In this paper, I investigate the relationship between preference and judgment aggregation, using the notion of ranking judgment introduced in List and Pettit. Ranking judgments were introduced in order to state the logical connections between the impossibility theorem of aggregating sets of judgments and Arrow’s theorem. I present a proof of the theorem concerning ranking judgments as a corollary of Arrow’s theorem, extending the translation between preferences and judgments defined in List and Pettit to the conditions on the aggregation procedure.

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 sufficient for liability; judgments on how to rank several options in an order of preference with the constraint of transitivity; and judgments on (...) budget items with budgetary constraints. Often more or less demanding constraints on decisions are imaginable. For instance, in preference ranking problems, the transitivity constraint is often contrasted with the weaker acyclicity constraint. In this paper, we make constraints explicit in judgment aggregation by relativizing the rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. We review several general results on judgment aggregation in light of such constraints. (shrink)

Judgment aggregation studies how individual opinions on a given set of propositions can be aggregated to form a consistent group judgment on the same propositions. Despite the simplicity of the problem, seemingly natural aggregation procedures fail to return consistent collective outcomes, leading to what is now known as the doctrinal paradox. The first occurrences of the paradox were discovered in the legal realm. However, the interest of judgment aggregation is much broader and extends to political philosophy, epistemology, social choice theory, (...) and computer science. The aim of this paper is to provide a concise survey of the discipline and to outline some of the most pressing questions and future lines of research. (shrink)

Social choice theory is the study of collective decision processes and procedures. It is not a single theory, but a cluster of models and results concerning the aggregation of individual inputs (e.g., votes, preferences, judgments, welfare) into collective outputs (e.g., collective decisions, preferences, judgments, welfare). Central questions are: How can a group of individuals choose a winning outcome (e.g., policy, electoral candidate) from a given set of options? What are the properties of different voting systems? When is a voting system (...) democratic? How can a collective (e.g., electorate, legislature, collegial court, expert panel, or committee) arrive at coherent collective preferences or judgments on some issues, on the basis of its members' individual preferences or judgments? How can we rank different social alternatives in an order of social welfare? Social choice theorists study these questions not just by looking at examples, but by developing general models and proving theorems. (shrink)

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 (...) an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are sigma-algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we compare our results with existing results on binary judgment aggregation and Arrovian preference aggregation. This paper is the first of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

The aggregation of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion where the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set of propositions (the (...) conclusion). This problem is known as the discursive dilemma (or paradox). The discursive dilemma is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox—the so-called premise-based procedure and the conclusion-based procedure—are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge belief bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions. (shrink)

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 (...) pooling functions (most of them classic, but one new) and argue that linear pooling can be justified procedurally, but not epistemically, while the other two pooling methods can be justified epistemically. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. We conclude by mentioning a number of other pooling methods. (shrink)

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager’s doctrinal paradox and List and Pettit’s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is to give the latter (...) its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the ‘general logic’ built in this framework. (shrink)

Can we design a perfect democratic decision procedure? Condorcet famously observed that majority rule, our paradigmatic democratic procedure, has some desirable properties, but sometimes produces inconsistent outcomes. Revisiting Condorcet’s insights in light of recent work on the aggregation of judgments, I show that there is a conflict between three initially plausible requirements of democracy: “robustness to pluralism”, “basic majoritarianism”, and “collective rationality”. For all but the simplest collective decision problems, no decision procedure meets these three requirements at once; at most (...) two can be met together. This “democratic trilemma” raises the question of which requirement to give up. Since different answers correspond to different views about what matters most in a democracy, the trilemma suggests a map of the “logical space” in which different conceptions of democracy are located. It also sharpens our thinking about other impossibility problems of social choice and how to avoid them, by capturing a core structure many of these problems have in common. More broadly, it raises the idea of “cartography of logical space” in relation to contested political concepts. (shrink)

According to a theorem recently proved in the theory of logical aggregation, any nonconstant social judgment function that satisfies independence of irrelevant alternatives (IIA) is dictatorial. We show that the strong and not very plausible IIA condition can be replaced with a minimal independence assumption plus a Pareto-like condition. This new version of the impossibility theorem likens it to Arrow’s and arguably enhances its paradoxical value.

