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

Condorcet's famous jury theorem reaches an optimistic conclusion on the correctness of majority decisions, based on two controversial premises about voters: they are competent and vote independently, in a technical sense. I carefully analyse these premises and show that: whether a premise is justi…ed depends on the notion of probability considered; none of the notions renders both premises simultaneously justi…ed. Under the perhaps most interesting notions, the independence assumption should be weakened.

In the emerging literature on judgment aggregation over logically connected proposi- tions, expert rights or liberal rights have not been investigated yet. A group making collective judgments may assign individual members or subgroups with expert know- ledge on, or particularly affected by, certain propositions the right to determine the collective judgment on those propositions. We identify a problem that generalizes Sen's 'liberal paradox'. Under plausible conditions, the assignment of rights to two or more individuals or subgroups is inconsistent with the (...) unanimity principle, whereby unanimously accepted propositions are collectively accepted. The inconsistency can be avoided if individual judgments or rights satisfy special conditions. (shrink)

This article provides a survey of existing studies of majority rule, outlines misconceptions of majority rule, and highlights underexplored fields of research. It argues that the reasons why the minority complies with majority decisions have been underexplored.

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)

Collective intentionality is one of the most fundamental notions in social ontology. However, it is often thought to refer to a capacity which does not presuppose the existence of any other social facts. This chapter critically examines this view from the perspective of one specific theory of collective intentionality, the theory of Margaret Gilbert. On the basis of Gilbert’s arguments, the chapter claims that collective intentionality is a highly contingent achievement of complex social practices and, thus, not a basic social (...) phenomenon. The argument proceeds in three steps. First, Gilbert’s thesis that certain kinds of collective intentionality presuppose joint normative commitments is introduced. Second, it is argued that, on this view, individual commitments can only constitute the relevant kinds of collective intentional states if there are socially shared “principles of membership” that connect the force of individual commitments to a shared content. Third, it is shown that strong collective intentionality depends on the practical acceptance of shared norms and on the establishment of authority relations through mutual recognition. (shrink)

The contemporary theory of epistemic democracy often draws on the Condorcet Jury Theorem to formally justify the ‘wisdom of crowds’. But this theorem is inapplicable in its current form, since one of its premises – voter independence – is notoriously violated. This premise carries responsibility for the theorem's misleading conclusion that ‘large crowds are infallible’. We prove a more useful jury theorem: under defensible premises, ‘large crowds are fallible but better than small groups’. This theorem rehabilitates the importance of deliberation (...) and education, which appear inessential in the classical jury framework. Our theorem is related to Ladha's (1993) seminal jury theorem for interchangeable (‘indistinguishable’) voters based on de Finetti's Theorem. We also prove a more general and simpler such jury theorem. (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)

The new field of judgment aggregation aims to merge many individual sets of judgments on logically interconnected propositions into a single collective set of judgments on these propositions. Judgment aggregation has commonly been studied using classical propositional logic, with a limited expressive power and a problematic representation of conditional statements ("if P then Q") as material conditionals. In this methodological paper, I present a simple unified model of judgment aggregation in general logics. I show how many realistic decision problems can (...) be represented in it. This includes decision problems expressed in languages of classical propositional logic, predicate logic (e.g. preference aggregation problems), modal or conditional logics, and some multi-valued or fuzzy logics. I provide a list of simple tools for working with general logics, and I prove impossibility results that generalise earlier theorems. (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)

This paper argues that group attitudes can be assessed in terms of standards of rationality and that group-level rationality need not be due to individual-level rationality. But it also argues that groups cannot be collective epistemic agents and are not collectively responsible for collective irrationality. I show that we do not need the concept of collective epistemic agency to explain how group-level irrationality can arise. Group-level irrationality arises because even rational individuals can fail to reason about how their attitudes will (...) combine with those of others. In some cases they are morally responsible for this failure, in others they are not. Moreover, the argument for collective epistemic agency is incoherent because reasons-for-groups are ipso facto reasons-for-individual. Instead of talking about reasons-for-groups, we should therefore distinguish between self-regarding reasons and group-regarding reasons. Both kinds of reasons are reasons-for-individuals. These conceptual considerations in favour of moderate individualism are strengthened by an analysis of our moral practice of responding to collective shortfalls of rationality and by the unpalatable moral implications of collectivism about epistemic agency. There is no need to change the subject. Groups can be rational or irrational, but they do not reason. (shrink)

