In two recent papers, Christian List and Philip Pettit have argued that there is a problem in the aggregation of reasoned judgements that is akin to the aggregation of the preference problem in social choice theory. 1 Indeed, List and Pettit prove a new general impossibility theorem for the aggregation of judgements, and provide a propositional interpretation of the social choice problem that suggests it is a special case of their impossibility result. 2 Specifically, they show that no judgement aggregation (...) function for a group is possible if the group seeks to satisfy certain `minimal conditions' designed to ensure that the function is both responsive to the individually rational views of its members and collectively rational in the set of judgements it holds. In this article, I resist the List and Pettit claim that there is the same propensity for collective irrationality or incoherence in the aggregation of reasoned judgements as there is in the aggregation of preference. I argue that reason, because it has a logical structure that is lacking in mere preference, has the effect of giving priority to some aggregations over others, a priority that is not permitted by one of the conditions imposed by List and Pettit. This avoids the incoherence that would otherwise exist if these different aggregations, not consistent with one another, were to compete at the same level of priority. The priority of some aggregations is particularly apparent, I shall argue, if one views the aggregation of judgements through the lens of common law decision-making. Key Words: social choice • judgement • Condorcet jury theorem • collective rationality • public reason • doctrinal paradox • discursive dilemma. (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)

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)

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)

The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. We also consider sequential (...) quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making. (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)

How sensitive should you be to the testimony of others? You saw the car that caused an accident going through traffic lights on the red; or so you thought. Should you revise your belief on discovering that the majority of bystanders, equally well-equipped, equally well-positioned and equally impartial, reported that it went through on the green? Or take another case. You believe that intelligent design is the best explanation for the order of the living universe. Should you revise that belief (...) on finding that most other people, or at least most who by your own lights are as intelligent, informed and impartial as yourself, believe that evolutionary theory offers the better account? Should you do this, in particular, if your own personal sense of where the evidence points – like your own vivid memory of the car going through on the red – remains firmly on the side of intelligent design? Assume, to take a third case, that there is a matter of fact about whether abortion is right or wrong. You believe that it is wrong, having a firm picture of it as an act on a par with murder. Should you revise that belief on discovering that among those whom you regard as equally intelligent, informed and impartial, most believe that abortion is not wrong, or at least not wrong in the way that murder is wrong? Should you do this, in particular, if your own personal sense of abortion remains unchanged; it still seems to you to be a grievous wrong? Should you put aside your own sense of things as mistaken, in the way you might put aside your imagined memory of the car going through on the red, and decide to go along with the majority view? (shrink)

Taken as a model for how groups should make collective judgments and decisions, the ideal of deliberative democracy is inherently ambiguous. Consider the idealised case where it is agreed on all sides that a certain conclusion should be endorsed if and only if certain premises are admitted. Does deliberative democracy recommend that members of the group debate the premises and then individually vote, in the light of that debate, on whether or not to support the conclusion? Or does it recommend (...) that members individually vote on the premises, and then let their commitment to the conclusion be settled by whether or not the group endorses the required premises? Deliberative-democratic theory has not addressed this issue, and this is a problem. The discursive dilemma of my title--a generalisation of the doctrinal paradox from analytical jurisprudence--shows that the procedures distinguished can come apart. Thus deliberative democrats must make up their minds on where they stand in relation to the issue; they cannot sit on the fence. This paper is an attempt to address the issue and look at the grounds on which it may be resolved. (shrink)

The goal of this paper is to frame a theory of reasons--what they are, how they support actions or conclusions--using the tools of default logic. After sketching the basic account of reasons as provided by defaults, I show how it can be elaborated to deal with two more complicated issues: first, situations in which the priority relation among defaults, and so reasons as well, is itself established through default reasoning; second, the treatment of undercutting defeat and exclusionary reasons. Finally, and (...) by way of application, I show how the resulting account can shed some light on Jonathan Dancy's argument from reason holism to a form of extreme particularism in moral theory. (shrink)

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)

List and Pettit have stated an impossibility theorem about the aggregation of individual opinion states. Building on recent work on the lottery paradox, this paper offers a variation on that result. The present result places different constraints on the voting agenda and the domain of profiles, but it covers a larger class of voting rules, which need not satisfy the proposition-wise independence of votes.

In this volume, John Horty brings to bear his work in logic to present a framework that allows for answers to key questions about reasons and reasoning, namely: What are reasons, and how do they support actions or conclusions?

