The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on those propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. The literature on judgment aggregation refers to that problem as the discursive dilemma. In this paper, we motivate that many groups do not only want to reach a factually right conclusion, but also want to correctly evaluate the reasons for that conclusion. In (...) other words, we address the problem of tracking the true situation instead of merely selecting the right outcome. We set up a probabilistic model analogous to Bovens and Rabinowicz (2006) and compare several aggregation procedures by means of theoretical results, numerical simulations and practical considerations. Among them are the premise-based, the situation-based and the distance-based procedure. Our findings confirm the conjecture in Hartmann, Pigozzi and Sprenger (2008) that the premise-based procedure is a crude, but reliable and sometimes even optimal form of judgment aggregation. (shrink)

This book elucidates the theoretical structure and scope of interpersonal and intra-personal aggregation--a trade-off between benefits to a group of individuals and losses to another group of individuals--and defends a form of aggregation -- formal aggregation -- that resolves a variety of outstanding problems arising from the conventional understanding of aggregation, including the Number Problem concerning the moral relevance of the number of individuals.

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 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)

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)

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)

This paper is concerned with the efficiency of information aggregation in a committee whose members have heterogeneous preferences over a binary decision variable. We study a voting game with a pre-vote communication stage and identify conditions under which full information aggregation is possible. In particular, if preferences are common knowledge and each committee member is endowed with information, full information aggregation is possible despite preference heterogeneity.

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

This paper is about 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)

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

In 'How Should We Aggregate Competing Claims', Alex Voorhoeve suggests accommodating intuitions about duties in rescue cases by combining aggregative and non-aggregative elements into one theory. In this paper, I discuss two problems Voorhoeve’s theory faces as a result of requiring a cyclic pattern of choice, and argue that his attempt to solve them does not succeed.

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)

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)

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)

In recent years, judgement aggregation has emerged as an important area of social choice theory. Judgement aggregation is concerned with aggregating sets of individual judgements over logically connected propositions into a set of collective judgements. It has been shown that even seemingly weak conditions on the aggregation function make it impossible to find functions that produce rational collective judgements from all possible rational individual judgements. This implies that the step from individual judgements to collective judgements requires trade-offs between different desiderata, (...) such as universal domain, rationality, epistemological quality, and unbiasedness. These dilemmas challenge us to decide which conditions we should relax. The typical application for judgement aggregation is the problem of group decision making. Juries and expert committees are the stock examples. However, the relevance of judgement aggregation goes beyond these cases. In this survey I review some core results in the field of judgement aggregation and social epistemology and discuss their implications for the analysis of distributed thinking. (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)

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)

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)

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)

Suppose you found that the universe around you was infinite—that it extended infinitely far in space or in time and, as a result, contained infinitely many persons. How should this change your moral decision-making? Radically, it seems, according to some philosophers. According to various recent arguments, any moral theory that is ’minimally aggregative’ will deliver absurd judgements in practice if the universe is (even remotely likely to be) infinite. This seems like sound justification for abandoning any such theory. -/- My (...) goal in this thesis is simple: to demonstrate that we need not abandon minimally aggregative theories, even if we happen to live in an infinite universe. I develop and motivate an extension of such theories, which delivers plausible judgements in a range of realistic cases. I show that this extended theory can overcome key objections—both old and new—and that it succeeds where other proposals do not. With this proposal in hand, we can indeed retain minimally aggregative theories and continue to make moral decisions based on what will promote the good. (shrink)

How might we extend aggregative moral theories to compare infinite worlds? In particular, how might we extend them to compare worlds with infinite spatial volume, infinite temporal duration, and infinitely many morally valuable phenomena? When doing so, we face various impossibility results from the existing literature. For instance, the view we adopt can endorse the claim that worlds are made better if we increase the value in every region of space and time, or that they are made better if we (...) increase the value obtained by every person. But they cannot endorse both claims, so we must choose. In this paper I show that, if we choose the latter, our view will face serious problems such as generating incomparability in many realistic cases. Opting instead to endorse the first claim, I articulate and defend a spatiotemporal, expansionist view of infinite aggregation. Spatiotemporal views such as this do face some difficulties, but I show that these can be overcome. With modification, they can provide plausible comparisons in cases that we care about most. (shrink)

Many critics of utilitarianism claim that we should reject interpersonal aggregation because aggregative principles do not take the separateness of persons seriously. In this article, I will reject this claim. I will first elucidate the theoretical structure of aggregation. I will then consider various interpretations of the notion of the separateness of persons and clarify what exactly those critics are trying to reject by appealing to the notion of the separateness of persons. I will argue that none of these interpretations (...) can serve as the ground for rejecting aggregation. (shrink)

An aggregation procedure merges a list of objects into a representative object. This paper considers the problem of aggregating n rows in an n-by-m matrix into a summary row, where every entry is an element in an algebraic field. It focuses on consistent aggregators, which require each entry in the summary row to depend only on its column entries in the matrix and to be the same as the column entry if the column is constant. Consistent aggregators are related to (...) additive, linear and.. (shrink)

This paper argues that, according to Leibniz's view of entia per aggregationem, there are (or, at any rate, there could be) aggregates that are entirely mind-independent.

