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  1. Franz Dietrich & C. List, Opinion Pooling on General Agendas: Linearity or Just Neutrality?
    How can di¤erent individuals’probability assignments to some events be aggregated into a collective probability assignment? Although there are several classic results on this problem, they all assume that the ‘agenda’ of relevant events forms a -algebra, an overly demanding assumption for many practical applications. We drop this assumption and explore probabilistic opinion pooling on general agendas. Our main theorems characterize linear pooling and neutral pooling for large classes of agendas, with standard results as special cases.
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  2. Christian List & Franz Dietrich, Judgment Aggregation with Consistency Alone.
  3. Franz Dietrich, Bayesian Group Belief.
    If a group is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of group members, who are themselves modelled as Bayesian agents, possibly with di¤erent priors and di¤erent information. Group beliefs are proven to take a simple multiplicative form if people’s information is independent, and a more complex form if information overlaps arbitrarily. This shows that group beliefs can incorporate all information spread over the individuals without (...)
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  4. Richard Bradley, Franz Dietrich & Christian List, Aggregating Causal Judgements.
    Decision making typically requires judgements about causal relations: we need to know both the causal e¤ects of our actions and the causal relevance of various environmental factors. Judgements about the nature and strength of causal rela- tions often di¤er, even among experts. How to handle such diversity is the topic of this paper. First we consider the possibility of aggregating causal judgements via the aggregation of probabilistic ones. The broadly negative outcome of this investigation leads us to look at aggregating (...)
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  5. Franz Dietrich, A Generalised Model of Judgment Aggregation.
    The new …eld of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements (“if P then Q”) as material conditionals. In this methodological paper, I present a simple uni…ed model of judgment aggregation in general logics. I show how many realistic decision problems can (...)
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  6. Franz Dietrich, A Liberal Paradox for Judgment Aggregation.
    In the emerging literature on judgment aggregation over logically connected propositions, expert rights or liberal rights have not been investigated yet. A group making collective judgments may assign individual members or subgroups with expert knowledge on, or particularly a¤ected 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 to two or more individuals or subgroups is inconsistent with the unanimity principle, (...)
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  7. Franz Dietrich, Anti-Terrorism Politics and the Risk of Provoking.
    A population’s level of terrorism depends on two factors: people’s preferences (would they like creating damage?) and the constraints under which people act (what damage could they create, and at what punishment?). Causerelated policies, e.g. improving social stability or education, aim at appeasing preferences, thereby reducing terrorism. Symptom-related policies, e.g. embargoes or wars, change the constraints (‘deterrence’), but may have side e¤ects on preferences (‘provocation’); terrorism increases if provocation overweighs deterrence. I model preferences for damage as endogenous and policy-dependent. I (...)
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  8. Franz Dietrich, Aggregation Theory and the Relevance of Some Issues to Others.
    I propose a general collective decision problem consisting in many issues that are interconnected in two ways: by mutual constraints and by connections of relevance. Aggregate decisions should respect the mutual constraints, and be based on relevant information only. This general informational constraint has many special cases, including premise-basedness and Arrow’s independence condition; they result from special notions of relevance. The existence and nature of (non-degenerate) aggregation rules depends on both types of connections. One result, if applied to the preference (...)
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  9. Franz Dietrich, General Representation of Epistemically Optimal Procedures.
    Assuming that votes are independent, the epistemically optimal procedure in a binary collective choice problem is known to be a weighted supermajority rule with weights given by personal log-likelihood-ratios. It is shown here that an analogous result holds in a much more general model. Firstly, the result follows from a more basic principle than expected-utility maximisation, namely from an axiom ("Epistemic Monotonicity") which requires neither utilities nor prior probabilities of the ‘correctness’ of alternatives. Secondly, a person’s input need not be (...)
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  10. Franz Dietrich, How to Reach Legitimate Decisions When the Procedure is Controversial.
    Imagine a group that faces a decision problem but does not agree on which decision procedure is appropriate. In that case, can a decision be reached that respects the procedural concerns of the group? There is a sense in which legitimate decisions are possible even if people disagree on which procedure to use. I propose to decide in favour of an option which maximizes the number of persons whose judged-right procedure happens to entail this decision given the profile. This decision (...)
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  11. Franz Dietrich, Judgment Aggregation: (Im)Possibility Theorems.
    The aggregation of individual judgments over interrelated propositions is a newly arising …eld of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a speci…c 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) agenda. However, independence conditions arguably undermine the logical structure of judgment aggregation. I therefore (...)
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  12. Franz Dietrich, Judgment Aggregation on Restricted Domains.
