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74The problem of constrained judgment aggregationIn Thomas Uebel, Stephan Hartmann, Wenceslao Gonzalez, Marcel Weber, Dennis Dieks & Friedrich Stadler (eds.), The Present Situation in the Philosophy of Science, Springer. pp. 125-139. 2010.Group decisions must often obey exogenous constraints. While in a preference aggregation problem constraints are modelled by restricting the set of feasible alternatives, this paper discusses the modelling of constraints when aggregating individual yes/no judgments on interconnected propositions. For example, court judgments in breach-of-contract cases should respect the constraint that action and obligation are necessary and sufficient for liability, and judgments on budget items should respect…Read more
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The problem of constrained judgment aggregationIn Thomas Uebel, Stephan Hartmann, Wenceslao Gonzalez, Marcel Weber, Dennis Dieks & Friedrich Stadler (eds.), The Present Situation in the Philosophy of Science, Springer. pp. 125-139. 2010.Group decisions must often obey exogenous constraints. While in a preference aggregation problem constraints are modelled by restricting the set of feasible alternatives, this paper discusses the modelling of constraints when aggregating individual yes/no judgments on interconnected propositions. For example, court judgments in breach-of-contract cases should respect the constraint that action and obligation are necessary and sufficient for liability, and judgments on budget items should respect…Read more
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11The problem of constrained judgment aggregationIn Thomas Uebel, Stephan Hartmann, Wenceslao Gonzalez, Marcel Weber, Dennis Dieks & Friedrich Stadler (eds.), The Present Situation in the Philosophy of Science, Springer. pp. 125-139. 2010.Group decisions must often obey exogenous constraints. While in a preference aggregation problem constraints are modelled by restricting the set of feasible alternatives, this paper discusses the modelling of constraints when aggregating individual yes/no judgments on interconnected propositions. For example, court judgments in breach-of-contract cases should respect the constraint that action and obligation are necessary and sufficient for liability, and judgments on budget items should respect…Read more
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296A probability aggregation rule assigns to each profile of probability functions across a group of individuals (representing their individual probability assignments to some propositions) a collective probability function (representing the group's probability assignment). The rule is “non-manipulable” if no group member can manipulate the collective probability for any proposition in the direction of his or her own probability by misrepresenting his or her probability function (“strategic voting”…Read more
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1137Reasoning in attitudesSynthese 200 (6). 2022.People reason not only in beliefs, but also in intentions, preferences, and other attitudes. They form preferences from existing preferences, or intentions from existing beliefs and intentions, and so on. This often involves choosing between rival conclusions. Building on Broome (Rationality through reasoning, Hoboken, Wiley. https://doi.org/10.1002/9781118609088, 2013) and Dietrich et al. (J Philos 116:585–614. https://doi.org/10.5840/jphil20191161138, 2019), we present a philosophical and form…Read more
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237Deliberation and the Wisdom of CrowdsEconomic Theory. forthcoming.Does pre-voting group deliberation improve majority outcomes? To address this question, we develop a probabilistic model of opinion formation and deliberation. Two new jury theorems, one pre-deliberation and one post-deliberation, suggest that deliberation is beneficial. Successful deliberation mitigates three voting failures: (1) overcounting widespread evidence, (2) neglecting evidential inequality, and (3) neglecting evidential complementarity. Formal results and simulations confirm this. But…Read more
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418Categorical versus graded beliefsFrontiers in Psychology 18. 2022.This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold both types of belief simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List (2018, 2021). The nature, relevance, and implications of the tension are explained and assessed.
