The debate on the epistemology of disagreement has so far focused almost exclusively on cases of disagreement between individual persons. Yet, many social epistemologists agree that at least certain kinds of groups are equally capable of having beliefs that are open to epistemic evaluation. If so, we should expect a comprehensive epistemology of disagreement to accommodate cases of disagreement between group agents, such as juries, governments, companies, and the like. However, this raises a number of fundamental questions concerning what it (...) means for groups to be epistemic peers and to disagree with each other. In this paper, we explore what group peer disagreement amounts to given that we think of group belief in terms of List and Pettit’s ‘belief aggregation model’. We then discuss how the so-called ‘equal weight view’ of peer disagreement is best accommodated within this framework. The account that seems most promising to us says, roughly, that the parties to a group peer disagreement should adopt the belief that results from applying the most suitable belief aggregation function for the combined group on all members of the combined group. To motivate this view, we test it against various intuitive cases, derive some of its notable implications, and discuss how it relates to the equal weight view of individual peer disagreement. (shrink)

Binarizing belief aggregation tackles the problem of aggregating individuals’ probabilistic beliefs on logically connected propositions into the group’s binary beliefs. One common approach to associating probabilistic beliefs with binary beliefs would be applying thresholds to probabilities. This paper aims to introduce and classify a range of threshold-based binarizing belief aggregation rules while characterizing them based on different forms of monotonicity and other properties.

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)

This paper addresses how multiple individual credences on logically related issues should be aggregated into collective binary beliefs. We call this binarizing belief aggregation. It is vulnerable to dilemmas such as the discursive dilemma or the lottery paradox: proposition-wise independent aggregation can generate inconsistent or not deductively closed collective judgments. Addressing this challenge using the familiar axiomatic approach, we introduce general conditions on a binarizing belief aggregation rule, including rationality conditions on individual inputs and collective (...) outputs, and determine which rules (if any) satisfy different combinations of these conditions. Furthermore, we analyze similarities and differences between our proofs and other related proofs in the literature and conclude that the problem of binarizing belief aggregation is a free-standing aggregation problem not reducible to judgment aggregation or probabilistic opinion pooling. (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 introduce a new operator – belief fusion– which aggregates the beliefs of two agents, each informed by a subset of sources ranked by reliability. In the process we definepedigreed belief states, which enrich standard belief states with the source of each piece of information. We note that the fusion operator satisfies the invariants of idempotence, associativity, and commutativity. As a result, it can be iterated without difficulty. We also define belief diffusion; whereas fusion generally produces (...) a belief state with more information than is possessed by either of its two arguments, diffusion produces a state with less information. Fusion and diffusion are symmetric operators, and together define a distributive lattice. Finally, we show that AGM revision can be viewed as fusion between a novice and an expert. (shrink)

In this paper we explore the relation between three areas: judgment aggregation, belief merging and social choice theory. Judgment aggregation studies how to aggregate individual judgments on logically interconnected propositions into a collective decision on the same propositions. When majority voting is applied to some propositions it may however give a different outcome than majority voting applied to another set of propositions. Starting from this so-called doctrinal paradox, the paper surveys the literature on judgment aggregation, and (...) shows that the application of a well known belief merging operator can dissolve the paradox. Finally, the use of distances is shown to establish a link between belief merging and preference aggregation in social choice theory. (shrink)

We introduce a new operator – belief fusion– which aggregates the beliefs of two agents, each informed by a subset of sources ranked by reliability. In the process we definepedigreed belief states, which enrich standard belief states with the source of each piece of information. We note that the fusion operator satisfies the invariants of idempotence, associativity, and commutativity. As a result, it can be iterated without difficulty. We also define belief diffusion; whereas fusion generally produces (...) a belief state with more information than is possessed by either of its two arguments, diffusion produces a state with less information. Fusion and diffusion are symmetric operators, and together define a distributive lattice. Finally, we show that AGM revision can be viewed as fusion between a novice and an expert. (shrink)

