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)

When members of a group doxastically disagree with each other, decisions in the group are often hard to make. The members are supposed to find an epistemic compromise. How do members of a group reach a rational epistemic compromise on a proposition when they have different (rational) credences in the proposition? I answer the question by suggesting the Fine-Grained Method of Aggregation, which is introduced in Brössel and Eder 2014 and is further developed here. I show how this method (...) faces challenges of the standard method of aggregation, Weighted Straight Averaging, in a successful way. One of the challenges concerns the fact that Weighted Straight Averaging does not respect the evidential states of agents. Another challenge arises because Weighted Straight Averaging does not account for synergetic effects. (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)

How should a group with different opinions (but the same values) make decisions? In a Bayesian setting, the natural question is how to aggregate credences: how to use a single credence function to naturally represent a collection of different credence functions. An extension of the standard Dutch-book arguments that apply to individual decision-makers recommends that group credences should be updated by conditionalization. This imposes a constraint on what aggregation rules can be like. Taking conditionalization as a basic (...) constraint, we gather lessons from the established work on credence aggregation, and extend this work with two new impossibility results. We then explore contrasting features of two kinds of rules that satisfy the constraints we articulate: one kind uses fixed prior credences, and the other uses geometric averaging, as opposed to arithmetic averaging. We also prove a new characterisation result for geometric averaging. Finally we consider applications to neighboring philosophical issues, including the epistemology of disagreement. (shrink)

Real human agents, even when they are rational by everyday standards, sometimes assign different credences to objectively equivalent statements, such as ‘Orwell is a writer’ and ‘E.A. Blair is a writer’, or credences less than 1 to necessarily true statements, such as not-yet-proven theorems of arithmetic. Anna Mahtani calls this the phenomenon of ‘opacity’. Opaque credences seem probabilistically incoherent, which goes against a key modelling assumption of probability theory. I sketch a modelling strategy for capturing opaque credence assignments without (...) abandoning probabilistic coherence. I draw on ideas from judgement-aggregation theory, where we face similar challenges of defining the ‘objects of judgement’. (shrink)

We introduce a family of rules for adjusting one's credences in response to learning the credences of others. These rules have a number of desirable features. 1. They yield the posterior credences that would result from updating by standard Bayesian conditionalization on one's peers' reported credences if one's likelihood function takes a particular simple form. 2. In the simplest form, they are symmetric among the agents in the group. 3. They map neatly onto the familiar Condorcet voting results. 4. They (...) preserve shared agreement about independence in a wide range of cases. 5. They commute with conditionalization and with multiple peer updates. Importantly, these rules have a surprising property that we call synergy - peer testimony of credences can provide mutually supporting evidence raising an individual's credence higher than any peer's initial prior report. At first, this may seem to be a strike against them. We argue, however, that synergy is actually a desirable feature and the failure of other updating rules to yield synergy is a strike against them. (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)

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)

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)

How should an agent decide what to do when she is uncertain not just about morally relevant empirical matters, like the consequences of some course of action, but about the basic principles of morality itself? This question has only recently been taken up in a systematic way by philosophers. Advocates of moral hedging claim that an agent should weigh the reasons put forward by each moral theory in which she has positive credence, considering both the likelihood that that theory (...) is true and the strength of the reasons it posits. The view that it is sometimes rational to hedge for one's moral uncertainties, however, has recently come under attack both from those who believe that an agent should always be guided by the dictates of the single moral theory she deems most probable and from those who believe that an agent's moral beliefs are simply irrelevant to what she ought to do. Among the many objections to hedging that have been pressed in the recent literature is the worry that there is no non-arbitrary way of making the intertheoretic comparisons of moral value necessary to aggregate the value assignments of rival moral theories into a single ranking of an agent's options. -/- This dissertation has two principal objectives: First, I argue that, contra these recent objections, an agent's moral beliefs and uncertainties are relevant to what she rationally ought to do, and more particularly, that agents are at least sometimes rationally required to hedge for their moral uncertainties. My principal argument for these claims appeals to the enkratic conception of rationality, according to which the requirements of practical rationality derive from an agent's beliefs about the objective, desire-independent value or choiceworthiness of her options. Second, I outline a new general theory of rational choice under moral uncertainty. Central to this theory is the idea of content-based aggregation, that the principles according to which an agent should compare and aggregate rival moral theories are grounded in the content of those theories themselves, including not only their value assignments but also the metaethical and other non-surface-level propositions that underlie, justify, or explain those value assignments. (shrink)

