With the rapidly growing amounts of information, visualization is becoming increasingly important, as it allows users to easily explore and understand large amounts of information. However the field of information visualiza- tion currently lacks sufficient theoretical foundations. This article addresses foundational questions connecting information visualization with computing and philosophy studies. The idea of multiscale information granula- tion is described based on two fundamental concepts: information (structure) and computation (process). A new information processing paradigm of Granular Computing enables stepwise increase of (...) granulation/aggregation of information on different levels of resolution, which makes possible dynamical viewing of data. Information produced by Google Earth is an illustration of visualization based on clustering (granulation) of information on a succession of layers. Depending on level, specific emergent properties become visible as a result of different ways of aggregation of data/information. As information visualization ultimately aims at amplifying cognition, we discuss the process of simulation and emulation in relation to cognition, and in particular visual cognition. (shrink)

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using "systematicity" and "independence" conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of (...) our second result. Although we thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model. JEL Classi…cation: D70, D71.. (shrink)

This paper provides an introductory review of the theory of judgment aggregation. It introduces the paradoxes of majority voting that originally motivated the field, explains several key results on the impossibility of propositionwise judgment aggregation, presents a pedagogical proof of one of those results, discusses escape routes from the impossibility and relates judgment aggregation to some other salient aggregation problems, such as preference aggregation, abstract aggregation and probability aggregation. The present illustrative rather than (...) exhaustive review is intended to give readers new to the field of judgment aggregation a sense of this rapidly growing research area. (shrink)

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

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than (...) “premise-based voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

In 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)

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)

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

We generalize Harsanyi's social aggregation theorem. We allow the population to be infi nite, and merely assume that individual and social preferences are given by strongly independent preorders on a convex set of arbitrary dimension. Thus we assume neither completeness nor any form of continuity. Under Pareto indifference, the conclusion of Harsanyi's theorem nevertheless holds almost entirely unchanged when utility values are taken to be vectors in a product of lexicographic function spaces. The addition of weak or strong Pareto (...) has essentially the same implications in the general case as it does in Harsanyi's original setting. (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)

Axiom weakening is a novel technique that allows for fine-grained repair of inconsistent ontologies. In a multi-agent setting, integrating ontologies corresponding to multiple agents may lead to inconsistencies. Such inconsistencies can be resolved after the integrated ontology has been built, or their generation can be prevented during ontology generation. We implement and compare these two approaches. First, we study how to repair an inconsistent ontology resulting from a voting-based aggregation of views of heterogeneous agents. Second, we prevent the generation (...) of inconsistencies by letting the agents engage in a turn-based rational protocol about the axioms to be added to the integrated ontology. We instantiate the two approaches using real-world ontologies and compare them by measuring the levels of satisfaction of the agents w.r.t. the ontology obtained by the two procedures. (shrink)

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)

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)

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or implication preservation. We fully characterize the agendas for which (...) there are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (2002), Nehring (2006), Dietrich and List (2007a) and Dokow and Holzman (2010a). (shrink)

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)

We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the outcome of a judgment aggregation procedure in her favour by reporting insincere judgments (the strategic manipulation problem); and (3) deciding whether a given judgment aggregation scenario is guaranteed to result in a logically consistent outcome, independently from what the judgments supplied by the (...) individuals are (the problem of the safety of the agenda). We provide results both for specific aggregation procedures (the quota rules, the premisebased procedure, and a distance-based procedure) and for classes of aggregation procedures characterised in terms of fundamental axioms. (shrink)

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

The aim of this article is to introduce the theory of judgment aggregation, a growing interdisciplinary research area. The theory addresses the following question: How can a group of individuals make consistent collective judgments on a given set of propositions on the basis of the group members' individual judgments on them? I begin by explaining the observation that initially sparked the interest in judgment aggregation, the so-called "doctinal" and "discursive paradoxes". I then introduce the basic formal model of (...) judgment aggregation, which allows me to present some illustrative variants of a generic impossibility result. I subsequently turn to the question of how this impossibility result can be avoided, going through several possible escape routes. Finally, I relate the theory of judgment aggregation to other branches of aggregation theory. Rather than offering a comprehensive survey of the theory of judgment aggregation, I hope to introduce the theory in a succinct and pedagogical way, providing an illustrative rather than exhaustive coverage of some of its key ideas and results. (shrink)

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

This work contributes to the theory of judgement aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgement aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, the Lambek calculus, Linear Logic and Relevant Logics. The motivation for studying judgement aggregation in non-classical logics is that they offer a number of modelling choices to represent agents’ reasoning in aggregation problems. By studying judgement (...) aggregation in logics that are weaker than classical logic, we investigate whether some well-known impossibility results, that were tailored for classical logic, still apply to those weak systems. (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)

This paper applies ideas and tools from social choice theory (such as Arrow's theorem and related results) to linguistics. Specifically, the paper investigates the problem of constraint aggregation in optimality theory from a social-choice-theoretic perspective.

