Christian List

Aggregating sets of judgments : an impossibility result

Suppose that the members of a certain group each hold a rational set of judgments on some interconnected questions. And imagine that the group itself now 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 Arrows famous theorem (Arrow, 1963 and 1984; Sen, 1970) and we elaborate that comparison in a companion paper (List and Pettit, 2002).

Social Choice Theory and Deliberative Democracy: A Reconciliation

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 one demonstrates the impossibility, instability or meaninglessness of the rational collective outcomes sought by the other. 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.

Arrow's Theorem in Judgment Aggregation

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.

Group decisions in humans and animals: a survey.

Humans routinely make many decisions collectively, whether they choose a restaurant with friends, elect political leaders or decide actions to tackle international problems, such as climate change, that affect the future of the whole planet. We might be less aware of it, but group decisions are just as important to social animals as they are for us. Animal groups have to collectively decide about communal movements, activities, nesting sites and enterprises, such as cooperative breeding or hunting, that crucially affect their survival and reproduction. While human group decisions have been studied for millennia, the study of animal group decisions is relatively young, but is now expanding rapidly. It emerges that group decisions in animals pose many similar questions to those in humans. The purpose of the present issue is to integrate and combine approaches in the social and natural sciences in an area in which theoretical challenges and research questions are often similar, and to introduce each discipline to the others key ideas, findings and successful methods. In order to make such an introduction as effective as possible, here, we briefly review conceptual similarities and differences between the sciences, and provide a guide to the present issue.

The Discursive Dilemma and Public Reason

Collective decisions are ubiquitous in complex democratic societies. Elections, referenda, decisions in legislatures, committees, multimember courts, expert panels, and boards of companies or other organizations are all examples. In such decisions, disagreement is equally ubiquitous. People disagree with each other on many levels. They disagree not only on what choices should be made but also on why those choices should be made. Political theorists have offered different accounts of how collective decisions should be made under conditions of pluralism and when such decisions are legitimate. Obviously, different decision problems may require different decision procedures or different criteria of legitimacy. But, even for a given decision problem, rival accounts of how to solve the problem, which differ on several dimensions, are usually on offer. In this article, I focus on one such dimension: the importance assigned not only to the choices made (the “what” question) but also to the reasons underlying those choices (the “why” question). This dimension can be seen as a spectrum between two extremes: the minimal liberal account at one end and the comprehensive deliberative account at the other. The minimal liberal account emphasizes the “what” question, the comprehensive deliberative account the “why” question. The minimal liberal account holds that collective decisions should be made only on

A model of path-dependence in decisions over multiple propositions [Journal Article]

I model sequential decisions over multiple interconnected propositions and investigate path-dependence in such decisions. The propositions and their interconnections are represented in propositional logic. A sequential decision process is path-dependent if its outcome depends on the order in which the propositions are considered. Assuming that earlier decisions constrain later ones, I prove three main results: First, certain rationality violations by the decision-making agent—individual or group—are necessary and sufficient for path-dependence. Second, under some conditions, path-dependence is unavoidable in decisions made by groups. Third, path-dependence makes decisions vulnerable to strategic agenda setting and strategic voting. I also discuss escape routes from path-dependence. My results are relevant to discussions on collective consistency and reason-based decision-making, focusing not only on outcomes, but also on underlying reasons, beliefs, and constraints.

STRATEGY-PROOF JUDGMENT AGGREGATION

A disposable container suitable for retaining liquids comprises two opposed container sections, each having a peripheral ring like flange about a recess with the flanges being sealed therebetween. The recesses of the opposed container sections define a common central cavity and the flanges include a throat opening into said cavity through which product within the cavity can be dispensed. The throat is at least partially defined by the opposed container flanges and each container section is of a thermoformable plastic material. These container sections are originally formed from flat strip packaging material having diecut side edges with the strip defining individual container body sections. A tapered neck portion of each body section accommodates dispensing of the contents and preferably a hot melt adhesive secures the opposed container sections. The plastic containers are formed by intermittently advancing, in timed sequence, two strips through separate thermoforming operations where each strip is shaped to form a series of half containers and thereafter the strips are married and secured for subsequent operations. The invention also includes an apparatus and process for forming, filling and sealing the containers by advancing the packaging material through a number of stations along a predetermined path. The formed container is shaped to reduce inadvertent tipping thereof when supported in a free-standing disposition.

Judgment aggregation without full rationality

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 Rubinstein’s group identification problem.

The theory of judgment aggregation: An introductory review

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 who are new to the field of judgment aggregation a sense of this rapidly growing research area.

The probability of inconsistencies in complex collective decisions

Abstract.Many groups make decisions over multiple interconnected propositions. The “doctrinal paradox” or “discursive dilemma” shows that propositionwise majority voting can generate inconsistent collective sets of judgments, even when individual sets of judgments are all consistent. I develop a simple model for determining the probability of the paradox, given various assumptions about the probability distribution of individual sets of judgments, including impartial culture and impartial anonymous culture assumptions. I prove several convergence results, identifying when the probability of the paradox converges to 1, and when it converges to 0, as the number of individuals increases. Drawing on the Condorcet jury theorem and work by Bovens and Rabinowicz (2001, 2003), I use the model to assess the “truth-tracking” performance of two decision procedures, the premise- and conclusion-based procedures. I compare the present results with existing results on the probability of Condorcet’s paradox. I suggest that the doctrinal paradox is likely to occur under plausible conditions.