The widely discussed "discursive dilemma" shows that majority voting in a group of individuals on logically connected propositions may produce irrational collective judgments. We generalize majority voting by considering quota rules, which accept each proposition if and only if the number of individuals accepting it exceeds a given threshold, where different thresholds may be used for different propositions. After characterizing quota rules, we prove necessary and sufficient conditions on the required thresholds for various collective rationality requirements. We also consider sequential (...) quota rules, which ensure collective rationality by adjudicating propositions sequentially and letting earlier judgments constrain later ones. Sequential rules may be path-dependent and strategically manipulable. We characterize path-independence and prove its essential equivalence to strategy-proofness. Our results shed light on the rationality of simple-, super-, and sub-majoritarian decision-making. (shrink)

All existing impossibility theorems on judgment aggregation require individual and collective judgment sets to be consistent and complete, arguably a demanding rationality requirement. They do not carry over to aggregation functions mapping profiles of consistent individual judgment sets to consistent collective ones. We prove that, whenever the agenda of propositions under consideration exhibits mild interconnections, any such aggregation function that is "neutral" between the acceptance and rejection of each proposition is dictatorial. We relate this theorem to the literature.

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. (shrink)

The project of public-reason liberalism faces a basic problem: publicly justified principles are typically too abstract and vague to be directly applied to practical political disputes, whereas applicable specifications of these principles are not uniquely publicly justified. One solution could be a legislative procedure that selects one member from the eligible set of inconclusively justified proposals. Yet if liberal principles are too vague to select sufficiently specific legislative proposals, can they, nevertheless, select specific legislative procedures? Based on the work of (...) Gerald Gaus, this article argues that the only candidate for a conclusively justified decision procedure is a majoritarian or otherwise ‘neutral’ democracy. If the justification of democracy requires an equality baseline in the design of political regimes and if justifications for departure from this baseline are subject to reasonable disagreement, a majoritarian design is justified by default. Gaus’s own preference for super-majoritarian procedures is based on disputable specifications of justified liberal principles. These procedures can only be defended as a sectarian preference if the equality baseline is rejected, but then it is not clear how the set of justifiable political regimes can be restricted to full democracies. (shrink)

Can collectives be wise? The thesis that they can has recently received a lot of attention. It has been argued that, in many judgmental or decision-making tasks, suitably organized groups can outperform their individual members. In this paper, I discuss the lessons we can learn about collective wisdom from the emerging theory of judgment aggregation, as distinct from the literature on Condorcet’s jury theorem.

This article provides a survey of existing studies of majority rule, outlines misconceptions of majority rule, and highlights underexplored fields of research. It argues that the reasons why the minority complies with majority decisions have been underexplored.

This essay analyses optimal voting rules for one form of deliberative democracy. Drawing on public choice analysis, it is argued that the voting rule that best institutionalises deliberative democracy is a type of a supermajority rule. Deliberative democracy is also committed to the standard neutrality condition according to which if x votes are enough to select alternative A, x votes must be enough to select not-A. Taken together, these imply that deliberative democracy will often be indeterminate. This result shows that (...) deliberative democracy is ill-equipped to provide guidance as to how actual political disputes are to be legitimately resolved. (shrink)