    We show that, when a group takes independent majority votes on interconnected propositions, the outcome is consistent once the pro…le of individual judgment sets respects appropriate structural conditions. We introduce several such conditions on pro…les, based on ordering the propositions or ordering the individuals, and we clarify the relations between these conditions. By restricting the conditions to appropriate subagendas, we obtain local conditions that are less demanding but still guarantee consistent majority judgments. By applying the conditions to agendas representing preference (...)
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  13. Franz Dietrich, Judgment Aggregation Under Constraints.
    In solving judgment aggregation problems, groups often face constraints. Many decision problems can be modelled in terms the acceptance or rejection of certain propositions in a language, and constraints as propositions that the decisions should be consistent with. For example, court judgments in breach-of-contract cases should be consistent with the constraint that action and obligation are necessary and su¢ - cient for liability; judgments on how to rank several options in an order of preference with the constraint of transitivity; and (...)
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  14. Franz Dietrich, Judgment Aggregation Without Full Rationality.
    Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal condition of (...)
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  15. Franz Dietrich, Judgment Aggregation with Consistency Alone.
    All existing impossibility theorems on judgment aggregation require individual and collective judgment sets to be consistent and complete (in some recent results with completeness relaxed to deductive closure), arguably a demanding rationality requirement. They do not carry over to aggregation functions mapping pro…les of (merely) consistent individual judgment sets to (merely) consistent collective ones. We prove that, whenever the agenda of propositions under consideration exhibits mild interconnections, any such aggregation function that is "neutral" between the acceptance and rejection of each (...)
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  16. Franz Dietrich, Modelling Change in Individual Characteristics: An Axiomatic Framework.
    Economic models describe individuals in terms of underlying characteristics, such as taste for some good, sympathy level for another player, time discount rate, risk attitude, and so on. In real life, such characteristics change: taste for Mozart changes by listening to it, sympathy for another player changes by observing his moves, and so on. Models typically ignore change, not just for simplicity but also because it is unclear how to incorporate change. I introduce a general axiomatic framework for analysing and (...)
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  17. Franz Dietrich, Majority Voting on Restricted Domains.
    In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments su¢ - cient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen’s triplewise value-restriction, itself the most general classic condition. We also prove a (...)
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  18. Franz Dietrich, Opinion Pooling on General Agendas.
    How can di¤erent individuals’probability assignments to some events be aggregated into a collective probability assignment? Although there are several classic results on this problem, they all assume that the ‘agenda’ of relevant events forms a -algebra, an overly demanding assumption for many practical applications. We drop this assumption and explore probabilistic opinion pooling on general agendas. Our main theorems characterize linear pooling and neutral pooling for large classes of agendas, with standard results as special cases.
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  19. Franz Dietrich, Opinion Pooling Under Informational Asymmetries.
    If a group as a whole is modelled as a single Bayesian agent, what should its beliefs be? I propose an axiomatic model that connects group beliefs to beliefs of group members, who are themselves modelled as Bayesian agents, possibly with di¤erent priors and di¤erent information. Group beliefs are shown to take a simple multiplicative form if people’s information is independent, and a more complex form if information can overlap arbitrarily. This shows that group beliefs can incorporate all information spread (...)
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  20. Franz Dietrich, The Possibility of Judgment Aggregation on Agendas with Subjunctive Implications.
    The new …eld of judgment aggregation aims to …nd collective judgments on logically interconnected propositions. Recent impossibility results establish limitations on the possibility to vote independently on the propositions. I show that, fortunately, the impossibility results do not apply to a wide class of realistic agendas once propositions like “if a then b” are adequately modelled, namely as subjunctive implications rather than material implications. For these agendas, consistent and complete collective judgments can be reached through appropriate quota rules (which decide (...)
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  21. Franz Dietrich, Welfarism, Preferencism, Judgmentism.
    In a single framework, I address the question of the informational basis for evaluating social states. I particularly focus on information about individual welfare, individual preferences and individual (moral) judgments, but the model is also open to any other informational input deemed relevant, e.g. sources of welfare and motivations behind preferences. In addition to proving some possibility and impossibility results, I discuss objections against using information about only one aspect (e.g. using only preference information). These objections suggest a multi-aspect informational (...)
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  22. Franz Dietrich & Christian List, Probabilistic Opinion Pooling.
    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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  23. Franz Dietrich & Christian List, Probabilistic Opinion Pooling Generalized -- Part One: General Agendas.
    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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  24. Franz Dietrich & Christian List, Probabilistic Opinion Pooling Generalised -- Part Two: The Premise-Based Approach.