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)

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)

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.

Neurodegenerative syndromes present as proteinopathies – does ribosomal infidelity contribute to the protein toxicity that is the driving force for neuronal cell loss? Intracellular and extracellular protein aggregates overwhelm the clearance capacity of cells and tissues. Proteins aggregate when hydrophobic residues are exposed. Hydrophobic residues become exposed when proteins are misfolded. Protein misfolding can originate from translational errors at the ribosome. Indeed, the most error‐prone process in gene expression is translation at the ribosome. Recent evidence indicates that manipulating the (...) ribosomal accuracy impacts on the lifespan of model organisms and a reduced translational accuracy is accompanied by neurodegeneration. The first hit in aging‐associated neurodegenerative disease may be the well‐documented decline of cellular buffering capacity by aging. A second hit that impacts on the quality of protein synthesis could be the driving force for the observed loss of proteostasis in neurodegeneration. This hypothesis provides an explanation for the late onset of most neurodegenerative diseases. (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)

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.

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)

This article considers the reach of arguments for saving the greater number without interpersonal aggregation, and argues that interpersonal aggregation is useful to encompass the proper respect due to each separate person. I first give a precise definition of interpersonal aggregation, which many non-utilitarians try to avoid. Then, I show that consequentialism and Scanlon can justify the case for the greater number without interpersonal aggregation. However, I propose the Aggregation Approach, which justifies the case for the greater number in some (...) cases and the case for tossing a fair coin in other cases. I conclude that interpersonal aggregation does not disrespect the separate person. (shrink)

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

Is there any number of people you should save from paralysis rather than saving one person from death? Is there any number of people you should save from a headache rather than saving one person from death? Many people answer ‘yes’ and ‘no’, respectively. They therefore accept a partially aggregative moral view. Patrick Tomlin has recently argued that the most promising partially aggregative views in the literature have implausible implications in certain cases in which there are additions or subtractions to (...) the groups of people that we can save. Several philosophers have begun responding to this argument by developing partially aggregative views that avoid the relevant implications. In this paper, I extend Tomlin’s argument to create a dilemma that no partially aggregative view can avoid. I conclude that we should accept a fully aggregative moral view. (shrink)

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

Polyglutamine (polyQ) diseases are genetically inherited neurodegenerative disorders. They are caused by mutations that result in polyQ expansions of particular proteins. Mutant proteins form intranuclear aggregates, induce cytotoxicity and cause neuronal cell death. Protein interaction data suggest that polyQ regions modulate interactions between coiled‐coil (CC) domains. In the case of the polyQ disease spinocerebellar ataxia type‐1 (SCA1), interacting proteins with CC domains further enhance aggregation and toxicity of mutant ataxin‐1 (ATXN1). Here, we suggest that CC partners interacting with the polyQ (...) region of a mutant protein, increase its aggregation while partners that interact with a different region reduce the formation of aggregates. Computational analysis of genetic screens revealed that CC‐rich proteins are highly enriched among genes that enhance pathogenicity of polyQ proteins, supporting our hypothesis. We therefore suggest that blocking interactions between mutant polyQ proteins and their CC partners might constitute a promising preventive strategy against neurodegeneration. (shrink)

This paper proves two theorems for homogeneous juries that arise from different solutions to the problem of aggregation of dichotomous choice. In the first theorem, negative correlation increases the competence of the jury, while positive correlation has the opposite effect. An enlargement of the jury with positive correlation can be detrimental up to a certain size, beyond which it becomes beneficial. The second theorem finds a family of distributions for which correlation has no effect on a jury’s competence. The approach (...) allows us to compute the bounds on a jury’s competence as the maximum and minimum probability of it being correct for a given individual competence and dependence structure. (shrink)