When a group of agents attempts to reach an agreement on certain issues, it is usually desirable that the resulting consensus be as close as possible to the original judgments of the individuals. However, when these judgments are logically connected to further beliefs, the notion of closeness should also take into account to what extent the individuals would have to revise their entire belief set to reach an agreement. In this work, we present a model for generation of agreement (...) with respect to a given agenda which allows individual epistemic entrenchment to influence the value of the consensus. While the postulates for the transformation function and their construction resemble those of AGM belief revision, the notion of an agenda is adapted from the theory of judgment aggregation. This allows our model to connect both frameworks. (shrink)

Betting methods, of which de Finetti's Dutch Book is by far the most well-known, are uncertainty modelling devices which accomplish a twofold aim. Whilst providing an interpretation of the relevant measure of uncertainty, they also provide a formal definition of coherence. The main purpose of this paper is to put forward a betting method for belief functions on MV-algebras of many-valued events which allows us to isolate the corresponding coherence criterion, which we term coherence in the aggregate. Our framework (...) generalises the classical Dutch Book method. (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)

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)

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)

As the ongoing literature on the paradoxes of the Lottery and the Preface reminds us, the nature of the relation between probability and rational acceptability remains far from settled. This article provides a novel perspective on the matter by exploiting a recently noted structural parallel with the problem of judgment aggregation. After offering a number of general desiderata on the relation between finite probability models and sets of accepted sentences in a Boolean sentential language, it is noted that a (...) number of these constraints will be satisfied if and only if acceptable sentences are true under all valuations in a distinguished non-empty set W. Drawing inspiration from distance-based aggregation procedures, various scoring rule based membership conditions for W are discussed and a possible point of contact with ranking theory is considered. The paper closes with various suggestions for further research. (shrink)

There are many reasons we might want to take the opinions of various individuals and pool them to give the opinions of the group they constitute. If all the individuals in the group have probabilistic opinions about the same propositions, there is a host of pooling functions we might deploy, such as linear or geometric pooling. However, there are also cases where different members of the group assign probabilities to different sets of propositions, which might overlap a lot, a little, (...) or not at all. There are far fewer proposals for how to proceed in these cases, and those there are have undesirable features. I begin by considering four proposals and arguing that they don't work. Then I'll describe my own proposal, which is intended to cover the situation in which we want to pool the individual opinions in order to ascribe an opinion to the group considered as an agent in its own right. (shrink)

In this paper, we explore how we should aggregate the degrees of belief of a group of agents to give a single coherent set of degrees of belief, when at least some of those agents might be probabilistically incoherent. There are a number of ways of aggregating degrees of belief, and there are a number of ways of fixing incoherent degrees of belief. When we have picked one of each, should we aggregate first and then fix, (...) or fix first and then aggregate? Or should we try to do both at once? And when do these different procedures agree with one another? In this paper, we focus particularly on the final question. (shrink)

This paper is about how to aggregate outside opinion. If two experts are on one side of an issue, while three experts are on the other side, what should a non-expert believe? Certainly, the non-expert should take into account more than just the numbers. But which other factors are relevant, and why? According to the view developed here, one important factor is whether the experts should have been expected, in advance, to reach the same conclusion. When the agreement of two (...) (or of twenty) thinkers can be predicted with certainty in advance, their shared belief is worth only as much as one of their beliefs would be worth alone. This expectational model of belief dependence can be applied whether we think in terms of credences or in terms of all-or-nothing beliefs. (shrink)

We present an abstract social aggregation theorem. Society, and each individual, has a preorder that may be interpreted as expressing values or beliefs. The preorders are allowed to violate both completeness and continuity, and the population is allowed to be infinite. The preorders are only assumed to be represented by functions with values in partially ordered vector spaces, and whose product has convex range. This includes all preorders that satisfy strong independence. Any Pareto indifferent social preorder is then shown (...) to be represented by a linear transformation of the representations of the individual preorders. Further Pareto conditions on the social preorder correspond to positivity conditions on the transformation. When all the Pareto conditions hold and the population is finite, the social preorder is represented by a sum of individual preorder representations. We provide two applications. The first yields an extremely general version of Harsanyi's social aggregation theorem. The second generalizes a classic result about linear opinion pooling. (shrink)

