A 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”). We show that, except in trivial cases, no probability aggregation rule satisfying two mild (...) conditions (non-dictatorship and consensus preservation) is non-manipulable. (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 …lling this gap in the literature. We sketch the ingredients of a general theory of propositional attitude aggregation and prove two new theorems. (...) Our …rst 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 speci…c 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)

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)

We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms of belief revision, based on compositional reduction axioms. Next, we show how various abstract postulates for (...) belief revision can be analyzed by standard modal frame correspondences for model-changing operations. (shrink)

We analyse the incentives of individuals to misrepresent their truthful judgments when engaged in collective decision-making. Our focus is on scenarios in which individuals reason about the incentives of others before choosing which judgments to report themselves. To this end, we introduce a formal model of strategic behaviour in logic-based judgment aggregation that accounts for such higher-level reasoning as well as the fact that individuals may only have partial information about the truthful judgments and preferences of their peers. We find (...) that every aggregation rule must belong to exactly one of three possible categories: it is either (i) immune to strategic manipulation for every level of reasoning, or (ii) manipulable for every level of reasoning, or (iii) immune to manipulation only for everykth level of reasoning, for some natural number kgreater than 1. (shrink)

Since the publication of Ekins’ The Nature of Legislative Intent, significant attention has been paid to common attitude models of legislative intention, that is, models that require unanimity among its group members. A common interpretation of Ekins is that these common attitudes are to be preferred over aggregated attitudes. I argue that any feasible theory of legislative attitudes will require non-trivial aggregation (ie. not based on unanimity rules alone). Two arguments are put forward in this regard: first, that non-trivial aggregation (...) better explains uncooperative legislative behaviour and second, that mathematical problems with aggregation apply to common attitudes as well since they involve trivial aggregation. These arguments generalise to theories of common attitudes other than Ekins’. (shrink)

Political practices often aim to reach valuable outcomes through democratic processes. However, philosophical considerations and democratic deliberations sometimes support different conclusions about what a valuable outcome would be. This paper contributes to a research agenda that aims to reconcile recommendations that follow from these different bases. The setting for this research agenda is capabilitarian. It affirms the idea that what we should distribute are substantive freedoms to be and do things that people have reason to value. Disagreements about these valuable (...) outcomes become particularly problematic in urgent situations such as pandemics, floods, and wildfires. These situations are urgent since they are time-sensitive and involve an impending loss of well-being. A method of compromise would help mitigate losses of well-being while respecting the aim of reaching valuable outcomes through democratic processes. I thus offer an equitable and decisive method of compromise that helps integrate philosophical considerations with democratic deliberations. (shrink)

Group decisions raise a number of substantial philosophical and methodological issues. We focus on the goal of the group decision exercise itself. We ask: What should be counted as a good group decision-making result? The right decision might not be accessible to, or please, any of the group members. Conversely, a popular decision can fail to be the correct decision. In this paper we discuss what it means for a decision to be "right" and what components are required in a (...) decision process to produce happy decision-makers. Importantly, we discuss how "right" decisions can produce happy decision-makers, or rather, the conditions under which happy decision-makers and right decisions coincide. In a large range of contexts, we argue for the adoption of formal consensus models to assist in the group decision-making process. In particular, we advocate the formal consensus convergence model of Lehrer and Wagner (1981), because a strong case can be made as to why the underlying algorithm produces a result that should make each of the experts in a group happy. Arguably, this model facilitates true consensus, where the group choice is effectively each person's individual choice. We analyse Lehrer and Wagner's algorithm for reaching consensus on group probabilities/utilities in the context of complex decision-making for conservation biology. While many conservation decisions are driven by a search for objective utility/probability distributions (regarding extinction risks of species and the like), other components of conservation management primarily concern the interests of stakeholders. We conclude with cautionary notes on mandating consensus in decision scenarios for which no fact of the matter exists. For such decision settings alternative types of social choice methods are more appropriate. (shrink)

The Pareto principle is a normative principle about preferences that advocates concordance with unanimous preference. However, people have perspectives not just preferences. Evaluating preferences...