:Preference-aggregation problems arise in various contexts. One such context, little explored by social choice theorists, is metaethical. ‘Ideal-advisor’ accounts, which have played a major role in metaethics, propose that moral facts are constituted by the idealized preferences of a community of advisors. Such accounts give rise to a preference-aggregation problem: namely, aggregating the advisors’ moral preferences. Do we have reason to believe that the advisors, albeit idealized, can still diverge in their rankings of a given set of alternatives? If so, (...) what are the moral facts when the advisors do diverge? These questions are investigated here using the tools of Arrovian social choice theory. (shrink)

This article explores public reason liberalism’s indeterminacy problem, a problem that obtains when we admit significant diversity into our justificatory model. The article argues first that Gerald Gaus’s solution to the indeterminacy problem is unsatisfactory and second that, contra Gaus’s concerns, social choice theory is able to solve public reason’s indeterminacy problem. Moreover, social choice theory can do so in a way that avoids the worries raised against Gaus’s solution to the indeterminacy problem as well as the worries Gaus himself (...) raises against the use of social choice mechanisms. Social choice theory thus rescues public reason liberalism by aggregating out of indeterminacy. (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)

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

This book argues that modern macroeconomics has completely overlooked the aggregate nature of the data. Standard models start with intertemporally maximizing agents and obtain dynamic equations linking economic variables like consumption, income, investment interest rate and employment. Such equations exhibit testable properties like cointegration, definite patterns of Granger causality, and restrictions on the parameters. The usual simplification that agents are identical leads to testing these properties directly on aggregate data. Here this simplification is systematically questioned. In Part I (...) the homogeneity assumption is tested using disaggregate data and strongly rejected. As shown in Part II, the consequence of introducing heterogeneity is that, apart from flukes, cointegration unidirectional Granger causality, restrictions on parameters do not survive aggregation: thus the claim that modern macroeconomics has solid microfoundations is unwarranted. However, it is argued in Part III that aggregation is not necessarily bad. Some important theory-based models that do not fit aggregate data well in their representative-agent version can be reconciled with aggregate data by introducing heterogeneity. (shrink)

Drawing on the so-called “doctrinal paradox”, List and Pettit (2002) have shown that, given an unrestricted domain condition, there exists no procedure for aggregating individual sets of judgments over multiple interconnected propositions into corresponding collective ones, where the procedure satisfies some minimal conditions similar to the conditions of Arrow’s theorem. I prove that we can avoid the paradox and the associated impossibility result by introducing an appropriate domain restriction: a structure condition, called unidimensional alignment, is shown to open up a (...) possibility result, similar in spirit to Black’s median voter theorem. Specifically, I prove that, given unidimensional alignment, propositionwise majority voting is the unique procedure for aggregating individual sets of judgments into collective ones in accordance with the above mentioned minimal conditions. (shrink)

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

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

Is there any number of people you should save from paralysis rather than saving one person from death? Is there any number of people you should save from a migraine rather than saving one person from death? Many people answer “yes” and “no,” respectively. The aim of partially aggregative moral views is to capture and justify combinations of intuitions like these. In this article, I develop a risk-based reductio argument that shows that there can be no adequate partially aggregative view. (...) I then argue that the only plausible response to this reductio is to accept a fully aggregative view. (shrink)

Theories of aggregated legislative intent posit that the legislative intent of parliament is what a significant enough proportion of legislators intended (e.g., legislative intent is p if a majority intend that p). After all, many think the same way about democracy (‘votes reveal the will of the people’) and about courts (‘a court decision is based on judicial voting’). The existing literature on aggregated legislative intent, however, tends to make two undefended assumptions: (i) Informed Assumption: all legislators have policy intentions; (...) and (ii) Group Intent Assumption: the existence of an aggregated intent entails the existence of a group intent. Despite these assumptions being subject to great scrutiny, they largely remain undefended. This paper defends the Group Intent Assumption and shows that aggregated theories can survive with a weaker version of the Informed Assumption. (shrink)

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)

A person possesses value from various components of wellbeing, but they also have overall wellbeing from various instances of value taken together. Most ethicists assume that there is an objectively unique way that wellbeing from components aggregates into overall wellbeing. However, I argue that aggregation is subjective and varies depending on what sort of aggregation a person values. I end with some implications for the significance of death.

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)

Is there any number of people you should save from paralysis rather than saving one person from death? Is there any number of people you should save from a migraine rather than saving one person from death? Many people answer ‘yes’ and ‘no’, respectively. The aim of partially aggregative moral views is to capture and justify combinations of intuitions like these. These views contrast with fully aggregative moral views, which imply that the answer to both questions is ‘yes’, and with (...) non-aggregative moral views, which imply that the answer to both questions is ‘no’. In this paper, I review the most natural and influential ways of developing partially aggregative views and explain the main problems they face. (shrink)