Christian List

Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of each class of pooling functions (most of them classic, but one new) and argue that linear pooling can be justified procedurally, but not epistemically, while the other two pooling methods can be justified epistemically. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. We conclude by mentioning a number of other pooling methods.

Distributed cognition refers to processes which are (i) cognitive and (ii) distributed across multiple agents or devices rather than performed by a single agent. Distributed cognition has attracted interest in several fields ranging from sociology and law to computer science and the philosophy of science. In this paper, I discuss distributed cognition from a social-choice-theoretic perspective. Drawing on models of judgment aggregation, I address two questions. First, how can we model a group of individuals as a distributed cognitive system? Second, can a group acting as a distributed cognitive system be ‘rational’ and ‘track the truth’ in the outputs it produces? I argue that a group’s performance as a distributed cognitive system depends on its ‘aggregation procedure’ – its mechanism for aggregating the group members’ inputs into collective outputs – and I investigate the properties of an aggregation procedure that matter.

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.

The concept of preference structuration not only provides possible escape-routes from socialchoice-theoretic impossibility problems, but also points towards ways of formalizing notions of 'pluralism', 'consensus' and 'issue-dimensionality'. The present note introduces two methods of (operationally) measuring preference structuration, giving attention to both their conceptual characteristics and their computational feasibility. The method to be advocated, called the 'fractionalization' approach, combines well-known social-choice-theoretic criteria of preference structuration (such as single-peakedness or value-restriction) with the frequently used Rae-Taylor (1970) and Laakso-Taagepera (1979) approaches towards measuring the level of fractionalization, and the effective number of components, in a system.

Political theorists have offered many accounts of collective decision-making under pluralism. I discuss a key dimension on which such accounts differ: the importance assigned not only to the choices made but also to the reasons underlying those choices. On that dimension, different accounts lie in between two extremes. The ‘minimal liberal account’ holds that collective decisions should be made only on practical actions or policies and that underlying reasons should be kept private. The ‘comprehensive deliberative account’ stresses the importance of giving reasons for collective decisions, where such reasons should also be collectively decided. I compare these two accounts on the basis of a formal model developed in the growing literature on the ‘discursive dilemma’ and ‘judgment aggregation’ and address several questions: What is the trade-off between the (minimal liberal) demand for reaching agreement on outcomes and the (comprehensive deliberative) demand for reason-giving? How large should the ‘sphere of public reason’ be? When do the decision procedures suggested by the two accounts agree and when not? How good are these procedures at truthtracking on factual matters? What strategic incentives do they generate for decision-makers? My discussion identifies what is at stake in the choice between minimal liberal and comprehensive deliberative accounts of collective decisionmaking, and sheds light not only on these two ideal-typical accounts themselves, but also on many characteristics that intermediate accounts share with them.

Most accounts of welfare aggregation in the tradition of Arrow's and Sen's social-choice-theoretic frameworks represent the welfare of an individual in terms of a single welfare ordering or a single scalar-valued welfare function. I develop a multidimensional generalization of Arrow's and Sen's frameworks, representing individual welfare in terms of multiple personal welfare functions, corresponding to multiple 'dimensions' of welfare. I show that, as in the one-dimensional case, the existence of attractive aggregation procedures depends on certain informational assumptions, specifically about the measurability of welfare and its comparability not only across individuals but also across dimensions. I state several impossibility and possibility results. Under Arrow-type conditions, insufficient comparability across individuals leads to dictatorship of a single individual, while insufficient comparability across dimensions leads to dominance of a single dimension. Given sufficient comparability both across individuals and across dimensions, a range of possibilities emerges. I discuss the substantive implications of the results.

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.

Arrow's account (1951/1963) of the problem of social choice is based upon the assumption that the preferences of each individual in the relevant group are expressible by a single ordering. This paper lifts that assumption and develops a multidimensional generalization of Arrow's framework. I show that, like Arrow's original framework, the multidimensional generalization is affected by an impossibility theorem, highlighting not only the threat of dictatorship of a single individual, but also the threat of dominance of a single dimension. In particular, even if preferences are single-peaked across individuals within each dimension – a situation called intradimensional single-peakedness – any aggregation procedure satisfying Arrow-type conditions will make one dimension dominant. I introduce lexicographic hierarchies of dimensions as a class of possible aggregation procedures under intradimensional single-peakedness. The interpretation of the results is discussed

I argue that free will and determinism are compatible, even when we take free will to require the ability to do otherwise and even when we interpret that ability modally, as the possibility of doing otherwise, and not just conditionally or dispositionally. My argument draws on a distinction between physical and agential possibility. Although in a deterministic world only one future sequence of events is physically possible for each state of the world, the more coarsely defined state of an agent and his or her environment can be consistent with more than one such sequence, and thus different actions can be “agentially possible”. The agential perspective is supported by our best theories of human behaviour, and so we should take it at face value when we refer to what an agent can and cannot do. On the picture I defend, free will is not a physical phenomenon, but a higher-level one on a par with other higher-level phenomena such as agency and intentionality.