Many of us believe (1) Saving a life is more important than averting any number of headaches. But what about risky cases? Surely: (2) In a single choice, if the risk of death is low enough, and the number of headaches at stake high enough, one should avert the headaches rather than avert the risk of death. And yet, if we will face enough iterations of cases like that in (2), in the long run some of those small risks of (...) serious harms will surely eventuate. And yet: (3) Isn't it still permissible for us to run these repeated risks, despite that knowledge? After all, if it were not, then many of the risky activities that we standardly think permissible would in fact be impermissible. Nobody has yet offered a principle that can accommodate all of 1-3. In this paper, I show that we can accommodate all of these judgements, by taking into account both ex ante and ex post perspectives. In doing so, I clear aside an important obstacle to a viable deontological decision theory. (shrink)

Interpersonal aggregation involves the combining and weighing of benefits and losses to multiple individuals in the course of determining what ought to be done. Most consequentialists embrace thoroughgoing interpersonal aggregation, the view that any large benefit to each of a few people can be morally outweighed by allocating any smaller benefit to each of many others, so long as this second group is sufficiently large. This would permit letting one person die in order to cure some number of (...) mild headaches instead. Most non-consequentialists reject thoroughgoing interpersonal aggregation despite also believing it is permissible to let one person die in order to prevent many cases of paraplegia instead. Non-consequentialists defend this asymmetry largely on the basis of intuition, and some rely on the notion of relevance to formalize the grounding intuitions. This article seeks to clarify and strengthen the non-consequentialist notion of relevance by engaging with three objections to it. (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 (...) class='Hi'>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)

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)

It is plausible to think that it is wrong to cure many people’s headaches rather than save someone else’s life. On the other hand, it is plausible to think that it is not wrong to expose someone to a tiny risk of death when curing this person’s headache. I will argue that these claims are inconsistent. For if we keep taking this tiny risk then it is likely that one person dies, while many others’ headaches are cured. In light of (...) this inconsistency, there is a conflict in our intuitions about beneficence and chance. This conflict is perplexing. And I have not been able to find a satisfactory way of resolving it. Perhaps you can do better? (shrink)

Combinations of molecules, of biological individuals, or of chemical processes can produce effects that are not simply attributable to the constituents. Such non-redundant causality warrants recognition of those coherences as ontologically significant whenever that efficacy is relevant. With respect to such interaction, the effective coherence is more real than are the components. This ontological view is a variety of structural realism and is also a kind of process philosophy. The designation ‘process structural realism’ (PSR) seems appropriate.

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

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)

Our aim in this chapter is to draw attention to what we see as a disturbing feature of conciliationist views of disagreement. Roughly put, the trouble is that conciliatory responses to in-group disagreement can lead to the frustration of a group's epistemic priorities: that is, the group's favoured trade-off between the "Jamesian goals" of truth-seeking and error-avoidance. We show how this problem can arise within a simple belief aggregation framework, and draw some general lessons about when the problem is (...) most pronounced. We close with a tentative proposal for how to solve the problem raised without rejecting conciliationism. (shrink)

Climate change appears to be a classic aggregation problem, in which billions of individuals perform actions none of which seem to be morally wrong taken in isolation, and yet which combine to drive the global concentration of greenhouse gases (GHGs) ever higher toward environmental (and humanitarian) catastrophe. When an individual can choose between actions that will emit differing amounts of GHGs―such as to choose a vegan rather than carnivorous meal, to ride a bike to work rather than drive a (...) car, or to take a reusable bag to the supermarket rather than send another plastic bag to landfill―does she have any reason to choose the lower-emitting actions? In this chapter I'll reject the claim that individuals don't make a difference when it comes to climate change. I first discuss making a difference with every action, as a way of getting clearer about how individuals' actions impact causally on the harms resulting from climate change, making a distinction so far overlooked in the climate ethics discussion between 'macro' thresholds like ice-cap melt, and 'micro' thresholds like severe weather events. I set aside making a difference with every action as implausible, and then move on to discuss both low probability of major difference, and high probability of minor difference. I argue that both of these are plausible characterizations of individuals' causal contributions to climate change. I conclude by noting some policy implications of having (probabilistic) individual difference-making back in play. (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)

In this paper, I set out and defend a new theory of value, whole-life welfarism. According to this theory, something is good only if it makes somebody better off in some way in his life considered as a whole. By focusing on lifetime, rather than momentary, well-being, a welfarist can solve two of the most vexing puzzles in value theory, The Badness of Death and The Problem of Additive Aggregation.