Logical puzzles like the doctrinal paradox raise the problem of how to aggregate individual judgements into a collective judgement, or alternatively, how to merge collectively inconsistent knowledge bases. In this paper, we view judgement aggregation as a function on propositional logic valuations, and we investigate how logic constrains judgement aggregation. In particular, we show that there is no non-dictatorial decision method for aggregating sets of judgements in a logically consistent way if the decision method is local, i.e., only depends on (...) the individual judgements on the proposition under consideration. (shrink)

The purpose of this paper is to question some commonly accepted patterns of reasoning involving nonmonotonic logics that generate multiple extensions. In particular, I argue that the phenomenon of floating conclusions indicates a problem with the view that the skeptical consequences of such theories should be identified with the statements that are supported by each of their various extensions.

This paper concerns voting with logical consequences, which means that anybody voting for an alternative x should vote for the logical consequences of x as well. Similarly, the social choice set is also supposed to be closed under logical consequences. The central result of the paper is that, given a set of fairly natural conditions, the only social choice functions that satisfy social logical closure are oligarchic (where a subset of the voters are decisive for the social choice). The set (...) of conditions needed for the proof include a version of Independence of Irrelevant Alternatives that also plays a central role in Arrow's impossibility theorem. (Published Online July 11 2006) Footnotes1 Much of this article was written while the author was a fellow at the Swedish Collegium for Advanced Study in the Social Sciences (SCASSS) in Uppsala. I want to thank the Collegium for providing me with excellent working conditions. Wlodek Rabinowicz and other fellows gave me valuable comments at a seminar at SCASSS when an early version of the paper was presented. I also want to thank Luc Bovens, Franz Dietrich, Christian List and an anonymous referee for their excellent comments on a later version. The final version was prepared during a stay at Oxford University for which I am grateful to the British Academy. (shrink)

Taken as a model for how groups should make collective judgments and decisions, the ideal of deliberative democracy is inherently ambiguous. Consider the idealised case where it is agreed on all sides that a certain conclusion should be endorsed if and only if certain premises are admitted. Does deliberative democracy recommend that members of the group debate the premises and then individually vote, in the light of that debate, on whether or not to support the conclusion? Or does it recommend (...) that members individually vote on the premises, and then let their commitment to the conclusion be settled by whether or not the group endorses the required premises? Is deliberative democracy to enforce the discipline of reason at the individual level, as in the first possibility, or at the collective level, as in the second? (shrink)

Our aim in this survey article is to provide an accessible overview of some key results and questions in the theory of judgment aggregation. We omit proofs and technical details, focusing instead on concepts and underlying ideas.

Although the study of reasons plays an important role in both epistemology and moral philosophy, little attention has been devoted to the question of how, exactly, reasons interact to support the actions or conclusions they do. In this book, John F. Horty attempts to answer this question by providing a precise, concrete account of reasons and their interaction, based on the logic of default reasoning. The book begins with an intuitive, accessible introduction to default logic itself, and then argues that (...) this logic can be adapted to serve as a foundation for a concrete theory of reasons. Horty then shows that the resulting theory helps to explain how the interplay among reasons can determine what we ought to do by developing two different deontic logics, capturing two different intuitions about moral conflicts.In the central part of the book, Horty elaborates the basic theory to account for reasoning about the strength of our own reasons, and also about the related concepts of undercutting defeaters and exclusionary reasons. The theory is illustrated with an application to particularist arguments concerning the role of principles in moral theory. The book concludes by introducing a pair of issues new to the philosophical literature: the problem of determining the epistemic status of conclusions supported by separate but conflicting reasons, and the problem of drawing conclusions from sets of reasons that can vary arbitrarily in strength, or importance. (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)

I present an original model in judgment aggregation theory that demonstrates the general impossibility of consistently describing decision-making purely at the group level. Only a type of unanimity rule can guarantee a group decision is consistent with supporting reasons, and even this possibility is limited to a small class of reasoning methods. The key innovation is that this result holds when individuals can reason in different ways, an allowance not previously considered in the literature. This generalizes judgment aggregation to subjective (...) decision situations, implying that the discursive dilemma persists without individual agreement on the logical constraints. Notably, the model mirrors the typical method of choosing political representatives, and thus suggests that no voting procedure other than unanimity rule can guarantee representation that reflects electorate opinion. Finally, I apply the results to a normative argument for unanimity rule in contract theory and juries, as well as to problems posed for deliberative democratic theory and the concept of representation. (shrink)

Logical puzzles like the doctrinal paradox raise the problem of how to aggregate individual judgements into a collective judgement, or alternatively, how to merge collectively inconsistent knowledge bases. In this paper, we view judgement aggregation as a function on propositional logic valuations, and we investigate how logic constrains judgement aggregation. In particular, we show that there is no non-dictatorial decision method for aggregating sets of judgements in a logically consistent way if the decision method is local, i.e., only depends on (...) the individual judgements on the proposition under consideration. (shrink)