This paper addresses the problem of judgment aggregation in science. How should scientists decide which propositions to assert in a collaborative document? We distinguish the question of what to write in a collaborative document from the question of collective belief. We argue that recent objections to the application of the formal literature on judgment aggregation to the problem of judgment aggregation in science apply to the latter, not the former question. The formal literature has introduced various (...) desiderata for an aggregation procedure. Proposition-wise majority voting emerges as a procedure that satisfies all desiderata which represent norms of science. An interesting consequence is that not all collaborating scientists need to endorse every proposition asserted in a collaborative document. (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)

The theory of belief revision and merging has recently been applied to judgement aggregation. In this paper I argue that judgements are best aggregated by merging the evidence on which they are based, rather than by directly merging the judgements themselves. This leads to a threestep strategy for judgement aggregation. First, merge the evidence bases of the various agents using some method of belief merging. Second, determine which degrees of belief one should adopt on the (...) basis of this merged evidence base, by applying objective Bayesian theory. Third, determine which judgements are appropriate given these degrees of belief by applying a decision-theoretic account of rational judgement formation. (shrink)

The Ostrogorski paradox and the discursive dilemma are seemingly unrelated paradoxes of aggregation. The former is discussed in traditional social choice theory, while the latter is at the core of the new literature on judgment aggregation. Both paradoxes arise when, in a group, each individual consistently makes a judgment, or expresses a preference, (in the form of yes or no) over specific propositions, and the collective outcome is in some respect inconsistent. While the result is logically inconsistent in (...) the case of the discursive paradox, it is not stable with respect to the level of aggregation in the case of the Ostrogorski paradox. In the following I argue that, despite these differences, the two problems have a similar structure. My conclusion will be twofold: on the one hand, the similarities between the paradoxes support the claim that these problems should be tackled using the same aggregation procedure; on the other hand, applying the same procedure to these paradoxes will help clarify the strengths and weaknesses of the aggregation method itself. More specifically, I will show that an operator defined in artificial intelligence to merge belief bases can deal with both paradoxes. (shrink)

One of the major problems that artificial intelligence needs to tackle is the combination of different and potentially conflicting sources of information. Examples are multi-sensor fusion, database integration and expert systems development. In this paper we are interested in the aggregation of propositional logic-based information, a problem recently addressed in the literature on information fusion. It has applications in multi-agent systems that aim at aggregating the distributed agent-based knowledge into an (ideally) unique set of propositions. We consider a group (...) of autonomous agents who individually hold a logically consistent set of propositions. Each set of propositions represents an agent’s beliefs on issues on which the group has to make a collective decision. To make the collective decision, several aggregation procedures have been proposed in the literature. Assuming that all propositions in question are factually right or wrong, we ask how good belief fusion is as a truth tracker. Will it single out the true set of propositions? And how does information fusion compare with other aggregation procedures? We address these questions in a probabilistic framework and show that information fusion does especially well for agents with a middling competence of hitting the truth of an individual proposition. (shrink)

The problem of how to rationally aggregate probability measures occurs in particular when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and when an individual whose belief system is compatible with several probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory. We investigate this problem by first recalling some negative results from preference (...) and judgment aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected utility preferences. We describe how McConway’s :410–414, 1981) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms à la McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed. (shrink)

Analyses of complex entities such as bureaucracies, courts, legislatures, and firms typically personify them. A strong conception of personification requires that these entities have rational interests, rational beliefs, and rational normative judgments. On one account of personification, such personified rationality should be aggregate rationality : the interests, beliefs, and normative judgments should depend only on the interests, beliefs, and judgments of the individuals who constitute the complex entity. I argue that aggregate rationality is too strong a normative requirement to impose (...) on courts and legislatures. Key Words: collective rationality • personification • adjudication • doctrinal paradox. (shrink)