This paper explores two non-standard supermajority rules in the context of judgment aggregation over multiple logically connected issues. These rules set the supermajority threshold in a local, context sensitive way—partly as a function of the input profile of opinions. To motivate the interest of these rules, I prove two results. First, I characterize each rule in terms of a condition I call ‘Block Preservation’. Block preservation says that if a majority of group members accept a judgment set, then so (...) should the group. Second, I show that one of these rules is, in a precise sense, a judgment aggregation analogue of a rule for connecting qualitative and quantitative belief that has been recently defended by Hannes Leitgeb. The structural analogy is due to the fact that Leitgeb sets thresholds for qualitative beliefs in a local, context sensitive way—partly as a function of the given credence function. (shrink)

A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by not all or (...) just one individual), or to non-representable information (not representable by any event in the domain where credences are held). I pro- pose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non-representable information, etc. Six corre- sponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.’s central result (with minor corrections). Another theorem—that for public non-representable information—fills a gap in the theory of externally Bayesian opinion pooling. (shrink)

This paper generalizes the preface paradox beyond the conjunctive aggregation of beliefs and constructs an analogous paradox for deontic reasoning. The analysis of the deontic case suggests a systematic restriction of intuitive rules for reasoning with obligations. This proposal can be transferred to the epistemic case: it avoids the preface and the lottery paradox and saves one of the two directions of the Lockean Thesis (i.e., high credence is sufficient, but not necessary for rational belief). The resulting account (...) compares favorably to competing proposals; in particular, we can formulate the rules of correct doxastic reasoning without reference to probabilistic features of the involved propositions. (shrink)

Dutch book and accuracy arguments are used to justify certain rationality constraints on credence functions. Underlying these Dutch book and accuracy arguments are associated theorems, and I show that the interpretation of these theorems can vary along a range of dimensions. Given that the theorems can be interpreted in a variety of different ways, what is the status of the associated arguments? I consider three possibilities: we could aggregate the results of the differently interpreted theorems in some way, and (...) motivate rationality constraints based on this aggregation; we could be permissive, and accept the conclusions of the Dutch book and accuracy arguments under all interpretations of the associated theorems; or we could select one uniquely correct interpretation of the Dutch book or accuracy theorem, and use that to justify certain rationality constraints. I show that each possibility faces problems, and conclude that Dutch book and accuracy theorems cannot be used to justify any principle of rationality. (shrink)

This paper compares two alternative explanations of pragmatic encroachment on knowledge (i.e., the claim that whether an agent knows that p can depend on pragmatic factors). After reviewing the evidence for such pragmatic encroachment, we ask how it is best explained, assuming it obtains. Several authors have recently argued that the best explanation is provided by a particular account of belief, which we call pragmatic credal reductivism. On this view, what it is for an agent to believe a proposition is (...) for her credence in this proposition to be above a certain threshold, a threshold that varies depending on pragmatic factors. We show that while this account of belief can provide an elegant explanation of pragmatic encroachment on knowledge, it is not alone in doing so, for an alternative account of belief, which we call the reasoning disposition account, can do so as well. And the latter account, we argue, is far more plausible than pragmatic credal reductivism, since it accords far better with a number of claims about belief that are very hard to deny. (shrink)