to appear in Szabó Gendler, T. & J. Hawthorne (eds.) Oxford Studies in Epistemology volume 6 -/- We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? (...) And how do they relate to the individual credences assigned by the members of the particular group in question? According to the credal judgment aggregation principle, Linear Pooling, the credence function of a group should be a weighted average or linear pool of the credence functions of the individuals in the group. In this paper, I give an argument for Linear Pooling based on considerations of accuracy. And I respond to two standard objections to the aggregation principle. (shrink)

Individualists hold that moral responsibility can be ascribed to single human beings only. An important collectivist objection is that individualism is morally deficient because it leaves a normative residue. Without attributing responsibility to collectives there remains a “deficit in the accounting books” (Pettit). This collectivist strategy often uses judgment aggregation paradoxes to show that the collective can be responsible when no individual is. I argue that we do not need collectivism to handle such cases because the individualist analysis leaves (...) no responsibility-deficit. Harm suffered in such situations can have only two sources. Harm is either due to culpable wrongdoing by individuals. Harm is then redressed by holding these individuals responsible. Or harm does not result from culpable wrongdoing. Such harm may have to be redressed too, but not because anyone is responsible for it. Therefore, the charge of moral insensitivity against individualist accounts can be rejected. Furthermore, in the last section of the chapter I will show that collectivist talk about moral responsibility can be used for ethically questionable purposes as well. Collectivists cannot claim the moral high ground. (shrink)

Criticism of big data has focused on showing that more is not necessarily better, in the sense that data may lose their value when taken out of context and aggregated together. The next step is to incorporate an awareness of pitfalls for aggregation into the design of data infrastructure and institutions. A common strategy minimizes aggregation errors by increasing the precision of our conventions for identifying and classifying data. As a counterpoint, we argue that there are pragmatic trade-offs (...) between precision and ambiguity that are key to designing effective solutions for generating big data about biodiversity. We focus on the importance of theory-dependence as a source of ambiguity in taxonomic nomenclature and hence a persistent challenge for implementing a single, long-term solution to storing and accessing meaningful sets of biological specimens. We argue that ambiguity does have a positive role to play in scientific progress as a tool for efficiently symbolizing multiple aspects of taxa and mediating between conflicting hypotheses about their nature. Pursuing a deeper understanding of the trade-offs and synthesis of precision and ambiguity as virtues of scientific language and communication systems then offers a productive next step for realizing sound, big biodiversity data services. (shrink)

This article first describes a dilemma for liberalism: On the one hand restricting their own options is an important means for groups of people to shape their lives. On the other hand, group members are typically divided over whether or not to accept option-restricting solutions or policies. Should we restrict the options of all members of a group even though some consent and some do not? This dilemma is particularly relevant to public health policy, which typically target groups of people (...) with no possibility for individuals to opt out. The article then goes on to propose and discuss a series of aggregation rules for individual into group consent. Consideration of a number of scenarios shows that such rules cannot be formulated only in terms of fractions of consenters and non-consenters, but must incorporate their motives and how much they stand to win or lose. This raises further questions, including what is the appropriate impact of altruistic consenters and non-consenters, what should be the impact of costs and benefits and whether these should be understood as gross or net. All these issues are dealt with in a liberal, anti-paternalistic spirit, in order to explore whether group consent can contribute to the justification of option-restricting public health policy. (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)

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

Harsanyi claimed that his Aggregation and Impartial Observer Theorems provide a justification for utilitarianism. This claim has been strongly resisted, notably by Sen and Weymark, who argue that while Harsanyi has perhaps shown that overall good is a linear sum of individuals’ von Neumann-Morgenstern utilities, he has done nothing to establish any con- nection between the notion of von Neumann-Morgenstern utility and that of well-being, and hence that utilitarianism does not follow. The present article defends Harsanyi against the Sen-Weymark (...) cri- tique. I argue that, far from being a term with precise and independent quantitative content whose relationship to von Neumann-Morgenstern utility is then a substantive question, terms such as ‘well-being’ suffer (or suffered) from indeterminacy regarding precisely which quantity they refer to. If so, then (on the issue that this article focuses on) Harsanyi has gone as far towards defending ‘utilitarianism in the original sense’ as could coherently be asked. (shrink)