The merging/fusion of belief/data collections in propositional logic form is a topic that has received due attention within the domains of database and AI research. A distinction can be made between two types of scenarios to which the process of merging can be applied. In the first type, the collections represent preferences, such as the voting choices of a group of people, that need to be aggregated so as to give a consistent result that in some way best represents (...) the collective judgement of the group. In the second type, the collections represent factual data that is to be aggregated with an aim of obtaining a result that maximises factual correctness. After introducing a general framework for belief merging via some prominent literature on the topic, this paper then introduces and considers a method for belief merging with the second type of scenario in mind. Its suitability is corroborated by demonstrating how it can be seen as a special case of a merging procedure that combines aggregation of probabilities and maximisation of expected truthlikeness. (shrink)

Judgment-aggregation theory has always focused on the attainment of rational collective judgments. But so far, rationality has been understood in static terms: as coherence of judgments at a given time, defined as consistency, completeness, and/or deductive closure. This paper asks whether collective judgments can be dynamically rational, so that they change rationally in response to new information. Formally, a judgment aggregation rule is dynamically rational with respect to a given revision operator if, whenever all individuals revise their judgments (...) in light of some information (a learnt proposition), then the new aggregate judgments are the old ones revised in light of this information, i.e., aggregation and revision commute. We prove an impossibility theorem: if the propositions on the agenda are non-trivially connected, no judgment aggregation rule with standard properties is dynamically rational with respect to any revision operator satisfying some basic conditions on revision. Our theorem is the dynamic-rationality counterpart of some well-known impossibility theorems for static rationality. We also explore how dynamic rationality might be achieved by relaxing some of the conditions on the aggregation rule and/or the revision operator. Notably, premise-based aggregation rules are dynamically rational with respect to so-called premise-based revision operators. (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)

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the linear-geometric rules, which combine individual values linearly and combine individual beliefs geometrically. Linear-geometric preference aggregation contrasts with classic linear-linear preference aggregation, which combines both values and beliefs linearly, but (...) achieves only static rationality. Our characterisation of linear-geometric preference aggregation has two corollaries: a characterisation of linear aggregation of values (Harsanyi's Theorem) and a characterisation of geometric aggregation of beliefs. (shrink)

The use of aggregated quality of life estimatesin the formation of public policy and practiceguidelines raises concerns about the moralrelevance of variability in values inpreferences for health care. This variabilitymay reflect unique and deeply held beliefs thatmay be lost when averaged with the preferencesof other individuals. Feminist moral theorieswhich argue for attention to context andparticularity underline the importance ofascertaining the extent to which differences inpreferences for health states revealinformation which is morally relevant toclinicians and policymakers. To facilitatethese considerations, we present (...) an empiricalstudy of preferences for the timing andoccurrence of health states associated withhormone replacement therapy (HRT). Sixteenwomen between the ages of 45 and 55 wereenrolled in this pilot study. Theirpreferences regarding five health statesassociated with HRT (menopausal symptoms, sideeffects of HRT, breast cancer, myocardialinfarction, and osteoporosis) were assessed inquantitative terms known as utilities. Twostandard methods, the visual analog scale (VAS) and the standard gamble (SG), were used toassess utility and time preference (calculatedas a discount rate). The wide variability ofresponses underlines the importance oftailoring health care to individual women'spreferences. Policy guidelines whichincorporate utility analysis must recognize thenormative limitations of aggregatedpreferences, and the moral relevance ofindividual conceptions of health. (shrink)

This essay raises new objections to the two dominant approaches to understanding the justification of group beliefs—_inflationary_ views, where groups are treated as entities that can float freely from the epistemic status of their members’ beliefs, and _deflationary_ views, where justified group belief is understood as nothing more than the aggregation of the justified beliefs of the group's members. If this essay is right, we need to look in an altogether different place for an adequate account of justified (...) group belief. From these objections emerges the skeleton of the positive view that this essay goes on to develop and defend, called the _group epistemic agent account_: groups are epistemic agents in their own right, with justified beliefs that respond to both evidence and normative requirements that arise only at the group level but that are nonetheless importantly constrained by the epistemic status of the beliefs of their individual members. (shrink)

