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)

The doctrinal paradox shows that aggregating individual judgments by taking a majority vote does not always yield a consistent set of collective judgments. Philip Pettit, Luc Bovens, and Wlodek Rabinowicz have recently argued for the epistemic superiority of an aggregation procedure that always yields a consistent set of judgments. This paper identifies several additional epistemic advantages of their consistency maintaining procedure. However, this paper also shows that there are some circumstances where the majority vote procedure is epistemically superior. The epistemic (...) value of maintaining consistency does not always outweigh the epistemic value of making true judgments. (shrink)

_ Source: _Page Count 19 Collectivities can have obligations beyond the aggregate of pre-existing obligations of their members. Certain such collective obligations _distribute_, i.e., become members’ obligations to do their fair share. In _incremental good_ cases, i.e., those in which a member’s fair share would go part way toward fulfilling the collectivity’s obligation, each member has an unconditional obligation to contribute.States are involuntary collectivities that bear moral obligations. Certain states, _democratic legal states_, are collectivities whose obligations can distribute. Many existing (...) states are democratic legal states, but none satisfies more rigorous requirements of distributive justice. There, citizens who hold assets, in excess of what is just, bear a distributed duty to dedicate that excess toward correcting the injustice. It is an incremental good case not conditioned on the conformity of others who are also wealthier than justice allows, nor on the diligence of the state in meeting its obligations. (shrink)

_ Source: _Page Count 19 Collectivities can have obligations beyond the aggregate of pre-existing obligations of their members. Certain such collective obligations _distribute_, i.e., become members’ obligations to do their fair share. In _incremental good_ cases, i.e., those in which a member’s fair share would go part way toward fulfilling the collectivity’s obligation, each member has an unconditional obligation to contribute.States are involuntary collectivities that bear moral obligations. Certain states, _democratic legal states_, are collectivities whose obligations can distribute. Many existing (...) states are democratic legal states, but none satisfies more rigorous requirements of distributive justice. There, citizens who hold assets, in excess of what is just, bear a distributed duty to dedicate that excess toward correcting the injustice. It is an incremental good case not conditioned on the conformity of others who are also wealthier than justice allows, nor on the diligence of the state in meeting its obligations. (shrink)

What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. In this paper, we seek (...) to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory. (shrink)

In normative political theory, it is widely accepted that democracy cannot be reduced to voting alone, but that it requires deliberation. In formal social choice theory, by contrast, the study of democracy has focused primarily on the aggregation of individual opinions into collective decisions, typically through voting. While the literature on deliberation has an optimistic flavour, the literature on social choice is more mixed. It is centred around several paradoxes and impossibility results identifying conflicts between different intuitively plausible desiderata. In (...) recent years, there has been a growing dialogue between the two literatures. This paper discusses the connections between them. Important insights are that (i) deliberation can complement aggregation and open up an escape route from some of its negative results; and (ii) the formal models of social choice theory can shed light on some aspects of deliberation, such as the nature of deliberation-induced opinion change. (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)

Judgment aggregation theory, which concerns the translation of individual judgments on logical propositions into consistent group judgments, has shown that group consistency generally cannot be guaranteed if each proposition is treated independently from the others. Developing the right method of abandoning independence is thus a high-priority goal. However, little work has been done in this area outside of a few simple approaches. To fill the gap, we compare four methods based on distance metrics between judgment sets. The methods generalize the (...) premise-based and sequential priority approaches to judgment aggregation, as well as distance-based preference aggregation. They each guarantee group consistency and implement a range of distinct functions with different properties, broadening the available tools for social choice. A central result is that only one of these methods (not previously considered in the literature) satisfies three attractive properties for all reasonable metrics. (shrink)

A sketch of my ethical views, or secular moral philosophy. Emphasis is on stating how it all hangs together.

Frente a problemas de decisión colectiva de cierta complejidad, distintos métodos de votación pueden considerarse igualmente democráticos. Ante esta situación, argumento que es posible investigar cuáles de esos métodos producen mejores resultados epistémicos sobre asuntos fácticos. Comienzo ilustrando la relación entre democracia y métodos de votación con un sencillo ejemplo. Muestro cómo el uso de modelos idealizados permite descubrir algunas propiedades de los métodos de votación; varios de estos descubrimientos muestran que, frente a problemas de cierta complejidad, no hay una (...) respuesta clara acerca de cuál es el resultado de una elección democrática. Frente a esto, sugiero que deberíamos tomar en cuenta un rasgo epistémico instrumental de varios métodos de votación: su capacidad para generar respuestas correctas ante varias situaciones. Esta intuición ofrece lecciones importantes para el diseño de instituciones electorales. (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)

