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A Theory of Bayesian Groups

Noûs 53 (3):708-736 (2019)

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  1. Why Average When You Can Stack? Better Methods for Generating Accurate Group Credences.David Kinney - forthcoming - Philosophy of Science:1-38.
    Formal and social epistemologists have devoted significant attention to the question of how to aggregate the credences of a group of agents who disagree about the probabilities of events. Most of this work focuses on strategies for calculating the mean credence function of the group. In particular, Moss and Pettigrew argue that group credences should be calculated by taking a linear mean of the credences of each individual in the group. Both of these arguments begin from the premise that that (...)
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  • Dynamically Rational Judgment Aggregation.Franz Dietrich & Christian List - manuscript
    Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments in light (...)
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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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  • 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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  • 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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