    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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  25. Franz Dietrich & Christian List, Reason-Based Rationalization.
    We introduce a “reason-based” way of rationalizing an agent’s choice behaviour, which explains choices by specifying which properties of the options or choice context the agent cares about (the “motivationally salient properties”) and how he or she cares about these properties (the “fundamental preference relation”). Reason-based rationalizations can explain non-classical choice behaviour, including boundedly rational and sophisticated rational behaviour, and predict choices in unobserved contexts, an issue neglected in standard choice theory. We characterize the behavioural implications of different reason-based models (...)
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  26. Christian List & Franz Dietrich, Judgment Aggregation by Quota Rules: Majority Voting Generalized.
  27. Christian List & Franz Dietrich, Judgment Aggregation on Restricted Domains.
    We show that, when a group takes independent majority votes on interconnected propositions, the outcome is consistent once the pro…le of individual judgment sets respects appropriate structural conditions. We introduce several such conditions on pro…les, based on ordering the propositions or ordering the individuals, and we clarify the relations between these conditions. By restricting the conditions to appropriate subagendas, we obtain local conditions that are less demanding but still guarantee consistent majority judgments. By applying the conditions to agendas representing preference (...)
     
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  28. Christian List & Franz Dietrich, Mentalism Versus Behaviourism in Economics: A Philosophy-of-Science Perspective.
    Behaviourism is the view that preferences, beliefs, and other mental states in social-scientific theories are nothing but constructs re-describing people's behavioural dispositions. Mentalism is the view that they capture real phenomena, no less existent than the unobservable entities and properties in the natural sciences, such as electrons and electromagnetic fields. While behaviourism has long gone out of fashion in psychology and linguistics, it remains influential in economics, especially in `revealed preference' theory. We aim to (i) clear up some common confusions (...)
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  29. Christian List & Franz Dietrich, Opinion Pooling on General Agendas.
  30. Franz Dietrich & Christian List (2013). A Reason-Based Theory of Rational Choice. Noûs 47 (1):104-134.
    There is a surprising disconnect between formal rational choice theory and philosophical work on reasons. The one is silent on the role of reasons in rational choices, the other rarely engages with the formal models of decision problems used by social scientists. To bridge this gap, we propose a new, reason-based theory of rational choice. At its core is an account of preference formation, according to which an agent’s preferences are determined by his or her motivating reasons, together with a (...)
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  31. Franz Dietrich & Christian List (2013). Reasons for (Prior) Belief in Bayesian Epistemology. Synthese 190 (5):781-786.
    Bayesian epistemology tells us with great precision how we should move from prior to posterior beliefs in light of new evidence or information, but says little about where our prior beliefs come from. It offers few resources to describe some prior beliefs as rational or well-justified, and others as irrational or unreasonable. A different strand of epistemology takes the central epistemological question to be not how to change one’s beliefs in light of new evidence, but what reasons justify a given (...)
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  32. Franz Dietrich & Christian List (2013). Where Do Preferences Come From? International Journal of Game Theory 42 (3):613-637.
    Rational choice theory analyzes how an agent can rationally act, given his or her preferences, but says little about where those preferences come from. Preferences are usually assumed to be fixed and exogenously given. Building on related work on reasons and rational choice, we describe a framework for conceptualizing preference formation and preference change. In our model, an agent's preferences are based on certain "motivationally salient" properties of the alternatives over which the preferences are held. Preferences may change as new (...)
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  33. Franz Dietrich & Christian List (2013). Propositionwise Judgment Aggregation: The General Case. 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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  34. Franz Dietrich & Kai Spiekermann (2013). Epistemic Democracy with Defensible Premises. Economics and Philosophy 29 (1):87--120.
    The contemporary theory of epistemic democracy often draws on the Condorcet Jury Theorem to formally justify the ‘wisdom of crowds’. But this theorem is inapplicable in its current form, since one of its premises – voter independence – is notoriously violated. This premise carries responsibility for the theorem's misleading conclusion that ‘large crowds are infallible’. We prove a more useful jury theorem: under defensible premises, ‘large crowds are fallible but better than small groups’. This theorem rehabilitates the importance of deliberation (...)
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  35. Franz Dietrich & Kai Spiekermann (2013). Independent Opinions? On the Causal Foundations of Belief Formation and Jury Theorems. Mind 122 (487):fzt074.