There are currently two robust traditions in philosophy dealing with doxastic attitudes: the tradition that is concerned primarily with all-or-nothing belief, and the tradition that is concerned primarily with degree of belief or credence. This paper concerns the relationship between belief and credence for a rational agent, and is directed at those who may have hoped that the notion of belief can either be reduced to credence or eliminated altogether when characterizing the norms governing ideally rational agents. (...) It presents a puzzle which lends support to two theses. First, that there is no formal reduction of a rational agent’s beliefs to her credences, because belief and credence are each responsive to different features of a body of evidence. Second, that if our traditional understanding of our practices of holding each other responsible is correct, then belief has a distinctive role to play, even for ideally rational agents, that cannot be played by credence. The question of which avenues remain for the credence-only theorist is considered. (shrink)

I argue that psychology and epistemology should posit distinct cognitive attitudes of religious credence and factual belief, which have different etiologies and different cognitive and behavioral effects. I support this claim by presenting a range of empirical evidence that religious cognitive attitudes tend to lack properties characteristic of factual belief, just as attitudes like hypothesis, fictional imagining, and assumption for the sake of argument generally lack such properties. Furthermore, religious credences have distinctive properties of their own. To summarize: factual (...) beliefs are practical setting independent, cognitively govern other attitudes, and are evidentially vulnerable. By way of contrast, religious credences have perceived normative orientation, are susceptible to free elaboration, and are vulnerable to special authority. This theory provides a framework for future research in the epistemology and psychology of religious credence. (shrink)

I explore how rational belief and rational credence relate to evidence. I begin by looking at three cases where rational belief and credence seem to respond differently to evidence: cases of naked statistical evidence, lotteries, and hedged assertions. I consider an explanation for these cases, namely, that one ought not form beliefs on the basis of statistical evidence alone, and raise worries for this view. Then, I suggest another view that explains how belief and credence relate to (...) evidence. My view focuses on the possibilities that the evidence makes salient. I argue that this makes better sense of the difference between rational credence and rational belief than other accounts. (shrink)

According to evidentialist views, credence in a proposition p should be proportional to the degree of evidential support that one has in favor of p. However, empirical evidence suggests that our credences are systematically sensitive to practical factors. In this article, I provide a cost–benefit analysis of credences' practical sensitivity. The upshot of this analysis is that credences sensitive to practical factors fare better than practically insensitive ones along several dimensions. All things considered, our credences should be sensitive to (...) practical factors. (shrink)

Reliabilists hold that a belief is doxastically justified if and only if it is caused by a reliable process. But since such a process is one that tends to produce a high ratio of true to false beliefs, reliabilism is on the face of it applicable to binary beliefs, but not to degrees of confidence or credences. For while beliefs admit of truth or falsity, the same cannot be said of credences in general. A natural question now arises: Can reliability (...) theories of justified belief be extended or modified to account for justified credence? In this paper, I address this question. I begin by showing that, as it stands, reliabilism cannot account for justified credence. I then consider three ways in which the reliabilist may try to do so by extending or modifying her theory, but I argue that such attempts face certain problems. After that, I turn to a version of reliabilism that incorporates evidentialist elements and argue that it allows us to avoid the problems that the other theories face. If I am right, this gives reliabilists a reason, aside from those given recently by Comesaña and Goldman, to move towards such a kind of hybrid theory. (shrink)

A question of recent interest in epistemology and philosophy of mind is how belief and credence relate to each other. A number of philosophers argue for a belief-first view of the relationship between belief and credence. On the belief-first view, what it is to have a credence just is to have a particular kind of belief, that is, a belief whose content involves probabilities or epistemic modals. Here, I argue against the belief-first view: specifically, I argue that (...) it cannot account for agents who have credences in propositions they barely comprehend. I conclude that, however credences differ from beliefs, they do not differ in virtue of adding additional content to the believed proposition. (shrink)

For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed (...) separately by Arntzenius, Bostrom, and Meacham), which is to compare the prospects for value at each individual location, and to then represent and compare lotteries by their expected values at each of those locations. But, as I show here, this approach violates several key principles of decision theory and generates some implausible verdicts. I propose an alternative—one which delivers plausible rankings of lotteries, which is implied by a plausible collection of axioms, and which can be applied alongside almost any ranking of infinite worlds. (shrink)