It is argued in this paper that there can be both normative and nonnormative, merely factual group beliefs. The former involve the whole social group in question, while the latter only relate to the distributions of personal beliefs within the group. The paper develops a detailed theory, called the positional account of group beliefs, to explicate normative, group-involving group beliefs. Normative group beliefs are characterized within this approach in terms of joint acceptances of views by the group members — or (...) their representatives — acting in their right positions and tasks, and in a sense creating group commitments for all the members to accept (and keep accepting) the view in question. Also aggregate accounts of group belief are considered in the paper, especially the shared we-belief approach. Such aggregate accounts purport to account for merely factual group beliefs. (shrink)

This paper aims to clarify a debate on philosophical method, and to give a probabilistic argument vindicating armchair philosophy under a wide range of plausible assumptions. The use of intuitions by so-called armchair philosophers has been criticized on empirical grounds. The debate between armchair philosophers and their empirical critics would benefit from greater clarity and precision in our understanding of what it takes for intuition-based approaches to philosophy to make sense. This paper discusses a set of rigorous, probability-based tools for (...) determining what we can and cannot learn from intuitions in various conditions. These tools can tell us whether beliefs can be justified by armchair practices, and what empirical findings would have to show to undermine the use of intuitions in philosophy. Using these tools, the paper shows that armchair philosophy makes sense in a broad range of situations, and that it is quite plausible that we are in those situations at the moment. (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)

In this paper I defend the claim that justification is closed under conjunction, and confront its most alarming consequence — that one can have justification for believing propositions that are unlikely to be true, given one's evidence.

How should the opinion of a group be related to the opinions of the group members? In this article, we will defend a package of four norms – coherence, locality, anonymity and unanimity. Existing results show that there is no tenable procedure for aggregating outright beliefs or for aggregating credences that meet these criteria. In response, we consider the prospects for aggregating credal pairs – pairs of prior probabilities and evidence. We show that there is a method of aggregating credal (...) pairs that possesses all four virtues. (shrink)

How does reflective thinking impact decisions about ethics, mind, politics, or other philosophical domains? Reflective reasoning often correlates with better decision-making performance and certain philosophical preferences (e.g., utilitarian moral decisions). However, experiments suggest that reflection is not always the cause of these outcomes. Further, some evidence casts doubt on the trustworthiness of data from certain online crowd work platforms such as Amazon Mechanical Turk (mTurk). This paper reports results of a pre-registered experiment on participants from multiple sources (mTurk, CloudResearch, Prolific, (...) and a university). The experiment investigated how reflective thinking relates to judgments about philosophical thought experiments (concerning knowledge, morality, personal identity, and more). First- and third-party data quality measures found up to 18 times as much low-quality data from mTurk as other sources. Analyzing across participant sources, some prior correlations between reflection and certain philosophical tendencies replicated (e.g., denying that accidentally true beliefs count as knowledge). However, a common reflection test prime failed to find evidence that reflection caused the corresponding philosophical preferences. Rather, a philosophical priming effect emerged: thinking through philosophical vignettes before taking a reflection test improved test performance—but only among those that passed the data quality checks. Together, these data suggest that the direction of causation between reflective and philosophical thinking may be the opposite of what dual process theories have suggested, and that researchers’ ability to detect such relationships can depend on participant source and data quality. (shrink)

Should we believe our controversial philosophical views? Recently, several authors have argued from broadly conciliationist premises that we should not. If they are right, we philosophers face a dilemma: If we believe our views, we are irrational. If we do not, we are not sincere in holding them. This paper offers a way out, proposing an attitude we can rationally take toward our views that can support sincerity of the appropriate sort. We should arrive at our views via a certain (...) sort of ‘insulated’ reasoning – that is, reasoning that involves setting aside certain higher-order worries, such as those provided by disagreement – when we investigate philosophical questions. (shrink)

