This work contributes to the theory of judgement aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgement aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, the Lambek calculus, Linear Logic and Relevant Logics. The motivation for studying judgement aggregation in non-classical logics is that they offer a number of modelling choices to represent agents’ reasoning in aggregation problems. By studying judgement aggregation in logics that (...) are weaker than classical logic, we investigate whether some well-known impossibility results, that were tailored for classical logic, still apply to those weak systems. (shrink)

Group agents have been represented as expressive fictions by those who treat ascriptions of agency to groups as metaphorical; as pragmatic fictions by those who think that the agency ascribed to groups belongs in the first place to a distinct individual or set of individuals; and as theoretical fictions by those who think that postulating group agents serves no indispensable role in our theory of the social world. This paper identifies, criticizes and rejects each of these views, defending a strong (...) realist position. (shrink)

By means of multi-agent simulations, it investigates the truth and consensus-conduciveness of controversial debates. The book brings together research in formal epistemology and argumentation theory.

Judgment aggregation theory, or rather, as we conceive of it here, logical aggregation theory generalizes social choice theory by having the aggregation rule bear on judgments of all kinds instead of merely preference judgments. It derives from Kornhauser and Sager’s doctrinal paradox and List and Pettit’s discursive dilemma, two problems that we distinguish emphatically here. The current theory has developed from the discursive dilemma, rather than the doctrinal paradox, and the final objective of the paper is to give the latter (...) its own theoretical development along the line of recent work by Dietrich and Mongin. However, the paper also aims at reviewing logical aggregation theory as such, and it covers impossibility theorems by Dietrich, Dietrich and List, Dokow and Holzman, List and Pettit, Mongin, Nehring and Puppe, Pauly and van Hees, providing a uniform logical framework in which they can be compared with each other. The review goes through three historical stages: the initial paradox and dilemma, the scattered early results on the independence axiom, and the so-called canonical theorem, a collective achievement that provided the theory with its specific method of analysis. The paper goes some way towards philosophical logic, first by briefly connecting the aggregative framework of judgment with the modern philosophy of judgment, and second by thoroughly discussing and axiomatizing the ‘general logic’ built in this framework. (shrink)

Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individuals' causal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem of causal-network aggregation. (...) Finally, we revisit the aggregation of probabilistic judgments when this is constrained by prior aggregation of qualitative causal judgments. (shrink)

We often encounter people who we believe are behaving immorally. We routinely try to change minds and often donate to charitable organizations that do the same. Of course, this does not always work. In a liberal, rights-based society, we have to tolerate this. But legal entitlements to act in ways that others find immoral are inefficiently allocated. For example, some meat-eaters value eating meat less than some vegetarians would be willing to pay them to stop. While many have written about (...) the limits of the market, market design, and abuse of right, few have considered the sale of these entitlements. This article proposes a market-based solution, encouraging the sale of these entitlements under certain conditions. This would lead to improvements both on an economic efficiency analysis and on a moral analysis. (shrink)

To investigate the relationship between logical reasoning and majority voting, we introduce logic with groups Lg in the style of Gentzen’s sequent calculus, where every sequent is indexed by a group of individuals. We also introduce the set-theoretical semantics of Lg, where every formula is interpreted as a certain closed set of groups whose members accept that formula. We present the cut-elimination theorem, and the soundness and semantic completeness theorems of Lg. Then, introducing an inference rule representing majority voting to (...) Lg, we introduce logic with majority voting Lv. Formalizing the discursive paradox in judgment aggregation theory, we show that Lv is inconsistent. Based on the premise-based and conclusion-based approaches to avoid the paradox, we introduce logic with majority voting for axioms Lva, where majority voting is applied only to non-logical axioms as premises to construct a proof in Lg, and logic with majority voting for conclusions Lvc, where majority voting is applied only to the conclusion of a proof in Lg. We show that both Lva and Lvc are syntactically complete and consistent, and we construct collective judgments based on the provability in Lva and Lvc, respectively. Then, we discuss how these systems avoid the discursive paradox. (shrink)

Abstract:We present a model of collective decision making in which aggregation and deliberation are treated simultaneously. Individuals debate in a public forum and potentially revise their judgements in light of deliberation. Once this process is exhausted, a rule is applied to aggregate post-deliberation judgements in order to make a social choice. Restricting attention to three alternatives, we identify conditions under which a democracy is ‘truth-revealing’. This condition says that the deliberation path and the aggregation rule always lead to the correct (...) social choice being made, irrespective of both the original profile of judgements and the size of the electorate. (shrink)

Judgment aggregation studies how to aggregate individual judgments on logically correlated propositions into collective judgments. Different logics can be used in judgment aggregation, for which Dietrich and Mongin have proposed a generalized model based on general logics. Despite its generality, however, all nonmonotonic logics are excluded from this model. This paper argues for using nonmonotonic logic in judgment aggregation. Then it generalizes Dietrich and Mongin’s model to incorporate a large class of nonmonotonic logics. This generalization broadens the theoretical boundaries of (...) judgment aggregation by proving that, even if these nonmonotonic logics are employed, certain typical impossibility results still hold. (shrink)

Group agency requires a number of people to combine in pursuit of shared goals across varied scenarios. Thus, a group or corporate agent must be organized (1) to act flexibly as its goals require, (2) with the intentional, if not always voluntary, acquiescence of members in the guidance of (3) an authorized spokesperson or (4) a constructed voice, thereby (5) becoming capable of making and honoring commitments.

Arrow’s axiomatic foundation of social choice theory can be understood as an application of Tarski’s methodology of the deductive sciences—which is closely related to the latter’s foundational contribution to model theory. In this note we show in a model-theoretic framework how Arrow’s use of von Neumann and Morgenstern’s concept of winning coalitions allows to exploit the algebraic structures involved in preference aggregation; this approach entails an alternative indirect ultrafilter proof for Arrow’s dictatorship result. This link also connects Arrow’s seminal result (...) to key developments and concepts in the history of model theory, notably ultraproducts and preservation results. (shrink)

Cybernetics, or self-governance of animal and machine, requires the ability to sense the world and to act on it in an appropriate manner. Likewise, self-governance of a human society requires groups of people to collectively sense and act on their environment. I argue that the evolution of political systems is characterized by a series of innovations that attempt to solve two ‘scalability’ problems: scaling up a group’s ability to make sense of an increasingly complex world, and to cooperate in increasingly (...) larger groups. I then explore some recent efforts toward using the Internet and social media to provide alternative means for addressing these scalability challenges, under the banners of crowdsourcing and computer-supported argumentation. I present some lessons from those efforts about the limits of technology, and the research directions more likely to bear fruit. (shrink)

Sports tournaments provide a procedure for producing a champion and ranking the contestants based on game results. As such, tournaments mirror aggregation methods in social choice theory, where diverse individual preferences are put together to form an overall social preference. This connection allows us a novel way of conceptualizing sports tournaments, their results, and significance. I argue that there are genuine intransitive dominance relationships in sports, that social choice theory provides a framework for understanding rankings in such situations and that (...) these considerations provide a new reason to endorse championship pluralism. (shrink)

We show how voting rules like the simple and the absolute majority rules, unanimity, consensus, etc. can be represented as logical operators in Łukasiewicz’s three-valued logic. First, we prove tha...

Belief merging aims at combining several pieces of information coming from different sources. In this paper we review the works on belief merging of propositional bases. We discuss the relationship between merging, revision, update and confluence, and some links between belief merging and social choice theory. Finally we mention the main generalizations of these works in other logical frameworks.