In this paper, I highlight an interesting difference between belief on the one hand, and suspended judgment and credence on the other hand. This difference is the following: credences and suspended judgments are suitable to serve as transitional as well as terminal attitudes in our reasoning, whereas beliefs are only appropriate as terminal attitudes. The notion of a transitional attitude is not an established one in the literature, but I argue that introducing it helps us better understand the different (...) roles suspended judgments and credences can play in our reasoning. Transitional and terminal attitudes have interestingly different descriptive and normative properties. I also compare my account of transitional attitudes to other inquiry-guiding attitudes that have recently been characterized in the literature and explain why they are different. (shrink)

The aggregation of individual judgments over interrelated propositions is a newly arising field of social choice theory. I introduce several independence conditions on judgment aggregation rules, each of which protects against a specific type of manipulation by agenda setters or voters. I derive impossibility theorems whereby these independence conditions are incompatible with certain minimal requirements. Unlike earlier impossibility results, the main result here holds for any (non-trivial) agenda. However, independence conditions arguably undermine the logical structure of judgment (...) class='Hi'>aggregation. I therefore suggest restricting independence to premises, which leads to a generalised premise-based procedure. This procedure is proven to be possible if the premises are logically independent. (shrink)

This paper explains and defends a belief-first view of the relationship between belief and credence. On this view, credences are a species of beliefs, and the degree of credence is determined by the content of what is believed. We begin by developing what we take to be the most plausible belief-first view. Then, we offer several arguments for it. Finally, we show how it can resist objections that have been raised to belief-first views. We conclude that the belief-first (...) view is more plausible than many have previously supposed. (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)

Radical moral encroachment is the view that belief itself is morally evaluable, and that some moral properties of belief itself make a difference to epistemic rationality. To date, almost all proponents of radical moral encroachment hold to an asymmetry thesis: the moral encroaches on rational belief, but not on rational credence. In this paper, we argue against the asymmetry thesis; we show that, insofar as one accepts the most prominent arguments for radical moral encroachment on belief, one should likewise (...) accept radical moral encroachment on credence. We outline and reject potential attempts to establish a basis for asymmetry between the attitude types. Then, we explore the merits and demerits of the two available responses to our symmetry claim: (i) embracing moral encroachment on credence and (ii) denying moral encroachment on belief. (shrink)

This is a three-part exchange on the relationship between belief and credence. It begins with an opening essay by Roger Clarke that argues for the claim that the notion of credence generalizes the notion of belief. Julia Staffel argues in her reply that we need to distinguish between mental states and models representing them, and that this helps us explain what it could mean that belief is a special case of credence. Roger Clarke's final essay reflects on (...) the compatibility of the previously discussed views with dualist and monist interpretations of our mental states and our ways of modeling them. (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)

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)

Credences are similar to levels of confidence, represented as a value on the [0,1] interval. This chapter sheds light on questions about credence, including its relationship to full belief, with an eye toward the empirical relevance of credence. First, I’ll provide a brief epistemological history of credence and lay out some of the main theories of the nature of credence. Then, I’ll provide an overview of the main views on how credences relate to full beliefs. Finally, (...) I’ll turn to the empirical, and suggest some ways that cognitive science does and could answer questions about credence, such as what credences one has, how credences relate to beliefs, and the extent to which we can control our credences. (shrink)

In this article, I argue that faith’s going beyond the evidence need not compromise faith’s epistemic rationality. First, I explain how some of the recent literature on belief and credence points to a distinction between what I call B-evidence and C-evidence. Then, I apply this distinction to rational faith. I argue that if faith is more sensitive to B-evidence than to C-evidence, faith can go beyond the evidence and still be epistemically rational.