In this paper, we investigate the problem of truth approximation via belief merging, i.e., we ask whether, and under what conditions, a group of inquirers merging together their beliefs makes progress toward the truth about the underlying domain. We answer this question by proving some formal results on how belief merging operators perform with respect to the task of truth approximation, construed as increasing verisimilitude or truthlikeness. Our results shed new light on the issue of how rational (dis)agreement (...) affects the inquirers’ quest for truth. In particular, they vindicate the intuition that scientific inquiry, and rational discussion in general, benefits from some heterogeneity in opinion and interaction among different viewpoints. The links between our approach and related analyses of truth tracking, judgment aggregation, and opinion dynamics, are also highlighted. (shrink)

My dissertation focuses on problems that arise when a group makes decisions that are in reasonable ways connected to the beliefs and values of the group members. These situations are represented by models of decision-theoretic aggregation: Suppose a model of individual rationality in decision-making applies to each of a group of agents. Suppose this model also applies to the group as a whole, and that this group model is aggregated from the individual models. Two questions arise. First, what sets (...) of reasonable conditions can we consistently impose on the aggregation? Second, what can we learn from insights gained in such models, in particular for ethics and political philosophy? The dissertation has three parts, each using a different model of individual rationality. Each part contains essays addressing questions of either the first or the second kind with regard to its underlying model. Part I uses a social-choice-theoretic model, in which agents are only assumed to rank alternatives. Arrow's "Impossibility Theorem" shows that certain conditions that it would be natural to impose on all aggregation cannot be so imposed, on pain of contradiction. I discuss the impact of this result on the evaluation of majority rule and on democratic theory. I also discuss Sen's "Liberal Paradox", which addresses the possibility of incorporating rights into a social-choice theoretic model. Part II uses the von Neumann/Morgenstern theory of expected utility. A result under this model has been regarded as providing an argument for utilitarianism. I locate a place within utilitarianism where the theorem can do some work. To prepare the ground, I interpret the von Neumann/Morgenstern theory as part of a theory of deliberation. Thereby, this version of expected utility theory can be embedded into the philosophy of practical reasoning. The underlying model in Part III is Bayesian decision theory. Whereas the other two inquiries focus on the philosophical assessment of formal results, the third makes a formal contribution. One essay surveys the area, and a second explores a curious phenomenon that occurs in determining outcomes under one type of Bayesian aggregation. (shrink)

Weakly Aggregative Modal Logic ) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. \ has interesting applications on epistemic logic, deontic logic, and the logic of belief. In this paper, we study some basic model theoretical aspects of \. Specifically, we first give a van Benthem–Rosen characterization theorem of \ based on an intuitive notion of bisimulation. Then, in contrast to many well known normal or non-normal modal logics, we show (...) that each basic \ system \ lacks Craig interpolation. Finally, by model theoretical techniques, we show that an extension of \ does have Craig interpolation, as an example of amending the interpolation problem of \. (shrink)

This paper is a first attempt to study the problem of aggregation of individual ordinal probabilistic beliefs in an Arrowian framework. We exhibit some properties an aggregation rule must fulfil; in particular we prove the existence of a “quasi-dictator”.

In [11] it is shown how propositional dynamic logic (PDL) can be interpreted as a logic of belief revision that extends the logic of communication and change (LCC) given in [7]. This new version of epistemic/doxastic PDL does not impose any constraints on the basic relations and because of this it does not suffer from the drawback of LCC that these constraints may get lost under updates that are admitted by the system. Here, we will impose one constraint, namely (...) that the agent’s plausibility relations are linked. Linkedness is a natural extension of local connectedness to the multi-agent case and it assures that we know the agent’s preferences between all relevant alternatives. Since the belief updates that are used in [11] may not preserve linkedness, we limit ourselves to a particular kind of belief change that does preserve it. Our framework has obvious connections to coalition logic [17] and social choice theory [19]. We show how we can use it to model consensus seeking in plenary Dutch meetings. In Dutch meetings, a belief update is done for all agents in the meeting if a majority beliefs the proposition that is under discussion. A special case of these meetings is judgement aggregation, and we apply our framework to the discursive dilemma in this field [15]. (shrink)

