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)

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)

We investigate under what conditions a given set of collective judgments can arise from a specific voting procedure. In order to answer this question, we introduce a language similar to modal logic for reasoning about judgment aggregation procedures. In this language, the formula expresses that is collectively accepted, or that is a group judgment based on voting. Different judgment aggregation procedures may be underlying the group decision making. Here we investigate majority voting, where holds if a majority of individuals accepts, (...) consensus voting, where holds if all individuals accept, and dictatorship. We provide complete axiomatizations for judgment sets arising from all three aggregation procedures. (shrink)

The ``doctrinal paradox'' or ``discursive dilemma'' shows that propositionwise majority voting over the judgments held by multiple individuals on some interconnected propositions can lead to inconsistent collective judgments on these propositions. List and Pettit (2002) have proved that this paradox illustrates a more general impossibility theorem showing that there exists no aggregation procedure that generally produces consistent collective judgments and satisfies certain minimal conditions. Although the paradox and the theorem concern the aggregation of judgments rather than preferences, they invite comparison (...) with two established results on the aggregation of preferences: the Condorcet paradox and Arrow's impossibility theorem. We may ask whether the new impossibility theorem is a special case of Arrow's theorem, or whether there are interesting disanalogies between the two results. In this paper, we compare the two theorems, and show that they are not straightforward corollaries of each other. We further suggest that, while the framework of preference aggregation can be mapped into the framework of judgment aggregation, there exists no obvious reverse mapping. Finally, we address one particular minimal condition that is used in both theorems – an independence condition – and suggest that this condition points towards a unifying property underlying both impossibility results. (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)

The literature on the theory of social choice has grown considerably beyond the few items in existence at the time the first edition of this book appeared in 1951. Some of the new literature has dealt with the technical, mathematical aspects, more with the interpretive. My own thinking has also evolved somewhat, although I remain far from satisfied with present formulations. The exhaustion of the first edition provides a convenient time for a selective and personal stocktaking in the form of (...) an appended commentary entitled, 'Notes on the Theory of Social Choice, 1963, ' containing reflections on the text and its omissions and on some of the more recent literature. This form has seemed more appropriate than a revision of the original text, which has to some extent acquired a life of its own. (shrink)

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

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 two most influential traditions of contemporary theorizing about democracy, social choice theory and deliberative democracy, are generally thought to be at loggerheads, in that the former demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the latter. We argue that the two traditions can be reconciled. After expounding the central Arrow and Gibbard-Satterthwaite impossibility results, we reassess their implications, identifying the conditions under which meaningful democratic decision making is possible. We argue that deliberation can promote (...) these conditions, and hence that social choice theory suggests not that democratic decision making is impossible, but rather that democracy must have a deliberative aspect. (shrink)

Condorcet’s voting paradox shows that pairwise majority voting may lead to cyclical majority preferences. In a famous paper, Sen identified a general condition on a profile of individual preference orderings, called triplewise value-restriction, which is sufficient for the avoidance of such cycles. This note aims to make Sen’s result easily accessible. We provide an elementary proof of Sen's possibility theorem and a simple reformulation of Sen’s condition. We discuss how Sen’s condition is logically related to a number of precursors. Finally, (...) we state a necessary and sufficient condition for the avoidance of cycles, and suggest that, although there is still some logical space between that condition and Sen’s sufficient condition, Sen’s condition cannot be further generalized in an appealing way. (shrink)