Aggregating sets of judgments : an impossibility result Christian List LSE has developed LSE Research Online so that users may access research output of the School.

Classical debates, recently rejoined, rage over the question of whether we want our political outcomes to be right or whether we want them to be fair.Democracy can be (and has been) justified in either way, or both at once.For epistemic democrats, the aim of democracy is to "track the truth." 1 For them, democracy is more desirable than alternative forms of decision-making because, and insofar as, it does that. One democratic decision rule is more desirable than another according to that same standard, so far as epistemic democrats are concerned. 2 For procedural democrats, the aim of democracy is instead to embody certain procedural virtues. 3 Procedural democrats are divided among themselves over what those virtues might be, as well as over which procedures best embody them. But all procedural democrats agree on the one central point

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 the opposite. After proving a general impossibility result on judgment aggregation, we construct an embedding of preference aggregation into judgment aggregation and prove Arrow's theorem as a corollary of our result. Although we 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

This is an electronic version of anNuffield College in 1998, and Dryzek thanks the College for its hospitality. For helpful comments, we thank Keith Dowding, James Fishkin, Natalie Gold, Robert Goodin, Iain McLean, Gerry Mackie, David Miller, Claus Offe, Anne Sliwka, the editor, and the anonymous reviewers of this paper.2 Social Choice Theory and Deliberative Democracy:A Reconciliation AbstractThe 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. Two Traditions of Democratic TheoryIn the past decade the theory of democracy has been dominated by two very different approaches. Within democratic theory as conventionally defined the strongest current is now deliberative. 1 For deliberative democrats, the essence of democratic legitimacy is the capacity of those affected by a collective decision to deliberate in the production of that decision. Deliberation involves discussion in which individuals are amenable to scrutinizing and changing their preferences in light of persuasion (but not manipulation, deception, or coercion) from other participants. Claims for and against courses of action must be justified to others in terms they can accept. Jürgen Habermas and John Rawls, respectively the most influential continental and Anglo-American political philosophers of the late 20 th century, have both identified themselves as deliberative democrats. 2 Deliberative democrats are uniformly optimistic that deliberation yields rational collective outcomes.The main competing tradition is social choice theory, whose proponents generally deduce far less optimistic results. To social choice theorists, the democratic problem involves aggregation of views, interests, or preferences across individuals, not deliberation over their content. From the seminal work of Kenneth Arrow on, it has been argued that such aggregation is bedeviled by impossibility, instability and arbitrariness. 3 Arrow proved the non-existence of any aggregation mechanism satisfying a set of seemingly innocuous conditions. This critique of democracy was radicalized by William Riker, who argued that any notion of a popular will independent of the mechanism used to aggregate preferences was untenable. 4 Given that there is no good reason to choose any particular mechanism over any other, supposedly democratic collective choices are arbitrary, and dem...

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 other's 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.Keywords: collective decisions; communal decisions; conflict resolution; cooperation; information sharing; social behaviour GENERAL BACKGROUNDHumans usually live in highly sophisticated societies. This implies that many important decisions are made not by individuals acting alone, but by groups of individuals acting collectively. Group decisions in humans range from small-scale decisions, such as those taken by groups of relatives, friends or colleagues, to large-scale decisions, such as nation-wide democratic elections and international agreements. Clearly, human societies cannot function without group decisions, and some of the most pressing problems facing humanity result from failures to reach a group consensus (e.g. the signing of the Kyoto treaty on controlling greenhouse gas emissions). Group decision making has been a central topic in all of the social sciences for millennia (e.g. Plato: The Republic 360 BC). Nevertheless, many questions remain open, particularly how conflicting interests and the sharing of dispersed information are actually, and should be, in principle, reconciled so as to facilitate cooperation and to reach outcomes that meet various optimality criteria. These are some of the fundamental questions of social choice theory (e.g. Arrow 1951Arrow /1963Austen-Smith & Banks 1999Sen 1999;Dryzek & List 2003). A large number of animal species also live in groups (Krause & Ruxton 2002), some of which can be very complex (e.g. eusocial bees, wasps, ants, termites and mole rats). Group decision making is just as important for social animals as it is for us (see Conradt & Roper 2005 for a review). Dispersing swarms of bees and ants collectively choose new nest sites on which their survival depends (Seeley & Buhrman 1999;Visscher 2007;Visscher & Seele...

seminar participants at the ANU, Brown University, CUNY and MIT for helpful comments or discussion. Non-Reductive Physicalism and the Limits of the Exclusion PrincipleIt is often argued that higher-level special-science properties cannot be causally efficacious since the lower-level physical properties on which they supervene are doing all the causal work. This claim is usually derived from an exclusion principle stating that if a higherlevel property F supervenes on a physical property F* that is causally sufficient for a property G, then F cannot cause G. We employ an account of causation as differencemaking to show that the truth or falsity of this principle is a contingent matter and derive necessary and sufficient conditions under which a version of it holds. We argue that one important instance of the principle, far from undermining non-reductive physicalism, actually supports the causal autonomy of certain higher-level properties.

In the theory of judgment aggregation on logically connected propositions, an important question remains open: Which aggregation rules are manipulable and which are strategyproof? We de…ne manipulability and strategy-proofness in judgment aggregation, characterize all strategy-proof aggregation rules, and prove an impossibility theorem similar to the Gibbard-Satterthwaite theorem. Among other escape-routes from the impossibility, we discuss weakening strategy-proofness itself. Comparing two prominent aggregation rules, we show that conclusion-based voting is strategy-proof, but generates incomplete judgments, while premise-based voting is only strategy-proof 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.

The chapter surveys the recent and fast‐growing literature on the aggregation of logically interrelated propositions, following List and Pettit's formalization of the “doctrinal paradox”. The classical preference aggregation problem is a special case in which propositions take the form of binary preference judgments (“alternative x is better than alternative y”). The first part of the chapter focuses on aggregation methods that satisfy an Arrowian independence condition (“propositionwise aggregation”). In the independent case, the literature has produced a number of general characterization results that precisely demarcate the circumstances in which satisfactory aggregation is possible from those in which it is not Arrow's impossibility theorem and Gibbards oligarchy theorem are special cases of these results. The independence condition is, however, not uncontroversial and the second part of the chapter considers various relaxations of it. Judgment aggregation is still a very active field and the chapter concludes with an outlook on what we believe are important topics for future research.