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Probabilistic Opinion Pooling

In Alan Hajek & Christopher Hitchcock (eds.), Oxford Handbook of Philosophy and Probability. Oxford: Oxford University Press (2016)

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  1. Beyond linear conciliation.Ko-Hung Kuan - 2020 - Synthese 198 (12):11483-11504.
    Formal epistemologists criticise the Conciliatory View of peer disagreement for being non-commutative with conditionalisation, path dependent and does not preserve the independence between propositions. Failing to commute with conditionalisation, one may switch the order between conciliating and conditionalising and obtain different outcomes. Failing to be path independent, the outcome of conciliation varies with the order of the acquisition of new testimonies. Failing to preserve the independence between propositions, one may suffer from a sure-loss and hence be deemed irrational. The three (...)
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  • On the Accuracy of Group Credences.Richard Pettigrew - 2019 - In Oxford Studies in Epistemology Vol.6. Oxford University Press.
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  • On the Accuracy of Group Credences.Richard Pettigrew - 2019 - Oxford Studies in Epistemology 6.
    We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising has increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And how do they relate to the individual credences assigned by the members of the particular (...)
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  • Probabilistic Opinion Pooling Generalized. Part One: General Agendas.Franz Dietrich & Christian List - 2017 - Social Choice and Welfare 48 (4):747–786.
    How can different individuals' probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events -- the agenda -- is a sigma-algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain or (...)
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  • Probabilistic Opinion Pooling Generalised. Part Two: The Premise-Based Approach.Franz Dietrich & Christian List - 2017 - Social Choice and Welfare 48 (4):787–814.
    How can different individuals' probability functions on a given sigma-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'event-wise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize (...)
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  • Making Confident Decisions with Model Ensembles.Joe Roussos, Richard Bradley & Roman Frigg - 2021 - Philosophy of Science 88 (3):439-460.
    Many policy decisions take input from collections of scientific models. Such decisions face significant and often poorly understood uncertainty. We rework the so-called confidence approach to tackl...
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  • Aggregating Agents with Opinions About Different Propositions.Richard Pettigrew - manuscript
    There are many reasons we might want to take the opinions of various individuals and aggregate them to give the opinions of the group they constitute. If all the individuals in the group have probabilistic opinions about the same propositions, there is a host of aggregation functions we might deploy, such as linear or geometric pooling. However, there are also cases where different members of the group assign probabilities to different sets of propositions, which might overlap a lot, a little, (...)
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  • Regret Averse Opinion Aggregation.Lee Elkin - forthcoming - Ergo: An Open Access Journal of Philosophy.
    It is often suggested that when opinions differ among individuals in a group, the opinions should be aggregated to form a compromise. This paper compares two approaches to aggregating opinions, linear pooling and what I call opinion agglomeration. In evaluating both strategies, I propose a pragmatic criterion, No Regrets, entailing that an aggregation strategy should prevent groups from buying and selling bets on events at prices regretted by their members. I show that only opinion agglomeration is able to satisfy the (...)
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  • Probabilistic Opinion Pooling with Imprecise Probabilities.Rush T. Stewart & Ignacio Ojea Quintana - 2018 - Journal of Philosophical Logic 47 (1):17-45.
    The question of how the probabilistic opinions of different individuals should be aggregated to form a group opinion is controversial. But one assumption seems to be pretty much common ground: for a group of Bayesians, the representation of group opinion should itself be a unique probability distribution, 410–414, [45]; Bordley Management Science, 28, 1137–1148, [5]; Genest et al. The Annals of Statistics, 487–501, [21]; Genest and Zidek Statistical Science, 114–135, [23]; Mongin Journal of Economic Theory, 66, 313–351, [46]; Clemen and (...)
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  • Sure-Wins Under Coherence: A Geometrical Perspective.Stefano Bonzio, Tommaso Flaminio & Paolo Galeazzi - 2019 - In Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2019. Lecture Notes in Computer Science.