My focus is on aggregation of individual value rankings of alternatives to a collective value ranking. This is compared with aggregation o individual prefrences to a collective preference. While in an individual preference ranking the alternatives are ordered in accordance with one’s preferences, the order in a value ranking expresses one’s comparative evaluation of the alternatives, from the best to the worst. I suggest that, despite their formal similarity as rankings, this difference in the nature of individual inputs in two (...) aggregation scenarios has important implications: The kind of procedure that looks fine for aggregation of judgments is inappropriate for aggregation of preferences. The procedure I have in mind consists in similarity maximization, or – more precisely – in minimization of the average distance from individual inputs. When applied to judgment aggregation, this procedure can also be approached from the epistemic perspective: the questions are posed concerning its advantages as a truth-tracker. From that perspective, what matters is not only the probability of the outcome of the procedure being true, but also the expected verisimilitude of the outcome: its expected distance from truth. (shrink)

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 this paper, I present an account of group competence that is explicitly framed for cases of epistemic performances. According to it, we must consider group epistemic competence as the group agents’ capacity to produce knowledge, and not the result of the summation of its individual members’ competences to produce knowledge. Additionally, I contend that group competence must be understood in terms of group normative status. To introduce my view, I present Jesper Kallestrup’s denial that group competence involves anything over (...) and beyond the aggregation of individual competences. I have divided my response into two parts. First, I compare two conceptions of competence from Ernest Sosa’s reliabilist virtue epistemology, Thinking about oneself: The place and value of reflection in philosophy and psychology, Springer, 2019) and David Löwenstein’s account of know-how. Second, I take the results from this comparison and apply them to the issue of group know-how, by the hand of Orestis Palermos and Deborah Tollefsen’s twofold approach to the topic Socially extended epistemology, Oxford University Press, 2018). Finally, I return to Kallestrup’s denial to make my point in favour of the conception of genuine group competence as the group normative status to achieve success. (shrink)

ABSTRACTEvidence, beliefs, and knowledge are words that are currently used in the intelligence community. The primary goal of intelligence is to provide knowledge and foreknowledge of an enemy’s in...

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)

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)

Critics and defenders of Rawls' idea of public reason have tended to neglect the relationship between this idea and his conception of democratic legitimacy. I shall argue that Rawls' idea of public reason can be interpreted in two different ways, and that the two interpretations support two different conceptions of legitimacy. What I call the substantive interpretation of Rawls' idea of public reason demands that it applies not just to the process of democratic decision-making, but that it extends to the (...) substantive justification of democratic decisions. I shall argue against this interpretation and suggest a procedural interpretation instead. On this view, public reason is invoked when it comes to the political justification of the principles that should govern the process of democratic decision-making, but not – at least not directly – in relation to the content of public deliberation. (shrink)

Group agency requires a number of people to combine in pursuit of shared goals across varied scenarios. Thus, a group or corporate agent must be organized (1) to act flexibly as its goals require, (2) with the intentional, if not always voluntary, acquiescence of members in the guidance of (3) an authorized spokesperson or (4) a constructed voice, thereby (5) becoming capable of making and honoring commitments.

Logical puzzles like the doctrinal paradox raise the problem of how to aggregate individual judgements into a collective judgement, or alternatively, how to merge collectively inconsistent knowledge bases. In this paper, we view judgement aggregation as a function on propositional logic valuations, and we investigate how logic constrains judgement aggregation. In particular, we show that there is no non-dictatorial decision method for aggregating sets of judgements in a logically consistent way if the decision method is local, i.e., only depends on (...) the individual judgements on the proposition under consideration. (shrink)

Social processes like voting procedures, debates, etc. depend crucially on the precise rules which define them. This rule sensitivity is illustrated by two examples, in the case of preference aggregation by the parliamentary debate concerning the German capital, and in the case of judgement aggregation by the doctrinal paradox or discursive dilemma. Using social choice functions and the theory of mechanism design, one can formulate what it means for a particular set of rules to be correct under a given game-theoretic (...) solution concept. Furthermore, it is argued that in particular methods from logic and computer science are useful to describe and reason about the rules of play in a precise manner. (shrink)