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637Abstract rationality: the ‘logical’ structure of attitudesEconomics and Philosophy 40 (1): 12-41. 2024.We present an abstract model of rationality that focuses on structural properties of attitudes. Rationality requires coherence between your attitudes, such as your beliefs, values, and intentions. We define three 'logical' conditions on attitudes: consistency, completeness, and closedness. They parallel the familiar logical conditions on beliefs, but contrast with standard rationality conditions like preference transitivity. We establish a formal correspondence between our logical conditions and…Read more
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320Jury TheoremsThe Stanford Encyclopedia of Philosophy. 2021.Jury theorems are mathematical theorems about the ability of collectives to make correct decisions. Several jury theorems carry the optimistic message that, in suitable circumstances, ‘crowds are wise’: many individuals together (using, for instance, majority voting) tend to make good decisions, outperforming fewer or just one individual. Jury theorems form the technical core of epistemic arguments for democracy, and provide probabilistic tools for reasoning about the epistemic quality of collec…Read more
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1421Dynamically rational judgment aggregationSocial Choice and Welfare. forthcoming.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 o…Read more
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425Fully Bayesian AggregationJournal of Economic Theory 194 105255. 2021.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 …Read more
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983Decision under normative uncertaintyEconomics and Philosophy 38 (3): 372-394. 2022.While ordinary decision theory focuses on empirical uncertainty, real decision-makers also face normative uncertainty: uncertainty about value itself. From a purely formal perspective, normative uncertainty is comparable to (Harsanyian or Rawlsian) identity uncertainty in the 'original position', where one's future values are unknown. A comprehensive decision theory must address twofold uncertainty -- normative and empirical. We present a simple model of twofold uncertainty, and show that the mo…Read more
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446A Broomean Model of Rationality and ReasoningJournal of Philosophy 116 (11): 585-614. 2019.John Broome has developed an account of rationality and reasoning which gives philosophical foundations for choice theory and the psychology of rational agents. We formalize his account into a model that differs from ordinary choice-theoretic models through focusing on psychology and the reasoning process. Within that model, we ask Broome’s central question of whether reasoning can make us more rational: whether it allows us to acquire transitive preferences, consistent beliefs, non-akratic inte…Read more
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480Independent Opinions? On the Causal Foundations of Belief Formation and Jury TheoremsMind 122 (487): 655-685. 2013.Democratic decision-making is often defended on grounds of the ‘wisdom of crowds’: decisions are more likely to be correct if they are based on many independent opinions, so a typical argument in social epistemology. But what does it mean to have independent opinions? Opinions can be probabilistically dependent even if individuals form their opinion in causal isolation from each other. We distinguish four probabilistic notions of opinion independence. Which of them holds depends on how individua…Read more
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396The problem of constrained judgment aggregationIn Thomas Uebel, Stephan Hartmann, Wenceslao Gonzalez, Marcel Weber, Dennis Dieks & Friedrich Stadler (eds.), The Present Situation in the Philosophy of Science, Springer. pp. 125-139. 2010.Group decisions must often obey exogenous constraints. While in a preference aggregation problem constraints are modelled by restricting the set of feasible alternatives, this paper discusses the modelling of constraints when aggregating individual yes/no judgments on interconnected propositions. For example, court judgments in breach-of-contract cases should respect the constraint that action and obligation are necessary and sufficient for liability, and judgments on budget items should respect…Read more
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632The Premises of Condorcet’s Jury Theorem Are Not Simultaneously JustifiedEpisteme 5 (1): 56-73. 2008.Condorcet's famous jury theorem reaches an optimistic conclusion on the correctness of majority decisions, based on two controversial premises about voters: they are competent and vote independently, in a technical sense. I carefully analyse these premises and show that: whether a premise is justi…ed depends on the notion of probability considered; none of the notions renders both premises simultaneously justi…ed. Under the perhaps most interesting notions, the independence assumption should be …Read more
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491A liberal paradox for judgment aggregationSocial Choice and Welfare 31 (1): 59-78. 2008.In the emerging literature on judgment aggregation over logically connected proposi- tions, expert rights or liberal rights have not been investigated yet. A group making collective judgments may assign individual members or subgroups with expert know- ledge on, or particularly affected by, certain propositions the right to determine the collective judgment on those propositions. We identify a problem that generalizes Sen's 'liberal paradox'. Under plausible conditions, the assignment of rights …Read more
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1843The relation between degrees of belief and binary beliefs: A general impossibility theoremIn Igor Douven (ed.), Lotteries, Knowledge, and Rational Belief. Essays on the Lottery Paradox., Cambridge University Press. pp. 223-54. 2021.Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this problem gen…Read more