Judgment aggregation theory, which concerns the translation of individual judgments on logical propositions into consistent group judgments, has shown that group consistency generally cannot be guaranteed if each proposition is treated independently from the others. Developing the right method of abandoning independence is thus a high-priority goal. However, little work has been done in this area outside of a few simple approaches. To fill the gap, we compare four methods based on distance metrics between judgment sets. The methods generalize the (...) premise-based and sequential priority approaches to judgment aggregation, as well as distance-based preference aggregation. They each guarantee group consistency and implement a range of distinct functions with different properties, broadening the available tools for social choice. A central result is that only one of these methods (not previously considered in the literature) satisfies three attractive properties for all reasonable metrics. (shrink)

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 (...) are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (2002), Nehring (2006), Dietrich and List (2007a) and Dokow and Holzman (2010a). (shrink)

Majority cycling and related social choice paradoxes are often thought to threaten the meaningfulness of democracy. But deliberation can prevent majority cycles – not by inducing unanimity, which is unrealistic, but by bringing preferences closer to single-peakedness. We present the first empirical test of this hypothesis, using data from Deliberative Polls. Comparing preferences before and after deliberation, we find increases in proximity to single-peakedness. The increases are greater for lower versus higher salience issues and for individuals who seem to have (...) deliberated more versus less effectively. They are not merely a byproduct of increased substantive agreement. Our results both refine and support the idea that deliberation, by increasing proximity to single-peakedness, provides an escape from the problem of majority cycling. (shrink)

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 (...) impossibilities, as discussed in the symposium. We then consider each of four possible escape-routes explored in the symposium. (shrink)

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 (...) new to the field of judgment aggregation a sense of this rapidly growing research area. (shrink)

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. (...) Finally, we revisit the aggregation of probabilistic judgments when this is constrained by prior aggregation of qualitative causal judgments. (shrink)

In this paper, I introduce the emerging theory of judgment aggregation as a framework for studying institutional design in social epistemology. When a group or collective organization is given an epistemic task, its performance may depend on its ‘aggregation procedure’, i.e. its mechanism for aggregating the group members’ individual beliefs or judgments into corresponding collective beliefs or judgments endorsed by the group as a whole. I argue that a group’s aggregation procedure plays an important role in determining whether the group (...) can meet two challenges: the ‘rationality challenge’ and the ‘knowledge challenge’. The rationality challenge arises when a group is required to endorse consistent beliefs or judgments; the knowledge challenge arises when the group’s beliefs or judgments are required to track certain truths. My discussion seeks to identify those properties of an aggregation procedure that affect a group’s success at meeting each of the two challenges. (shrink)

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. (...) Our first theorem simultaneously characterizes some prominent aggregation rules in the cases of probability, judgment and preference aggregation, including linear opinion pooling and Arrovian dictatorships. Our second theorem abstracts even further from the specific kinds of attitudes in question and describes the properties of a large class of aggregation rules applicable to a variety of belief-like attitudes. Our approach integrates some previously disconnected areas of investigation. (shrink)

While a large social-choice-theoretic literature discusses the aggregation of individual judgments into collective ones, there is much less formal work on the transformation of judgments in group communication. I develop a model of judgment transformation and prove a baseline impossibility theorem: Any judgment transformation function satisfying some initially plausible conditions is the identity function, under which no opinion change occurs. I identify escape routes from this impossibility and argue that the kind of group communication envisaged by deliberative democats must be (...) "holistic": It must focus on webs of connected propositions, not on one proposition at a time, which echoes the Duhem-Quine "holism thesis" on scientific theory testing. My approach provides a map of the logical space in which different possible group communication processes are located. (shrink)

I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people’s judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people’s judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a (...) dichotomous premise/conclusion order resp. a linear priority order. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow’s Theorem (in its general and indifference-free versions) and the well-known Arrow-like theorem in judgment aggregation. (shrink)

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 (...) provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model. JEL Classi…cation: D70, D71.. (shrink)

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 (...) rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinsteinís group identification problem. (shrink)

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 (...) new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results provide new support for the robustness of majority rule. (shrink)

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. (...) When applied illustratively to (strict) preference aggregation represented in our model, the result implies that every unbiased social welfare function with universal domain is effectively dictatorial. (shrink)