Judgment aggregation studies how individual opinions on a given set of propositions can be aggregated to form a consistent group judgment on the same propositions. Despite the simplicity of the problem, seemingly natural aggregation procedures fail to return consistent collective outcomes, leading to what is now known as the doctrinal paradox. The first occurrences of the paradox were discovered in the legal realm. However, the interest of judgment aggregation is much broader and extends to political philosophy, epistemology, social choice theory, (...) and computer science. The aim of this paper is to provide a concise survey of the discipline and to outline some of the most pressing questions and future lines of research. (shrink)

Majority rule is often adopted almost by default as a group decision rule. One might think, therefore, that the conditions under which it applies, and the argument on its behalf, are well understood. However, the standard arguments in support of majority rule display systematic deficiencies. This article explores these weaknesses, and assesses what can be said on behalf of majority rule.

The combination of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion in which the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set of propositions (...) (the conclusion). This problem is known as the doctrinal paradox. The doctrinal paradox is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox - the so-called premise-based procedure and the conclusion-based procedure - are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge knowledge bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions. (shrink)

This introduces the symposium on judgment aggregation. The theory of judgment aggregation asks how several individuals' judgments on some logically connected propositions can be aggregated into consistent collective judgments. The aim of this introduction is to show how ideas from the familiar theory of preference aggregation can be extended to this more general case. We first translate a proof of Arrow's impossibility theorem into the new setting, so as to motivate some of the central concepts and conditions leading to analogous (...) impossibilities, as discussed in the symposium. We then consider each of four possible escape-routes explored in the symposium. (shrink)

In this companion piece to 'On the Philosophy of Group Decision Methods I: The Non-Obviousness of Majority Rule', we take a closer look at some competitors of majority rule. This exploration supplements the conclusions of the other piece, as well as offers a further-reaching introduction to some of the challenges that this field currently poses to philosophers.

The aggregation of individual judgments on logically connected issues often leads to collective inconsistency. This study examines two collective decision-making procedures designed to avoid such inconsistency—one premise-based and the other conclusion-based. While the relative desirability of the two procedures has been studied extensively from a theoretical perspective, the preference of individuals regarding the two procedures has been less studied empirically. In the present study, a scenario-based questionnaire survey of participant preferences for the two procedures was conducted, taking into consideration prevailing (...) social norms in the society to which the participants belong and the heterogeneity of the participants’ past experiences. Results show that a minority opinion not matching a prevailing social norm is more likely to be supported when the conclusion-based procedure is used. This can be explained by a basic property of the conclusion-based procedure: The procedure does not require voters to reveal their reasons for reaching a particular conclusion. This property proves appealing for participants who have a minority opinion. Such a finding is highly relevant to future studies on strategic behaviors in choosing a collective decision-making procedure. (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)

When scientists are asked to give expert advice on risk-related questions, such as the authorization of medical drugs, deliberation often does not eliminate all disagreements. I propose to model these remaining discrepancies as differences in risk assessments and/or in risk acceptability thresholds. The normative question I consider, then, is how the individual expert views should best be aggregated. I discuss what “best” could mean, with an eye to some robustness considerations. I argue that the majority rule, which is currently often (...) used in expert panels, has significant drawbacks. (shrink)

This essay defends a rational reconstruction of a genealogical debunking argument that begins with the premise “that's just what the economic elite want you to believe” and ends in the conclusion “you should lower your confidence in your belief.” The argument is genealogical because it includes a causal explanation of your beliefs; it is debunking because it claims that the contingencies uncovered by the genealogy undermine your beliefs. The essay begins by defending a plausible causal explanation of your belief in (...) terms of the wants of the elite. Then a number of recent objections to genealogical debunking arguments are considered. It is argued that the genealogy offered in the first part constitutes evidence that a testimony-based belief is not safe and therefore does not constitute knowledge if the economic elite wants you to believe it. (shrink)

Scientists are often asked to advise political institutions on pressing risk-related questions, like climate change or the authorization of medical drugs. Given that deliberation will often not eliminate all disagreements between scientists, how should their risk assessments be aggregated? I argue that this problem is distinct from two familiar and well-studied problems in the literature: judgment aggregation and probability aggregation. I introduce a novel decision-theoretic model where risk assessments are compared with acceptability thresholds. Majority voting is then defended by means (...) of robustness considerations. (shrink)