In the biomedical context, policy makers face a large amount of potentially discordant evidence from different sources. This prompts the question of how this evidence should be aggregated in the interests of best-informed policy recommendations. The starting point of our discussion is Hunter and Williams’ recent work on an automated aggregation method for medical evidence. Our negative claim is that it is far from clear what the relevant criteria for evaluating an evidence aggregator of this sort are. What is (...) the appropriate balance between explicitly coded algorithms and implicit reasoning involved, for instance, in the packaging of input evidence? In short: What is the optimal degree of ‘automation’? On the positive side: We propose the ability to perform an adequate robustness analysis as the focal criterion, primarily because it directs efforts to what is most important, namely, the structure of the algorithm and the appropriate extent of automation. Moreover, where there are resource constraints on the aggregation process, one must also consider what balance between volume of evidence and accuracy in the treatment of individual evidence best facilitates inference. There is no prerogative to aggregate the total evidence available if this would in fact reduce overall accuracy. (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)

The impossibility results in judgement aggregation show a clash between fair aggregation procedures and rational collective outcomes. In this paper, we are interested in analysing the notion of rational outcome by proposing a proof-theoretical understanding of collective rationality. In particular, we use the analysis of proofs and inferences provided by linear logic in order to define a fine-grained notion of group reasoning that allows for studying collective rationality with respect to a number of logics. We analyse the well-known (...) paradoxes in judgement aggregation and we pinpoint the reasoning steps that trigger the inconsistencies. Moreover, we extend the map of possibility and impossibility results in judgement aggregation by discussing the case of substructural logics. In particular, we show that there exist fragments of linear logic for which general possibility results can be obtained. (shrink)

Faced with the choice between saving one person and saving two others, what should we do? It seems intuitively plausible that we ought to save the two, and many forms of consequentialists offer a straightforward rationale for the intuition by appealing to interpersonal aggregation. But still many other philosophers attempt to provide a justification for the duty to save the greater number without combining utilities or claims of separate individuals. I argue against one such attempt proposed by Iwao Hirose. (...) Despite being consequentialist, his argument is aggregation-free since it relies on a non-aggregative value judgement method, instead of interpersonal aggregation, to establish that (other things being equal) a state of affairs is better when more people survive therein. I do not take issue with its consequentialist element; rather, I claim that there is no good reason to adopt the method in question, and thus no good reason to be moved by his argument overall. What we are in search of is not merely a logically possible method that can produce the conclusion that we already want, but one that we have good reason to adopt. Hirose's argument elegantly demonstrates how it could possibly be true that it is right to save the greater number; but it fails to show that we have reason to believe so - even when we do not combine the interests of different individuals. (shrink)

How can different individuals' probability functions on a given sigma-algebra of events be aggregated into a collective probability function? Classic approaches to this problem often require 'event-wise independence': the collective probability for each event should depend only on the individuals' probabilities for that event. In practice, however, some events may be 'basic' and others 'derivative', so that it makes sense first to aggregate the probabilities for the former and then to let these constrain the probabilities for the latter. We formalize (...) this idea by introducing a 'premise-based' approach to probabilistic opinon pooling, and show that, under a variety of assumptions, it leads to linear or neutral opinion pooling on the 'premises'. This paper is the second of two self-contained, but technically related companion papers inspired by binary judgment-aggregation theory. (shrink)

When do claims to be saved of a small or moderate harm aggregate against a competing claim to be saved from an early death? In this short response to Kamm's Bioethical Prescriptions, I argue for the following answer: aggregation of weaker claims against a life is permitted just in case, in a one-to-one contest, a person with a weaker claim would have a personal prerogative to prioritize her claim over a stranger’s competing claim to life.

This is a chapter of a collective volume of Rawls's and Harsanyi's theories of distributive justice. It focuses on Harsanyi's important Social Aggregation Theorem and technically reconstructs it as a theorem in welfarist social choice.

This paper (first published under the same title in Journal of Mathematical Economics, 29, 1998, p. 331-361) is a sequel to "Consistent Bayesian Aggregation", Journal of Economic Theory, 66, 1995, p. 313-351, by the same author. Both papers examine mathematically whether the the following assumptions are compatible: the individuals and the group both form their preferences according to Subjective Expected Utility (SEU) theory, and the preferences of the group satisfy the Pareto principle with respect to those of the individuals. (...) While the 1995 paper explored these assumptions in the axiomatic context of Savage's (1954-1972) SEU theory, the present paper explores them in the context of Anscombe and Aumann's (1963) alternative SEU theory. We first show that the problematic assumptions become compatible when the Anscombe-Aumann utility functions are state-dependent and no subjective probabilities are elicited. Then we show that the problematic assumptions become incompatible when the Anscombe-Aumann utility functions are state-dependent, like before, but subjective probabilities are elicited using a relevant technical scheme. This last result reinstates the impossibilities proved by the 1995 paper, and thus shows them to be robust with respect to the choice of the SEU axiomatic framework. The technical scheme used for the elicitation of subjective probabilities is that of Karni, Schmeidler and Vind (1983). (shrink)