While a large social-choice-theoretic literature discusses the aggregation of individual judgments into collective ones, there is much less formal work on the transformation of judgments in group communication. I develop a model of judgment transformation and prove a baseline impossibility theorem: Any judgment transformation function satisfying some initially plausible conditions is the identity function, under which no opinion change occurs. I identify escape routes from this impossibility and argue that the kind of group communication envisaged by deliberative democats must be "holistic": It must focus on webs of connected propositions, not on one proposition at a time, which echoes the Duhem-Quine "holism thesis" on scientific theory testing. My approach provides a map of the logical space in which different possible group communication processes are located.

Free will is widely thought to require (i) the possibility of acting otherwise and (ii) the intentional endorsement of one’s actions (“indeterministic picking is not enough”). According to (i), a necessary condition for free will is agential-level indeterminism: at some points in time, an agent’s prior history admits more than one possible continuation. According to (ii), however, a free action must be intentionally endorsed, and indeterminism may threaten freedom: if several alternative actions could each have been actualized, then none of them is necessitated by the agent’s prior history, and the actual action seems nothing more than the result of indeterministic picking. We argue that this tension is only apparent. We distinguish between actions an agent can possibly do and actions he or she can do with endorsement. One can consistently say that someone who makes a choice has several alternative possibilities, and yet that, far from merely indeterministically picking an action, the agent chooses one he or she endorses. An implication is that although free will can consistently require (i) and (ii), it cannot generally require the possibility of acting otherwise with endorsement.

Can there be a global demos? The current debate about this topic is divided between two opposing camps: the “pessimist” or “impossibilist” camp, which holds that the emergence of a global demos is either conceptually or empirically impossible, and the “optimist” or “possibilist” camp, which holds that the emergence of a global demos is conceptually as well as empirically possible and an embryonic version of it already exists. However, the two camps agree neither on a common working definition of a global demos, nor on the relevant empirical facts, so it is difficult to reconcile their conflicting outlooks. We seek to move the debate beyond this stalemate. We argue that existing conceptions of a demos are ill-suited for capturing what kind of a global demos is needed to facilitate good global governance, and we propose a new conception of a demos that is better suited for this purpose. We suggest that some of the most prominent conceptions of a demos have focused too much on who the members of a demos are and too little on what functional characteristics the demos must have in order to perform its role in facilitating governance within the relevant domain. Our new proposal shifts the emphasis from the first, “compositional” question to the second, “performative” one, and provides a more “agency-based” account of a global demos. The key criterion that a collection of individuals must meet in order to qualify as a demos is that it is not merely demarcated by an appropriate membership criterion, but that it can be organized, democratically, so as to function as a state-like agent. Compared to the existing, predominantly “compositional” approaches to thinking about the demos, this agency-based approach puts us into a much better position to assess the empirical prospects for the emergence of a global demos that can facilitate good global governance.

Can we design a perfect democratic decision procedure? Condorcet famously observed that majority rule, our paradigmatic democratic procedure, has some desirable properties, but sometimes produces inconsistent outcomes. Revisiting Condorcet’s insights in light of recent work on the aggregation of judgments, I show that there is a conflict between three initially plausible requirements of democracy: “robustness to pluralism”, “basic majoritarianism”, and “collective rationality”. For all but the simplest collective decision problems, no decision procedure meets these three requirements at once; at most two can be met together. This “democratic trilemma” raises the question of which requirement to give up. Since different answers correspond to different views about what matters most in a democracy, the trilemma suggests a map of the “logical space” in which different conceptions of democracy are located. It also sharpens our thinking about other impossibility problems of social choice and how to avoid them, by capturing a core structure many of these problems have in common. More broadly, it raises the idea of “cartography of logical space” in relation to contested political concepts.