Christian List

Complaints are common about the arbitrary and conservative bias of special-majority rules. Such complaints, however, apply to asymmetrical versions of those rules alone. Symmetrical special-majority rules remedy that defect, albeit at the cost of often rendering no determinate verdict. Here what is formally at stake, both procedurally and epistemically, is explored in the choice between those two forms of special-majority rule and simple-majority rule; and practical ways are suggested of resolving matters left open by symmetrical special-majority rules – such as ‘judicial extrapolation’ or ‘subsidiarity’ in a federal system.

Consider the hypothesis H that a defendant is guilty, and the evidence E that a majority of h out of n independent jurors have voted for H and a minority of k:=n-h against H. How likely is the majority verdict to be correct? By a formula of Condorcet, the probability that H is true given E depends only on each juror's competence and on the absolute margin between the majority and the minority h-k, but neither on the number n, nor on the proportion h/n. This paper reassesses that result and explores its implications. First, using the classical Condorcet jury model, I derive a more general version of Condorcet's formula, confirming the significance of the absolute margin, but showing that the probability that H is true given E depends also on an additional parameter: the prior probability that H is true. Second, I show that a related result holds when we consider not the degree of belief we attach to H given E, but the degree of support E gives to H. Third, I address the implications for the definition of special majority voting, a procedure used to capture the asymmetry between false positive and false negative decisions. I argue that the standard definition of special majority voting in terms of a required proportion of the jury is epistemically questionable, and that the classical Condorcet jury model leads to an alternative definition in terms of a required absolute margin between the majority and the minority. Finally, I show that the results on the significance of the absolute margin can be resisted if the so-called assumption of symmetrical juror competence is relaxed.

Social choice theory is the study of collective decision processes and procedures. It is not a single theory, but a cluster of models and results concerning the aggregation of individual inputs (e.g., votes, preferences, judgments, welfare) into collective outputs (e.g., collective decisions, preferences, judgments, welfare). Central questions are: How can a group of individuals choose a winning outcome (e.g., policy, electoral candidate) from a given set of options? What are the properties of different voting systems? When is a voting system democratic? How can a collective (e.g., electorate, legislature, collegial court, expert panel, or committee) arrive at coherent collective preferences or judgments on some issues, on the basis of its members' individual preferences or judgments? How can we rank different social alternatives in an order of social welfare? Social choice theorists study these questions not just by looking at examples, but by developing general models and proving theorems.

One fundamental thesis within the rapidly growing literature on deliberative democracy is that the stability and quality of a democracy depend not only on formal institutions such as the electoral system or the structure of parliamentary representation. They depend also on certain democratic competences of the citizens, especially their capacity for democratic communication. According to this thesis, above all the capacity for democratic deliberation, i.e., for argumentation, evaluation and for a balanced decision between policy alternatives, belongs to the central competences relevant to maintaining and developing a democracy.

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.

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.

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.

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.

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.