Belief-credence dualism is the view that we have both beliefs and credences and neither attitude is reducible to the other. Pragmatic encroachment is the view that practical stakes can affect the epistemic rationality of states like knowledge or justified belief. In this paper, I argue that dualism offers a unique explanation of pragmatic encroachment cases. First, I explain pragmatic encroachment and what motivates it. Then, I explain dualism and outline a particular argument for dualism. Finally, I show how dualism (...) can explain the intuitions that underlie pragmatic encroachment. My basic proposal is that in high-stakes cases, it is not that one cannot rationally believe that p; instead, one ought not to rely on one's belief that p. One should rather rely on one's credence in p. I conclude that we need not commit ourselves to pragmatic encroachment in order to explain the intuitiveness of the cases that motivate it. (shrink)

Optimization algorithms such as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) are employed to determine the optimal aggregation and transmission schedules, taking into account factors such as network topology, node energy levels, and data urgency. The proposed approach is validated through extensive simulations, demonstrating significant improvements in energy consumption, packet delivery ratio, and overall network performance. The results suggest that the optimized aggregated packet transmission method can effectively extend the lifespan of duty-cycled WSNs while ensuring reliable data communication. (...) Future work will explore the integration of machine learning techniques for adaptive scheduling and the application of the proposed method to heterogeneous WSNs. (shrink)

This paper is about the role of interpersonal comparisons in Harsanyi's aggregation theorem. Harsanyi interpreted his theorem to show that a broadly utilitarian theory of distribution must be true even if there are no interpersonal comparisons of well-being. How is this possible? The orthodox view is that it is not. Some argue that the interpersonal comparability of well-being is hidden in Harsanyi's premises. Others argue that it is a surprising conclusion of Harsanyi's theorem, which is not presupposed by any (...) one of the premises. I argue instead that Harsanyi was right: his theorem and its weighted-utilitarian conclusion do not require interpersonal comparisons of well-being. The key to making sense of this possibility is to treat Harsanyi's weights as dimensional constants rather than dimensionless numbers. (shrink)

Most non-consequentialists “let the numbers count” when one can save either a lesser or greater number from equal or similar harm. But they are wary of doing so when one can save either a small number from grave harm or instead a very large number from minor harm. Limited aggregation is an approach that reconciles these two commitments. It is motivated by a powerful idea: our decision whom to save should respect each person who has a claim to our (...) help, including those whom we fail to save. However, it has recently been argued that it is open to decisive objections. I develop a new limitedly aggregative view:Hybrid Balance Relevant Claims. This view is well grounded in the reasons we have to be skeptical of aggregation and resolves all recent challenges by paying careful attention to the rationale for limited aggregation. (shrink)

Whereas Bayesians have proposed norms such as probabilism, which requires immediate and permanent certainty in all logical truths, I propose a framework on which credences, including credences in logical truths, are rational because they are based on reasoning that follows plausible rules for the adoption of credences. I argue that my proposed framework has many virtues. In particular, it resolves the problem of logical omniscience.

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)

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)

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)

According to the Rational Threshold View, a rational agent believes p if and only if her credence in p is equal to or greater than a certain threshold. One of the most serious challenges for this view is the problem of statistical evidence: statistical evidence is often not sufficient to make an outright belief rational, no matter how probable the target proposition is given such evidence. This indicates that rational belief is not as sensitive to statistical evidence as rational (...) credence. The aim of this paper is twofold. First, we argue that, in addition to playing a decisive role in rationalizing outright belief, non-statistical evidence also plays a preponderant role in rationalizing credence. More precisely, when both types of evidence are present in a context, non-statistical evidence should receive a heavier weight than statistical evidence in determining rational credence. Second, based on this result, we argue that a modified version of the Rational Threshold View can avoid the problem of statistical evidence. We conclude by suggesting a possible explanation of the varying sensitivity to different types of evidence for belief and credence based on the respective aims of these attitudes. (shrink)

Aggregative moral theories face a series of devastating problems when we apply them in a physically realistic setting. According to current physics, our universe is likely _infinitely large_, and will contain infinitely many morally valuable events. But standard aggregative theories are ill-equipped to compare outcomes containing infinite total value so, applied in a realistic setting, they cannot compare any outcomes a real-world agent must ever choose between. This problem has been discussed extensively, and non-standard aggregative theories proposed to overcome it. (...) This paper addresses a further problem of similar severity. Physics tells us that, in our universe, how remotely in time an event occurs is _relative_. But our most promising aggregative theories, designed to compare outcomes containing infinitely many valuable events, are sensitive to how remote in time those events are. As I show, the evaluations of those theories are then relative too. But this is absurd; evaluations of outcomes must be absolute. So we must reject such theories. Is this objection fatal for all aggregative theories, at least in a relativistic universe like ours? I demonstrate here that, by further modifying these theories to fit with the physics, we can overcome it. (shrink)

