably become less opinionated toward some propositions as they gather more evidence. The fact that an agent's imprecise credal state can dilate in this way is often treated as a strike against the imprecise approach to inductive inference. Here, we show that dilation is not a mere artifact of this approach by demonstrating that opinion loss is countenanced as rational by a substantially (...)
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  • Credal imprecision and the value of evidence.Nilanjan Das - 2023 - Noûs 57 (3):684-721.
    This paper is about a tension between two theses. The first is Value of Evidence: roughly, the thesis that it is always rational for an agent to gather and use cost‐free evidence for making decisions. The second is Rationality of Imprecision: the thesis that an agent can be rationally required to adopt doxastic states that are imprecise, i.e., not representable by a single credence function. While others have noticed this tension, I offer a new diagnosis of it. I show that (...)
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