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120On coherent sets and the transmission of confirmationPhilosophy of Science 72 (3): 403-424. 2005.In this paper, we identify a new and mathematically well-defined sense in which the coherence of a set of hypotheses can be truth-conducive. Our focus is not, as usual, on the probability but on the confirmation of a coherent set and its members. We show that, if evidence confirms a hypothesis, confirmation is “transmitted” to any hypotheses that are sufficiently coherent with the former hypothesis, according to some appropriate probabilistic coherence measure such as Olsson’s or Fitelson’s meas…Read more
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318Introduction to the special issue “Beliefs in Groups” of Theory and DecisionTheory and Decision 85 (1): 1-4. 2018.This symposium in the overlap of philosophy and decision theory is described well by its title “Beliefs in Groups”. Each word in the title matters, with one intended ambiguity. The symposium is about beliefs rather than other attitudes such as preferences; these beliefs take the form of probabilities in the first three contributions, binary yes/no beliefs (‘judgments’) in the fourth contribution, and qualitative probabilities (‘probability grades’) in the fifth contributio…Read more
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652From Degrees of Belief to Binary Beliefs: Lessons from Judgment-Aggregation TheoryJournal of Philosophy 115 (5): 225-270. 2018.What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been…Read more
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426A Theory of Bayesian GroupsNoûs 53 (3): 708-736. 2017.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-publ…Read more
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1305What matters and how it matters: A choice-theoretic representation of moral theoriesPhilosophical Review 126 (4): 421-479. 2017.We present a new “reason-based” approach to the formal representation of moral theories, drawing on recent decision-theoretic work. We show that any moral theory within a very large class can be represented in terms of two parameters: a specification of which properties of the objects of moral choice matter in any given context, and a specification of how these properties matter. Reason-based representations provide a very general taxonomy of moral theories, as differences among theories can be …Read more
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524Jury TheoremsIn M. Fricker, N. J. L. L. Pedersen, D. Henderson & P. J. Graham (eds.), The Routledge Handbook of Social Epistemology, Routledge. 2019.We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the t…Read more
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691Belief revision generalized: A joint characterization of Bayes's and Jeffrey's rulesJournal of Economic Theory 162 352-371. 2016.We present a general framework for representing belief-revision rules and use it to characterize Bayes's rule as a classical example and Jeffrey's rule as a non-classical one. In Jeffrey's rule, the input to a belief revision is not simply the information that some event has occurred, as in Bayes's rule, but a new assignment of probabilities to some events. Despite their differences, Bayes's and Jeffrey's rules can be characterized in terms of the same axioms: "responsiveness", which requires th…Read more
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144A model of jury decisions where all jurors have the same evidenceSynthese 142 (2). 2004.Under the independence and competence assumptions of Condorcet’s classical jury model, the probability of a correct majority decision converges to certainty as the jury size increases, a seemingly unrealistic result. Using Bayesian networks, we argue that the model’s independence assumption requires that the state of the world (guilty or not guilty) is the latest common cause of all jurors’ votes. But often – arguably in all courtroom cases and in many expert panels – the latest such common caus…Read more
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893Reason-based choice and context-dependence: An explanatory frameworkEconomics and Philosophy 32 (2): 175-229. 2016.We introduce a “reason-based” framework for explaining and predicting individual choices. It captures the idea that a decision-maker focuses on some but not all properties of the options and chooses an option whose motivationally salient properties he/she most prefers. Reason-based explanations allow us to distinguish between two kinds of context-dependent choice: the motivationally salient properties may (i) vary across choice contexts, and (ii) include not only “intrinsic” properties of the op…Read more
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111The two-envelope paradox: An axiomatic approachMind 114 (454): 239-248. 2005.There has been much discussion on the two-envelope paradox. Clark and Shackel (2000) have proposed a solution to the paradox, which has been refuted by Meacham and Weisberg (2003). Surprisingly, however, the literature still contains no axiomatic justification for the claim that one should be indifferent between the two envelopes before opening one of them. According to Meacham and Weisberg, "decision theory does not rank swapping against sticking [before opening any envelope]" (p. 686). To fill…Read more
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354Probabilistic opinion pooling generalised. Part two: The premise-based approachSocial Choice and Welfare 48 (4). 2017.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 …Read more
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86Judgment aggregation: (Im)possibility theoremsJournal of Economic Theory 1 (126): 286-298. 2006.The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) age…Read more
University of Oxford
Alumnus, 2004
Areas of Specialization
Philosophy of Social Science |
Decision Theory |
Social Choice Theory |
Social Epistemology |
Meta-Ethics |