In the framework of judgment aggregation, we assume that some formulas of the agenda are singled out as premisses, and that both Independence (formula-wise aggregation) and Unanimity Preservation hold for them. Whether premiss-based aggregation thus defined is compatible with conclusion-based aggregation, as defined by Unanimity Preservation on the non-premisses, depends on how the premisses are logically connected, both among themselves and with other formulas. We state necessary and sufficient conditions under which the combination of both approaches leads to dictatorship (resp. (...) oligarchy), either just on the premisses or on the whole agenda. This framework is inspired by the doctrinal paradox of legal theory and arguably relevant to this field as well as political science and political economy. When the set of premisses coincides with the whole agenda, a limiting case of our assumptions, we obtain several existing results in judgment aggregation theory. (shrink)

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 (...) propositions using acceptance thresholds). I characterise the class of these quota rules. I also prove an abstract result that characterises consistent aggregation for arbitrary agendas in a general logic. (shrink)

Social epistemology is the study of the social dimensions of knowledge or information. There is little consensus, however, on what the term "knowledge" comprehends, what is the scope of the "social", or what the style or purpose of the study should be. According to some writers, social epistemology should retain the same general mission as classical epistemology, revamped in the recognition that classical epistemology was too individualistic. According to other writers, social epistemology should be a more radical departure from classical (...) epistemology, a successor discipline that would replace epistemology as traditionally conceived. The classical approach could be realized in at least two forms. One would emphasize the traditional epistemic goal of acquiring true beliefs. It would study social practices in terms of their impact on the truth-values of agents’ beliefs. A second version of the classical approach would focus on the epistemic goal of having justified or rational beliefs. Applied to the social realm, it might concentrate, for example, on when a cognitive agent is justified or warranted in accepting the statements and opinions of others. Proponents of the anti-classical approach have little or no use for concepts like truth and justification. In addressing the social dimensions of knowledge, they understand "knowledge" as simply what is believed, or what beliefs are "institutionalized" in this or that community, culture, or context. They seek to identify the social forces and influences responsible for knowledge production so conceived. Social epistemology is theoretically significant because of the central role of society in the knowledge-forming process. It also has practical importance because of its possible role in the redesign of information-related social institutions. (shrink)

The combination of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion in which the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set of propositions (...) (the conclusion). This problem is known as the doctrinal paradox. The doctrinal paradox is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox - the so-called premise-based procedure and the conclusion-based procedure - are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge knowledge bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions. (shrink)

Judgment aggregation problems are language dependent in that they may be framed in different yet equivalent ways. We formalize this dependence via the notion of translation invariance, adopted from the philosophy of science, and we argue for the normative desirability of translation invariance. We characterize the class of translation invariant aggregation functions in the canonical judgment aggregation model, which requires collective judgments to be complete. Since there are reasonable translation invariant aggregation functions, our result can be viewed as a possibility (...) theorem. At the same time, we show that translation invariance does have certain normatively undesirable consequences (e.g. failure of anonymity). We present a way of circumventing them by moving to a more general model of judgment aggregation, one that allows for incomplete collective judgments. (shrink)

How sensitive should you be to the testimony of others? You saw the car that caused an accident going through traffic lights on the red; or so you thought. Should you revise your belief on discovering that the majority of bystanders, equally well-equipped, equally well-positioned and equally impartial, reported that it went through on the green? Or take another case. You believe that intelligent design is the best explanation for the order of the living universe. Should you revise that belief (...) on finding that most other people, or at least most who by your own lights are as intelligent, informed and impartial as yourself, believe that evolutionary theory offers the better account? Should you do this, in particular, if your own personal sense of where the evidence points – like your own vivid memory of the car going through on the red – remains firmly on the side of intelligent design? Assume, to take a third case, that there is a matter of fact about whether abortion is right or wrong. You believe that it is wrong, having a firm picture of it as an act on a par with murder. Should you revise that belief on discovering that among those whom you regard as equally intelligent, informed and impartial, most believe that abortion is not wrong, or at least not wrong in the way that murder is wrong? Should you do this, in particular, if your own personal sense of abortion remains unchanged; it still seems to you to be a grievous wrong? Should you put aside your own sense of things as mistaken, in the way you might put aside your imagined memory of the car going through on the red, and decide to go along with the majority view? (shrink)

The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. We also consider sequential (...) quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making. (shrink)

All existing impossibility theorems on judgment aggregation require individual and collective judgment sets to be consistent and complete, arguably a demanding rationality requirement. They do not carry over to aggregation functions mapping profiles of consistent individual judgment sets to 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 proposition is dictatorial. We relate this theorem to the literature.