In this paper, I argue that the relationship between belief and credence is a central question in epistemology. This is because the belief-credence relationship has significant implications for a number of current epistemological issues. I focus on five controversies: permissivism, disagreement, pragmatic encroachment, doxastic voluntarism, and the relationship between doxastic attitudes and prudential rationality. I argue that each debate is constrained in particular ways, depending on whether the relevant attitude is belief or credence. This means that epistemologists (...) should pay attention to whether they are framing questions in terms of belief or in terms of credence and the success or failure of a reductionist project in the belief-credence realm has significant implications for epistemology generally. (shrink)

It is often claimed that credences are not reducible to ordinary beliefs about probabilities. Such a reduction appears to be decisively ruled out by certain sorts of triviality results–analogous to those often discussed in the literature on conditionals. I show why these results do not, in fact, rule out the view. They merely give us a constraint on what such a reduction could look like. In particular they show that there is no single proposition belief in which suffices for having (...) a particular credence, regardless of one’s evidence. But if we allow such propositions to vary with evidence–as we should–then the results do not rule out a reduction. So, at least on this count, credences might very well just be beliefs about probabilities. (shrink)

Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system Kn lacks Craig Interpolation.

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. (shrink)

Limited aggregationists argue that when deciding between competing claims to aid we are sometimes required and sometimes forbidden from aggregating weaker claims to outweigh stronger claims. Joe Horton presents a ‘fatal dilemma’ for these views. Views that land on the First Horn of his dilemma suggest that a previously losing group strengthened by fewer and weaker claims can be more choice-worthy than the previously winning group strengthened by more and stronger claims. Views that land on the Second Horn suggest that (...) combining two losing groups together and two winning groups together can turn the losing groups into the winning groups and the winning groups into the losing groups. This paper demonstrates that the ‘fatal dilemma’ is neither fatal nor a dilemma. The First Horn is devastating but avoidable and the Second Horn is unavoidable but not devastating. Nevertheless, Horton’s argument does help to narrow down the acceptable range of views. (shrink)

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)

Deferential Monadic Panpsychism is a view that accepts that physical science is capable of discovering the basic structure of reality. However, it denies that reality is fully and exhaustively de- scribed purely in terms of physical science. Consciousness is missing from the physical description and cannot be reduced to it. DMP explores the idea that the physically fundamental features of the world possess some intrinsic mental aspect. It thereby faces a se- vere problem of understanding how more complex mental states (...) emerge from the mental features of the fundamental features. Here I explore the idea that a new form of aggregative emergence, which I call 'combinatorial infusion', could shed light on this problem and bolster the prospects for this form of panpsychism. (shrink)

This article applies the tools of experimental philosophy to the ongoing debate about both the theoretical viability and the practical import of partially aggregative moral theories in distributive ethics. We conduct a series of three experiments (N=383): First, we document the widespread occurrence of the intuitions that motivate this position. Our study then moves beyond establishing the existence of partially aggregative intuitions in two dimensions: First, we extend experimental work in such a way as to ascertain which amongst existing versions (...) of partial aggregation (localised vs. global) chimes more fully with moral common sense. Specifically, we document how, in tie-breaking cases, ‘irrelevant goods’ judgments (Kamm) are just as robust as the original aggregative/non-aggregative pair of judgments that constitute partial aggregation. Second, by pairing laypeople’s moral judgments in standard cases with their intuitions about the limits of permissible self-prioritisation, we investigate whether one prominent explanation of why irrelevant claims may not be aggregated (Voorhoeve’s ‘personal prerogative’ argument) can be said to underpin people’s intuitions about the (ir)relevance relation of claims in conflict cases. We close with a discussion of our findings’ practical and theoretical import and highlight avenues for future research. (shrink)