This symposium in the overlap of philosophy and decision theory is described well by its title “Beliefs in Groups”. Each word in the title matters, with one intended ambiguity. The symposium is about beliefs rather than other attitudes such as preferences; these beliefs take the form of probabilities in the first three contributions, binary yes/no beliefs (‘judgments’) in the fourth contribution, and qualitative probabilities (‘probability grades’) in the fifth contribution. The beliefs occur in groups, which is ambiguous between beliefs of (...) groups as a whole and beliefs of group members. The five contributions – all of them interesting, we believe – address several aspects of this general theme. (shrink)

In this paper we forge a connection between dynamic epistemic logics of belief revision on one hand and studies of collective judgement and multi-agent preference change on the other. Belief revision in the spirit of dynamic epistemic logic uses updating with relational substitutions to change the beliefs of individual agents. Collective judgement in social choice theory studies the collective outcomes of individual belief changes. We start out from the logic of communication and change (LCC), which is basically (...) epistemic propositional dynamic logic (PDL) extended with update action modalities. We show how epistemic PDL can be made to handle belief operators. Our new version of epistemic/doxastic PDL does not impose any constraints on the basic relations. Because of this it does not suffer from the drawback of LCC that constraints on epistemic relations, such as transitivity and reflexivity, may get lost under updates that are admitted by the system. After introducing the base system without constraints, we study the effects of imposing a single constraint, namely the constraint that the agent’s preference relations are linked. Linkedness is a natural extension of local connectedness to the multi-agent case. It assures that if Alice prefers y to x and Bob prefers z to x, then both Alice and Bob can make up their minds when given a choice between y and z. Since general belief changes may not preserve linkedness, we propose a recipe for belief change that does preserve it. Finally, we show that the resulting framework can be used to model consensus seeking procedures. We focus on the case of plenary Dutch meetings. In Dutch meetings, a belief change (or rather: preference change) is performed for all agents in the meeting if a majority believes (or: is in favour of) the proposition that is under discussion. A special case of these meetings is judgement aggregation, and we apply our framework to the discursive dilemma in.. (shrink)

We often prefer non-deferential belief to deferential belief. In the last twenty years, epistemology has seen a surge of sympathetic interest in testimony as a source of knowledge. We are urged to abandon ‘epistemic individualism’ and the ideal of the ‘autonomous knower’ in favour of ‘social epistemology’. In this connection, you might think that a preference for non-deferential belief is a manifestation of vicious individualism, egotism, or egoism. I shall call this the selfishness challenge to preferring non-deferential (...) belief. The aim of this paper is to meet the selfishness challenge by arguing that non-deferential belief is socially valuable. (shrink)

ABSTRACTJack Knight and James Johnson argue in The Priority of Democracy that democracy should be theorized and justified pragmatically: Democratic deliberations should be given a central coordinating role in society not because they realize any particular abstract ideal, but because they would elicit the information needed to solve real-world problems. However, Knight and Johnson rely on a naïve economic understanding of knowledge that assumes implausibly that individuals know what they need to know and need only aggregate thier separate beliefs. It (...) is precisely because we may not know what we need to know that we need to continually test our ideas. Contra Knight and Johnson, moreover, we ought to accept that our ability to interpret social experiments properly is questionable. A pragmatic approach to social inquiry, therefore, ought to investigate what beliefs political actors actually bring to collective decisions rather than how theoretically perfect beliefs ought to be elicited and aggregated. (shrink)

The problem of the aggregation of inputs coming from different sources arises in several contexts. Examples are the combination of individual preferences (studied in social choice theory), opinions (judgment aggregation), and data (artificial intelligence). While a number of results are available in each of these disciplines, a question that has been addressed only recently is how similar these aggregation problems are, despite the different types of inputs they try to combine.