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  1. An Application of Peircean Triadic Logic: Modelling Vagueness.Asim Raza, Asim D. Bakhshi & Basit Koshul - 2019 - Journal of Logic, Language and Information 28 (3):389-426.
    Development of decision-support and intelligent agent systems necessitates mathematical descriptions of uncertainty and fuzziness in order to model vagueness. This paper seeks to present an outline of Peirce’s triadic logic as a practical new way to model vagueness in the context of artificial intelligence. Charles Sanders Peirce was an American scientist–philosopher and a great logician whose triadic logic is a culmination of the study of semiotics and the mathematical study of anti-Cantorean model of continuity and infinitesimals. After presenting Peircean semiotics (...)
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  • The Theory of Judgment Aggregation: An Introductory Review.Christian List - 2012 - Synthese 187 (1):179-207.
    This paper provides an introductory review of the theory of judgment aggregation. It introduces the paradoxes of majority voting that originally motivated the field, explains several key results on the impossibility of propositionwise judgment aggregation, presents a pedagogical proof of one of those results, discusses escape routes from the impossibility and relates judgment aggregation to some other salient aggregation problems, such as preference aggregation, abstract aggregation and probability aggregation. The present illustrative rather than exhaustive review is intended to give readers (...)
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  • Probabilistic Opinion Pooling.Franz Dietrich & Christian List - 2016 - In A. Hajek & C. Hitchcock (eds.), Oxford Handbook of Philosophy and Probability. Oxford: Oxford University Press.
    Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of each class of (...)
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  • Three Kinds of Collective Attitudes.Christian List - 2014 - Erkenntnis 79 (S9):1601-1622.
    This paper offers a comparison of three different kinds of collective attitudes: aggregate, common, and corporate attitudes. They differ not only in their relationship to individual attitudes—e.g., whether they are “reducible” to individual attitudes—but also in the roles they play in relation to the collectives to which they are ascribed. The failure to distinguish them can lead to confusion, in informal talk as well as in the social sciences. So, the paper’s message is an appeal for disambiguation.
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  • Logics for Modelling Collective Attitudes.Daniele Porello - 2018 - Fundamenta Infromaticae 158 (1-3):239-27.
    We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal modalities (...)
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  • The Theory of Judgment Aggregation: An Introductory Review.Christian List - 2010 - LSE Choice Group Working Paper Series 6 (1).
    This paper provides an introductory review of the theory of judgment aggregation. It introduces the paradoxes of majority voting that originally motivated the field, explains several key results on the impossibility of propositionwise judgment aggregation, presents a pedagogical proof of one of those results, discusses escape routes from the impossibility and relates judgment aggregation to some other salient aggregation problems, such as preference aggregation, abstract aggregation and probability aggregation. The present illustrative rather than exhaustive review is intended to give readers (...)
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  • An Impossibility Theorem for Allocation Aggregation.Carl Wagner & Mark Shattuck - unknown
    In axiomatic approaches to expert opinion aggregation, so-called independence conditions have been ubiquitous. Such conditions dictate that the group value assigned to each decision variable should depend only on the values assigned by individuals to that variable, taking no account of values that they assign to other variables. This radically anti-holistic stricture on the synthesis of expert opinion severely limits the set of allowable aggregation methods. As we show, the limitations are particularly acute in the case of three or more (...)
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  • Realistic Opinion Aggregation: Lehrer-Wagner with a Finite Set of Opinion Values.R. Bradley & C. Wagner - 2012 - Episteme 9 (2):91-99.
    An allocation problem is a type of aggregation problem in which the values of individuals' opinions on some set of variables sum to a constant. This paper shows that for realistic allocation problems, namely ones in which the set of possible opinion values is finite, the only universal aggregation methods that satisfy two commonly invoked conditions are the dictatorial ones. The two conditions are, first, that the aggregate opinion on any variable depends only on the individuals' opinions on that variable (...)