This thesis defends John Rawls’s constructivist theory of justice against three distinct challenges. -/- Part one addresses G. A. Cohen’s claim that Rawls’s constructivism is committed to a mistaken thesis about the relationship between facts and principles. It argues that Rawls’s constructivist procedure embodies substantial moral commitments, and offers an intra-normative reduction rather than a metaethical account. Rawls’s claims about the role of facts in moral theorizing in A Theory of Justice should be interpreted as suggesting that some of our (...) moral beliefs, which we are inclined to hold without reference to facts, are, in fact, true, because certain facts obtain. This thesis and the acknowledgement of the moral assumptions of Rawls’s constructivism help to show that Rawls does not, and does not need to, deny Cohen’s thesis. -/- Part two defends the characterization of the decision problem in Rawls’s original position as a decision problem under uncertainty. Rawls stipulates that the denizens of the original position lack information that they could use to arrive at estimates of the likelihood of ending up in any given social position. It has been argued that Rawls does not have good grounds for this stipulation. I argue that given the nature of the value function we should attribute to the denizens of the original position and our cognitive limitations, which also apply to the denizens of the original position, their decision problem can be characterized as one under uncertainty even if we stipulate that they know that they have an equal chance of being in any individual’s place. -/- Part three assesses the claim that a true commitment to Rawls’s difference principle requires a further commitment to an egalitarian ethos. This egalitarian ethos is offered as a means to bring about equality and Pareto-optimality. Accordingly, I try to undermine the case for an egalitarian ethos by challenging the desirability of the ends it is supposed to further or by showing that it is redundant. I argue that if primary goods are the metric of justice, then Pareto optimality in the space of the metric of justice is undesirable. I then argue that if the metric of justice is welfare, depending on the theory of welfare we adopt, an egalitarian ethos will either be redundant or will have objectionably paternalistic consequences. (shrink)

Leaving aside the usual approach to deliberation as a private or simulated weighing, based on the traditional model for practical reasoning, normative logic and argumentation schemes, we aim to characterize deliberation as a particular instance of discursive interaction in the public arena in which information, options and preferences are evaluated and handled in order to achieve a decision or a practical resolution in a responsible and reasoned way; a crossroads between epistemic-discursive conditions and ethical-political programs.

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)

Can collectives be wise? The thesis that they can has recently received a lot of attention. It has been argued that, in many judgmental or decision-making tasks, suitably organized groups can outperform their individual members. In this paper, I discuss the lessons we can learn about collective wisdom from the emerging theory of judgment aggregation, as distinct from the literature on Condorcet’s jury theorem.

Pettit (2006) argues that deferring to majority testimony is not generally rational: it may lead to inconsistent beliefs. He suggests that “another ... approach will do better”: deferring to supermajority testimony. But this approach may also lead to inconsistencies. In this paper, I describe conditions under which deference to supermajority testimony ensures consistency, and conditions under which it does not. I also introduce the concept of “consistency of degree k”, which is weaker than full consistency by ruling out only “blatant” (...) inconsistencies in an agent’s beliefs while permitting less blatant ones, and show that, while super-majoritarian deference often fails to ensure full consistency, it is a route to consistency in this weaker sense. (shrink)

The problem of the aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. The dificulty lies in the fact that a seemingly reasonable aggregation procedure, such as propositionwise majority voting, cannot ensure an equally consistent collective outcome. The literature on judgment aggregation refers to such dilemmas as the discursive paradox. So far, three procedures have been proposed to overcome the paradox: the premise-based and conclusion-based procedures on the (...) one hand, and the merging approach on the other hand. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, the question is how good the merging approach is in tracking the truth, and how it compares with the premise-based and conclusion-based procedures. (shrink)

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same 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 such a problem as the \textit{discursive dilemma}. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, we address the question of how good (...) the various approaches are at selecting the right conclusion. We focus on two approaches: distance-based procedures and a Bayesian analysis. They correspond to group-internal and group-external decision-making, respectively. We compare those methods in a probabilistic model, demonstrate the robustness of our results over various generalizations and discuss their applicability in different situations. The findings vindicate (i) that in judgment aggregation problems, reasons should carry higher weight than conclusions and (ii) that considering members of an advisory board to be highly competent is a better strategy than to underestimate their advice.". (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 opinion 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)

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)

Majority cycling and related social choice paradoxes are often thought to threaten the meaningfulness of democracy. But deliberation can prevent majority cycles – not by inducing unanimity, which is unrealistic, but by bringing preferences closer to single-peakedness. We present the first empirical test of this hypothesis, using data from Deliberative Polls. Comparing preferences before and after deliberation, we find increases in proximity to single-peakedness. The increases are greater for lower versus higher salience issues and for individuals who seem to have (...) deliberated more versus less effectively. They are not merely a byproduct of increased substantive agreement. Our results both refine and support the idea that deliberation, by increasing proximity to single-peakedness, provides an escape from the problem of majority cycling. (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)

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)