In a highly influential work, List and Pettit (Group Agency: The Possibility, Design, and Status of Corporate Agents, Oxford University Press, 2011) draw upon the theory of judgement aggregation to offer an argument for the existence of nonreductive group agents; they also suggest that nonreductive group agency is a widespread phenomenon. In this paper, we argue for the following two claims. First, that the axioms they consider cannot naturally be interpreted as either descriptive characterisations or normative constraints upon group judgements, (...) in general. This makes it unclear how the List and Pettit argument is to apply to real world group behaviour. Second, by examining empirical data about how group judgements are made by a powerful international regulatory board, we show how each of the List and Pettit axioms can be violated in ways which are straightforwardly explicable at the level of the individual. This suggests that group agency may best be understood as a pluralistic phenomenon, where close inspection of the dynamics of intragroup deliberation can reveal that what prima facie appears to be a nonreductive group agent is, in fact, reducible. (shrink)

I present an original model in judgment aggregation theory that demonstrates the general impossibility of consistently describing decision-making purely at the group level. Only a type of unanimity rule can guarantee a group decision is consistent with supporting reasons, and even this possibility is limited to a small class of reasoning methods. The key innovation is that this result holds when individuals can reason in different ways, an allowance not previously considered in the literature. This generalizes judgment aggregation to subjective (...) decision situations, implying that the discursive dilemma persists without individual agreement on the logical constraints. Notably, the model mirrors the typical method of choosing political representatives, and thus suggests that no voting procedure other than unanimity rule can guarantee representation that reflects electorate opinion. Finally, I apply the results to a normative argument for unanimity rule in contract theory and juries, as well as to problems posed for deliberative democratic theory and the concept of representation. (shrink)

This is the introduction of the special issue,.

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)

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)

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)

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)

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)

In a recent paper on ‘The Many as One’, Lewis A. Kornhauser and Lawrence G. Sager look at an issue that we take to be of great importance in political theory. How far should groups in public life try to speak with one voice, and act with one mind? How far should public groups try to display what Ronald Dworkin calls integrity? We do not expect the many on the market to be integrated in this sense. But should we expect (...) integration among the many in the legislature, for example, or among the many on the courts? We agree with Kornhauser and Sager about a number of their claims but think that they miss out on important detail and do not achieve a fully general perspective on the issues raised. Our own contribution is in three sections. We address, first, the nature of the integrity challenge; second, the range of cases in which the challenge arises; and third, the question of whether public groups should be designed and required to meet that challenge. (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)

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)

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)

Suppose that the members of a group each hold a rational set of judgments on some interconnected questions, and imagine that the group itself has to form a collective, rational set of judgments on those questions. How should it go about dealing with this task? We argue that the question raised is subject to a difficulty that has recently been noticed in discussion of the doctrinal paradox in jurisprudence. And we show that there is a general impossibility theorem that that (...) difficulty illustrates. Our paper describes this impossibility result and provides an exploration of its significance. The result naturally invites comparison with Kenneth Arrow's famous theorem (Arrow, 1963 and 1984; Sen, 1970) and we elaborate that comparison in a companion paper (List and Pettit, 2002). The paper is in four sections. The first section documents the need for various groups to aggregate its members' judgments; the second presents the discursive paradox; the third gives an informal statement of the more general impossibility result; the formal proof is presented in an appendix. The fourth section, finally, discusses some escape routes from that impossibility. (shrink)

The budget-voting paradox states that, when social alternatives are proper subsets of a finite set of decisions, choosing decision-wise according to the majority rule may select an alternative that is covered in the majority tournament among alternatives. Individual preferences are defined on single decisions, and are extended to preferences over the alternative set by means of a preference extension rule. We prove the existence of the paradox for any rank-based, monotone, and independent extension rule.