    In this contribution we will present a generalization of de Finetti's betting game in which a gambler is allowed to buy and sell unknown events' betting odds from more than one bookmaker. In such a framework, the sole coherence of the books the gambler can play with is not sucient, as in the original de Finetti's frame, to bar the gambler from a sure-win opportunity. The notion of joint coherence which we will introduce in this paper characterizes those coherent books (...)
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  • Learning From Others: Conditioning Versus Averaging.Richard Bradley - 2017 - Theory and Decision 85 (1):5-20.
    How should we revise our beliefs in response to the expressed probabilistic opinions of experts on some proposition when these experts are in disagreement? In this paper I examine the suggestion that in such circumstances we should adopt a linear average of the experts’ opinions and consider whether such a belief revision policy is compatible with Bayesian conditionalisation. By looking at situations in which full or partial deference to the expressed opinions of others is required by Bayesianism I show that (...)
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  • A Theory of Bayesian Groups.Franz Dietrich - 2019 - Noûs 53 (3):708-736.
    A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by not all or (...)
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  • Judgment Aggregation and Minimal Change: A Model of Consensus Formation by Belief Revision.Marcel Heidemann - 2018 - Theory and Decision 85 (1):61-97.
    When a group of agents attempts to reach an agreement on certain issues, it is usually desirable that the resulting consensus be as close as possible to the original judgments of the individuals. However, when these judgments are logically connected to further beliefs, the notion of closeness should also take into account to what extent the individuals would have to revise their entire belief set to reach an agreement. In this work, we present a model for generation of agreement with (...)
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  • A Pragmatic Argument Against Equal Weighting.Ittay Nissan-Rozen & Levi Spectre - 2019 - Synthese 196 (10):4211-4227.
    We present a minimal pragmatic restriction on the interpretation of the weights in the “Equal Weight View” regarding peer disagreement and show that the view cannot respect it. Based on this result we argue against the view. The restriction is the following one: if an agent, $$\hbox {i}$$ i, assigns an equal or higher weight to another agent, $$\hbox {j}$$ j,, he must be willing—in exchange for a positive and certain payment—to accept an offer to let a completely rational and (...)
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  • Support for Geometric Pooling.Jean Baccelli & Rush T. Stewart - forthcoming - Review of Symbolic Logic:1-40.
    Supra-Bayesianism is the Bayesian response to learning the opinions of others. Probability pooling constitutes an alternative response. One natural question is whether there are cases where probability pooling gives the supra-Bayesian result. This has been called the problem of Bayes-compatibility for pooling functions. It is known that in a common prior setting, under standard assumptions, linear pooling cannot be non-trivially Bayes-compatible. We show by contrast that geometric pooling can be non-trivially Bayes-compatible. Indeed, we show that, under certain assumptions, geometric and (...)
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  • Utilitarianism with and Without Expected Utility.David McCarthy, Kalle Mikkola & Joaquin Teruji Thomas - 2020 - Journal of Mathematical Economics 87:77-113.
    We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are (...)
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  • Aggregation for Potentially Infinite Populations Without Continuity or Completeness.David McCarthy, Kalle M. Mikkola & J. Teruji Thomas - 2019 - arXiv:1911.00872 [Econ.TH].
    We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown to (...)
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  • Fully Bayesian Aggregation.Franz Dietrich - forthcoming - Journal of Economic Theory.
    Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but achieves only static (...)
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  • Towards a Pluralistic View of Formal Methods.Ko-Hung Kuan - 2020 - Dissertation, London School of Economics
    This thesis is a collection of three self-contained papers on related themes in the area of formal and social epistemology. The first paper explores the possibility of measuring the coherence of a set with multiplicative averaging. It has been pointed out that all the existing probabilistic measures of coherence are flawed for taking the relevance between a set of propositions as the primary factor which determines the coherence of the set. What I show in this paper is that a group (...)
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  • On the Accuracy of Group Credences.Richard Pettigrew - 2020 - Oxford Studies in Epistemology 6.
    to appear in Szabó Gendler, T. & J. Hawthorne (eds.) Oxford Studies in Epistemology volume 6 We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And (...)
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  • The Principal Principle and subjective Bayesianism.Christian Wallmann & Jon Williamson - 2020 - European Journal for Philosophy of Science 10 (1):1-14.