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  • Propositionwise Judgment Aggregation: The General Case.Franz Dietrich & Christian List - 2013 - Social Choice and Welfare 40 (4):1067-1095.
    In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or implication preservation. We fully characterize the agendas for which there (...)
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  • Sleeping Beauty and De Nunc Updating.Namjoong Kim - 2010 - Dissertation, University of Massachusetts
    About a decade ago, Adam Elga introduced philosophers to an intriguing puzzle. In it, Sleeping Beauty, a perfectly rational agent, undergoes an experiment in which she becomes ignorant of what time it is. This situation is puzzling for two reasons: First, because there are two equally plausible views about how she will change her degree of belief given her situation and, second, because the traditional rules for updating degrees of belief don't seem to apply to this case. In this dissertation, (...)
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  • A Puzzle About Belief Updating.Carlo Martini - 2013 - Synthese 190 (15):3149-3160.
    In recent decades much literature has been produced on disagreement; the puzzling conclusion being that epistemic disagreement is, for the most part, either impossible (e.g. Aumann (Ann Stat 4(6):1236–1239, 1976)), or at least easily resolvable (e.g. Elga (Noûs 41(3):478–502, 2007)). In this paper I show that, under certain conditions, an equally puzzling result arises: that is, disagreement cannot be rationally resolved by belief updating. I suggest a solution to the puzzle which makes use of some of the principles of Hintikka’s (...)
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  • Aggregating Causal Judgments.Richard Bradley, Franz Dietrich & Christian List - 2014 - Philosophy of Science 81 (4):491-515.
    Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individuals' causal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem of causal-network aggregation. (...)
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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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  • Introduction to Judgment Aggregation.Christian List & Ben Polak - 2010 - Journal of Economic Theory 145 (2):441-466.
    This introduces the symposium on judgment aggregation. The theory of judgment aggregation asks how several individuals' judgments on some logically connected propositions can be aggregated into consistent collective judgments. The aim of this introduction is to show how ideas from the familiar theory of preference aggregation can be extended to this more general case. We first translate a proof of Arrow's impossibility theorem into the new setting, so as to motivate some of the central concepts and conditions leading to analogous (...)
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  • The Theory of Judgment Aggregation: An Introductory Review.Christian List - 2010 - LSE Choice Group Working Paper Series 6 (1).
    This paper provides an introductory review of the theory of judgment aggregation. It introduces the paradoxes of majority voting that originally motivated the field, explains several key results on the impossibility of propositionwise judgment aggregation, presents a pedagogical proof of one of those results, discusses escape routes from the impossibility and relates judgment aggregation to some other salient aggregation problems, such as preference aggregation, abstract aggregation and probability aggregation. The present illustrative rather than exhaustive review is intended to give readers (...)
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  • Peer Disagreement: A Call for the Revision of Prior Probabilities.Sven Rosenkranz & Moritz Schulz - 2015 - Dialectica 69 (4):551-586.
    The current debate about peer disagreement has so far mainly focused on the question of whether peer disagreements provide genuine counterevidence to which we should respond by revising our credences. By contrast, comparatively little attention has been devoted to the question by which process, if any, such revision should be brought about. The standard assumption is that we update our credences by conditionalizing on the evidence that peer disagreements provide. In this paper, we argue that non-dogmatist views have good reasons (...)
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  • Resolving Disagreement Through Mutual Respect.Carlo Martini, Jan Sprenger & Mark Colyvan - 2013 - Erkenntnis 78 (4):881-898.
    This paper explores the scope and limits of rational consensus through mutual respect, with the primary focus on the best known formal model of consensus: the Lehrer–Wagner model. We consider various arguments against the rationality of the Lehrer–Wagner model as a model of consensus about factual matters. We conclude that models such as this face problems in achieving rational consensus on disagreements about unknown factual matters, but that they hold considerable promise as models of how to rationally resolve non-factual disagreements.
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  • Judgment Aggregation.Fabrizio Cariani - 2011 - Philosophy Compass 6 (1):22-32.
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