Groups and other sorts of collective entities are frequently said to believe things. Sarah Huckabee Sanders, for instance, was asked by reporters at White House press conferences whether the Trump administration ‘believes in climate change’ or ‘believes that slavery is wrong’. Similarly, it is said on the website of the Aclu of Illinois that the organization ‘firmly believes that rights should not be limited based on a person’s sexual orientation or gender identity’. A widespread philosophical view is that belief on (...) the part of a group’s members is neither necessary nor sufficient for group belief. In other words, groups are said to be able to believe that p even when not a single individual member of the group believes that p. In this paper, I challenge this view by focusing on two phenomena that have been entirely ignored in the literature: group lies and group bullshit. I show that when group belief is understood in terms of actions over which group members have voluntarily control, as is standardly thought, paradigmatic instances of a group lying or bullshitting end up counting as a group believing. Thus we need to look elsewhere for an adequate account of group belief. (shrink)

This paper draws from two central intuitions that characterize modern western societies. The first is the normative claim that our identities should be recognized in an authentic way. The second intuition is that our common matters are best organized through democratic decision-making and democratic institutions. It is argued here that while deliberative democracy is a promising candidate for just organization of recognition relationships, it cannot fulfil its promise if recognition is understood either as recognition of ‘authentic’ collective identities or as (...) recognition of too atomistic or individualized subjects. If deliberative democracy is to be understood as successfully providing authentic recognition of individual identities, it requires a specific understanding of how individuals’ recognition needs and desires are collectively and institutionally constituted. Furthermore, it is argued that even if deliberative democracy can provide the necessary circumstances for individual self-realization, it comes with homogenizing tendencies and cannot fully avoid the problems of multiculturalism. (shrink)

Topics in Cognitive Science, Volume 14, Issue 3, Page 602-620, July 2022.

A framing effect occurs when an agent's choices are not invariant under changes in the way a decision problem is presented, e.g. changes in the way options are described (violation of description invariance) or preferences are elicited (violation of procedure invariance). Here we identify those rationality violations that underlie framing effects. We attribute to the agent a sequential decision process in which a “target” proposition and several “background” propositions are considered. We suggest that the agent exhibits a framing effect if (...) and only if two conditions are met. First, different presentations of the decision problem lead the agent to consider the propositions in a different order (the empirical condition). Second, different such “decision paths” lead to different decisions on the target proposition (the logical condition). The second condition holds when the agent's initial dispositions on the propositions are “implicitly inconsistent,” which may be caused by violations of “deductive closure.” Our account is consistent with some observations made by psychologists and provides a unified framework for explaining violations of description and procedure invariance. (shrink)

The options that people face are rarely ideal: they are good in some ways and poor in others. People have problems choosing among such options because they don’t know which ends to favor. Multiple objectives pose a problem not only for decision makers, but also for our account of decision making. People act to achieve their ends given their beliefs. In order to handle decisions with multiple objectives, however, this story must be supplemented by an account of which ends are (...) implicated in which decisions (e.g., do individual goals guide particular choices? do different ends jointly pick out courses of action?). Unfortunately, such an account is lacking. As a result, there is a gap (at least) in our most basic account of human behavior. In this paper I explore that gap and examine some proposals for closing it. (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)

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)

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)

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)

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)

In this study, we propose a new direction of research on the axiomatic analysis of approval voting, which is a common democratic decision method. Its novelty is to examine an infinite population setting, which includes an application to intergenerational problems. In particular, we assume that the set of the population is countably infinite. We provide several extensions of the method of approval voting for this setting. As our main result, axiomatic characterizations of the extensions are offered by revealing a direct (...) link between approval voting and the Borda rule. The characterized methods are natural extensions of the standard approval voting method for the finite-population case and are regarded as minimum requirements for other possible infinite-population extensions, which are reasonably democratic. (shrink)

Judgment aggregation studies how collective opinions arise from the aggregation of individual ones. This article surveys a variety of aggregation rules (possible ways of aggregating individual judgments into collective ones). Aggregation by majority opinion is known to satisfy some but not all the desiderata for an aggregation rule. More general impossibility results show that not all the natural desiderata can be satisfied by a single aggregation rule. To interpret these results, we focus here on some applications of judgment aggregation models (...) in Epistemology. In particular, we explore their possible role in an account of collective belief and collective reason. The focus on these applications allows us to give precise answers concerning which of the natural desiderata must be abandoned. (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)

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)