    It is often claimed that opinions are more likely to be correct if they are held independently by many individuals. But what does it mean to hold independent opinions? To clarify this condition, we distinguish four notions of probabilistic opinion independence. Which notion applies depends on environmental factors such as commonly perceived evidence. More formally, it depends on the causal network that determines how people interact and form their opinions. In a general theorem, we identify conditions on this network that (...)
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  36. Franz Dietrich & Christian List (2011). A Model of Non-Informational Preference Change. Journal of Theoretical Politics 23 (2):145-164.
    According to standard rational choice theory, as commonly used in political science and economics, an agent's fundamental preferences are exogenously fixed, and any preference change over decision options is due to Bayesian information learning. Although elegant and parsimonious, such a model fails to account for preference change driven by experiences or psychological changes distinct from information learning. We develop a model of non-informational preference change. Alternatives are modelled as points in some multidimensional space, only some of whose dimensions play a (...)
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  37. Franz Dietrich (2010). The Impossibility of Unbiased Judgment Aggregation. Theory and Decision 68 (3):281-299.
    Standard impossibility theorems on judgment aggregation over logically connected propositions either use a controversial systematicity condition or apply only to agendas of propositions with rich logical connections. Are there any serious impossibilities without these restrictions? We prove an impossibility theorem without requiring systematicity that applies to most standard agendas: Every judgment aggregation function (with rational inputs and outputs) satisfying a condition called unbiasedness is dictatorial (or effectively dictatorial if we remove one of the agenda conditions). Our agenda conditions are tight. (...)
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  38. Franz Dietrich & Christian List (2010). The Aggregation of Propositional Attitudes: Towards a General Theory. Oxford Studies in Epistemology 3.
    How can the propositional attitudes of several individuals be aggregated into overall collective propositional attitudes? Although there are large bodies of work on the aggregation of various special kinds of propositional attitudes, such as preferences, judgments, probabilities and utilities, the aggregation of propositional attitudes is seldom studied in full generality. In this paper, we seek to contribute to filling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove two new theorems. (...)
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  39. Franz Dietrich & Christian List (2010). The Problem of Constrained Judgment Aggregation. In. In Thomas Uebel, Stephan Hartmann, Wenceslao Gonzalez, Marcel Weber, Dennis Dieks & Friedrich Stadler (eds.), The Present Situation in the Philosophy of Science. Springer. 125--139.
  40. Franz Dietrich & Philippe Mongin (2010). The Premiss-Based Approach to Judgment Aggregation. Journal of Economic Theory 145 (2):562-582.
    We investigate judgment aggregation by assuming that some formulas of the agenda are singled out as premisses, and the Independence condition (formula-wise aggregation) holds for them, though perhaps not for others. Whether premiss-based aggregation thus de…ned is non-degenerate depends on how premisses are logically connected, both among themselves and with other formulas. We identify necessary and su¢ cient conditions for dictatorship or oligarchy on the premisses, and investigate when these results extend to the whole agenda. Our theorems recover or strengthen (...)
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  41. Franz Dietrich (2008). The Premises of Condorcet's Jury Theorem Are Not Simultaneously Justified. Episteme 5 (1):56-73.
    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: (i) whether a premise is justified depends on the notion of probability considered and (ii) none of the notions renders both premises simultaneously justified. Under the perhaps most interesting notions, the independence assumption should be weakened.
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  42. Franz Dietrich (2007). Strategy-Proof Judgment Aggregation. Economics and Philosophy 23 (3):269-300.
    Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard-Satterthwaite theorem. We also discuss weaker forms of nonmanipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premisebased voting”, (...)
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  43. Franz Dietrich & Christian List (2007). Arrow's Theorem in Judgment Aggregation. Social Choice and Welfare 29 (1):19-33.
    In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby (...)
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  44. Christian List & Franz Dietrich (2007). Strategy-Proof Judgment Aggregation. Economics and Philosophy 23 (3):269-300.
    Economics and Philosophy 23(3) (in press).
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  45. Franz Dietrich & Christian List (2005). The Two-Envelope Paradox: An Axiomatic Approach. Mind 114 (454):239-248.
    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 this gap in the literature, (...)
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  46. Franz Dietrich & Luca Moretti (2005). On Coherent Sets and the Transmission of Confirmation. Philosophy of Science 72 (3):403-424.
    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 usually, 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 measure. Our findings have (...)
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  47. Franz Dietrich & Christian List (2004). A Model of Jury Decisions Where All Jurors Have the Same Evidence. Synthese 142 (2):175 - 202.
    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 cause is a (...)
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  48. Franz Dietrich & Christian List, Judgment Aggregation by Quota Rules: Majority Voting Generalized.