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 non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based voting”, (...) which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

This paper examines the role of evidential considerations in relation to pragmatic concerns in statements of group belief, focusing on scientific collaborations that are constituted in part by the aim of evaluating the evidence for scientific claims (evidential collaborations). Drawing upon a case study in high energy particle physics, I seek to show how pragmatic factors that enter into the decision to issue a group statement contribute positively to the epistemic functioning of such groups, contrary to the implications of much (...) of the existing discussion of group belief. I conclude by suggesting that applying social epistemological considerations to scientific collaborations could be practically beneficial, but only if an appropriately broad range of epistemic values is considered. (shrink)

List and Pettit have stated an impossibility theorem about the aggregation of individual opinion states. Building on recent work on the lottery paradox, this paper offers a variation on that result. The present result places different constraints on the voting agenda and the domain of profiles, but it covers a larger class of voting rules, which need not satisfy the proposition-wise independence of votes.

The rationality of individual agents is secured for the most part by their make-up or design. Some agents, however – in particular, human beings – rely on the intentional exercise of thinking or reasoning in order to promote their rationality further; this is the activity that is classically exemplified in Rodin’s sculpture of Le Penseur. Do group agents have to rely on reasoning in order to maintain a rational profile? Recent results in the theory of judgment aggregation show that under (...) a range of plausible conditions they do. In a slogan: group agents are made, not born. (shrink)

We investigate under what conditions a given set of collective judgments can arise from a specific voting procedure. In order to answer this question, we introduce a language similar to modal logic for reasoning about judgment aggregation procedures. In this language, the formula expresses that is collectively accepted, or that is a group judgment based on voting. Different judgment aggregation procedures may be underlying the group decision making. Here we investigate majority voting, where holds if a majority of individuals accepts, (...) consensus voting, where holds if all individuals accept, and dictatorship. We provide complete axiomatizations for judgment sets arising from all three aggregation procedures. (shrink)

Political theorists have offered many accounts of collective decision-making under pluralism. I discuss a key dimension on which such accounts differ: the importance assigned not only to the choices made but also to the reasons underlying those choices. On that dimension, different accounts lie in between two extremes. The ‘minimal liberal account’ holds that collective decisions should be made only on practical actions or policies and that underlying reasons should be kept private. The ‘comprehensive deliberative account’ stresses the importance of (...) giving reasons for collective decisions, where such reasons should also be collectively decided. I compare these two accounts on the basis of a formal model developed in the growing literature on the ‘discursive dilemma’ and ‘judgment aggregation’ and address several questions: What is the trade-off between the (minimal liberal) demand for reaching agreement on outcomes and the (comprehensive deliberative) demand for reason-giving? How large should the ‘sphere of public reason’ be? When do the decision procedures suggested by the two accounts agree and when not? How good are these procedures at truthtracking on factual matters? What strategic incentives do they generate for decision-makers? My discussion identifies what is at stake in the choice between minimal liberal and comprehensive deliberative accounts of collective decisionmaking, and sheds light not only on these two ideal-typical accounts themselves, but also on many characteristics that intermediate accounts share with them. (shrink)

Suppose the members of a group (e.g., committee, jury, expert panel) each form a judgment on which worlds in a given set are possible, subject to the constraint that at least one world is possible but not all are. The group seeks to aggregate these individual judgments into a collective judgment, subject to the same constraint. I show that no judgment aggregation rule can solve this problem in accordance with three conditions: “unanimity,” “independence” and “non-dictatorship,” Although the result is a (...) variant of an existing theorem on “group identification” (Kasher and Rubinstein, Logique et Analyse 160:385–395, 1997), the aggregation of judgments on which worlds are possible (or permissible, desirable, etc.) appears not to have been studied yet. The result challenges us to take a stance on which of its conditions to relax. (shrink)

Our aim in this survey article is to provide an accessible overview of some key results and questions in the theory of judgment aggregation. We omit proofs and technical details, focusing instead on concepts and underlying ideas.

