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Probabilistic Opinion Pooling

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

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  1. 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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  • 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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  • Utilitarianism with and Without Expected Utility.David McCarthy, Kalle Mikkola & Teruji Thomas - 2016 - MPRA Paper No. 90125.
    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 individual preorder then uniquely determines a social 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 also consistent with the rejection of all (...)
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  • On the Accuracy of Group Credences.Richard Pettigrew - manuscript
    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? (...)
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  • A Pragmatic Argument Against Equal Weighting.Ittay Nissan-Rozen & Levi Spectre - forthcoming - Synthese.
    We present a minimal pragmatic restriction on the interpretation of the weights in the “Equal Weight View” (and, more generally, in the “Linear Pooling” 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, i, assigns an equal or higher weight to another agent, j, (i.e. if i takes j to be as epistemically competent as him or epistemically superior to (...)
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  • Reasons, Coherence, and Group Rationality.Brian Hedden - forthcoming - Philosophy and Phenomenological Research.
    Philosophy and Phenomenological Research, EarlyView.
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  • Choosing for Changing Selves.Richard Pettigrew - manuscript
    *This is the first draft of this book* -/- What you value and the extent to which you value it changes over the course of your life. A person might currently greatly value pursuing philosophy, and value spending time in nature much less; but, having watched their parents as they have grown older, and noting that they are very much like their parents, that person might have good reason to think that they will value the pursuit of philosophy much less (...)
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  • The Joint Aggregation of Beliefs and Degrees of Belief.Paul D. Thorn - forthcoming - Synthese:1-21.
    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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  • 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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  • 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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  • 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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  • The Meta-Inductive Justification of Induction.Tom F. Sterkenburg - forthcoming - Episteme:1-23.
    I evaluate Schurz's proposed meta-inductive justification of induction, a refinement of Reichenbach's pragmatic justification that is founded on results from the machine learning branch of prediction with expert advice.
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  • Probabilistic Opinion Pooling Generalised -- Part Two: The Premise-Based Approach.Franz Dietrich & Christian List - 2017 - Social Choice and Welfare 48:787–814.
    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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  • Probabilistic Opinion Pooling Generalized -- Part One: General Agendas.Franz Dietrich & Christian List - 2017 - Social Choice and Welfare 48:747–786.
    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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  • 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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  • A Theory of Bayesian Groups.Franz Dietrich - manuscript
    A group is often construed as a single agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated contribution “Groupthink”, Russell et al. (2015) apply the Bayesian paradigm to groups by requiring group credences to undergo a Bayesian revision whenever new information is learnt, i.e., whenever the individual credences undergo a Bayesian revision based on this information. Bayesians should often strengthen this requirement by extending it to non-public (...)
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