    This paper poses a problem for Lewis’ Principal Principle in a subjective Bayesian framework: we show that, where chances inform degrees of belief, subjective Bayesianism fails to validate normal informal standards of what is reasonable. This problem points to a tension between the Principal Principle and the claim that conditional degrees of belief are conditional probabilities. However, one version of objective Bayesianism has a straightforward resolution to this problem, because it avoids this latter claim. The problem, then, offers some support (...)
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  • Challenging the Majority Rule in Matters of Truth.Bernd Lahno - 2014 - Erasmus Journal for Philosophy and Economics 7 (2):54-72.
    The majority rule has caught much attention in recent debate about the aggregation of judgments. But its role in finding the truth is limited. A majority of expert judgments is not necessarily authoritative, even if all experts are equally competent, if they make their judgments independently of each other, and if all the judgments are based on the same source of (good) evidence. In this paper I demonstrate this limitation by presenting a simple counterexample and a related general result. I (...)
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  • Aggregating Incoherent Agents Who Disagree.Richard Pettigrew - unknown
    In this paper, we explore how we should aggregate the degrees of belief of a group of agents to give a single coherent set of degrees of belief, when at least some of those agents might be probabilistically incoherent. There are a number of ways of aggregating degrees of belief, and there are a number of ways of fixing incoherent degrees of belief. When we have picked one of each, should we aggregate first and then fix, or fix first and (...)
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  • The Meta-Inductive Justification of Induction.Tom F. Sterkenburg - 2020 - Episteme 17 (4):519-541.
    ABSTRACTI evaluate Schurz's proposed meta-inductive justification of induction, a refinement of Reichenbach's pragmatic justification that rests on results from the machine learning branch of prediction with expert advice.My conclusion is that the argument, suitably explicated, comes remarkably close to its grand aim: an actual justification of induction. This finding, however, is subject to two main qualifications, and still disregards one important challenge.The first qualification concerns the empirical success of induction. Even though, I argue, Schurz's argument does not need to spell (...)
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  • The joint aggregation of beliefs and degrees of belief.Paul D. Thorn - 2020 - Synthese 197 (12):5389-5409.
    The article proceeds upon the assumption that the beliefs and degrees of belief of rational agents satisfy a number of constraints, including: consistency and deductive closure for belief sets, conformity to the axioms of probability for degrees of belief, and the Lockean Thesis concerning the relationship between belief and degree of belief. Assuming that the beliefs and degrees of belief of both individuals and collectives satisfy the preceding three constraints, I discuss what further constraints may be imposed on the aggregation (...)
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  • Learning and Pooling, Pooling and Learning.Rush T. Stewart & Ignacio Ojea Quintana - 2018 - Erkenntnis 83 (3):1-21.
    We explore which types of probabilistic updating commute with convex IP pooling. Positive results are stated for Bayesian conditionalization, imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of externally Bayesian pooling operators due to Wagner :336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.
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  • Imprecise Probability in Epistemology.Elkin Lee - 2017 - Dissertation, Ludwig–Maximilians–Universitat
    There is a growing interest in the foundations as well as the application of imprecise probability in contemporary epistemology. This dissertation is concerned with the application. In particular, the research presented concerns ways in which imprecise probability, i.e. sets of probability measures, may helpfully address certain philosophical problems pertaining to rational belief. The issues I consider are disagreement among epistemic peers, complete ignorance, and inductive reasoning with imprecise priors. For each of these topics, it is assumed that belief can be (...)
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  • Prospect Theory and the Wisdom of the Inner Crowd.Stephan Hartmann - unknown
    We give a probabilistic justification of the shape of one of the probability weighting functions used in Prospect Theory. To do so, we use an idea recently introduced by Herzog and Hertwig. Along the way we also suggest a new method for the aggregation of probabilities using statistical distances.
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  • Reasons, Coherence, and Group Rationality.Brian Hedden - 2019 - Philosophy and Phenomenological Research 99 (3):581-604.
    Philosophy and Phenomenological Research, EarlyView.
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  • Formal Representations of Belief.Franz Huber - 2008 - Stanford Encyclopedia of Philosophy.
    Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...)
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