Distributed cognition refers to processes which are (i) cognitive and (ii) distributed across multiple agents or devices rather than performed by a single agent. Distributed cognition has attracted interest in several fields ranging from sociology and law to computer science and the philosophy of science. In this paper, I discuss distributed cognition from a social-choice-theoretic perspective. Drawing on models of judgment aggregation, I address two questions. First, how can we model a group of individuals as a distributed cognitive system? Second, (...) can a group acting as a distributed cognitive system be ‘rational’ and ‘track the truth’ in the outputs it produces? I argue that a group’s performance as a distributed cognitive system depends on its ‘aggregation procedure’ – its mechanism for aggregating the group members’ inputs into collective outputs – and I investigate the properties of an aggregation procedure that matter. (shrink)

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 budgetary constraints. In this paper, we make constraints in judgment aggregation explicit by relativizing the (...) rationality conditions of consistency and deductive closure to a constraint set, whose variation yields more or less strong notions of rationality. This approach of modelling constraints explicitly contrasts with that of building constraints as axioms into the logic, which turns compliance with constraints into a matter of logical consistency and thereby conflates requirements of ordinary logical consistency and requirements dictated by the environment . We present some general impossibility results on constrained judgment aggregation; they are immediate corollaries of known results on judgment aggregation. (shrink)

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 to two or more individuals or subgroups is inconsistent with the (...) unanimity principle, whereby unanimously accepted propositions are collectively accepted. The inconsistency can be avoided if individual judgments or rights satisfy special conditions. (shrink)

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 (...) of beliefs and degrees of belief. Some possibility and impossibility results are presented. The possibility results suggest that the three proposed rationality constraints are compatible with reasonable aggregation procedures for belief and degree of belief. (shrink)

This chapter briefly reviews the present state of judgment aggregation theory and tentatively suggests a future direction for that theory. In the review, we start by emphasizing the difference between the doctrinal paradox and the discursive dilemma, two idealized examples which classically serve to motivate the theory, and then proceed to reconstruct it as a brand of logical theory, unlike in some other interpretations, using a single impossibility theorem as a key to its technical development. In the prospective part, having (...) mentioned existing applications to social choice theory and computer science, which we do not discuss here, we consider a potential application to law and economics. This would be based on a deeper exploration of the doctrinal paradox and its relevance to the functioning of collegiate courts. On this topic, legal theorists have provided empirical observations and theoretical hints that judgment aggregation theorists would be in a position to clarify and further elaborate. As a general message, the chapter means to suggest that the future of judgment aggregation theory lies with its applications rather than its internal theoretical development. (shrink)

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 studied in full generality. In this paper, we seek (...) to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory. (shrink)

We investigate the research programme of dynamic doxastic logic (DDL) and analyze its underlying methodology. The Ramsey test for conditionals is used to characterize the logical and philosophical differences between two paradigmatic systems, AGM and KGM, which we develop and compare axiomatically and semantically. The importance of Gärdenfors’s impossibility result on the Ramsey test is highlighted by a comparison with Arrow’s impossibility result on social choice. We end with an outlook on the prospects and the future of DDL.

Tim Crane's ‘Cosmic Hermeneutics vs. Emergence: The Challenge of the Explanatory Gap’ claims that non‐reductive physicalism must either close the explanatory gap, addressing the challenge famously posed by Levine's argument, or become identical to emergentism. Since no way to close the gap is available, the result is that there can be no interesting philosophical position intermediate between physicalism and emergentism. This chapter argues that if we look at the relation between physicalism and emergentism from the vantage point of reduction, Crane's (...) analysis is rather persuasive. However, if we switch from reduction to causality, its conclusions appear more disputable. In particular, if we shift from ‘novelty and explanation’ to ‘novelty and causality’ as key features of emergent properties, we may introduce a distinction between two kinds of emergentism (moderate and radical) based on their attitude towards the causal inheritance principle. If the causal inheritance principle is accepted (some versions of) moderate emergentism may be considered as non‐trivial forms of non‐reductive physicalism. (shrink)

Judgment aggregation is naturally applied to the modeling of collective attitudes. In the individual case, we represent agents as having not just beliefs, but also as supporting them with reasons. Can the Judgment Aggregation help model a concept of collective reason? I argue that the resources of the standard judgment aggregation framework are insufficiently general. I develop a generalization of the framework that improves along this dimension. In the new framework, new aggregation rules become available, as well as a natural (...) account of collective reasons. (shrink)