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)

The aim of this exploratory paper is to review an under-appreciated parallel between group agency and artificial intelligence. As both phenomena involve non-human goal-directed agents that can make a difference to the social world, they raise some similar moral and regulatory challenges, which require us to rethink some of our anthropocentric moral assumptions. Are humans always responsible for those entities’ actions, or could the entities bear responsibility themselves? Could the entities engage in normative reasoning? Could they even have rights and (...) a moral status? I will tentatively defend the (increasingly widely held) view that, under certain conditions, artificial intelligent systems, like corporate entities, might qualify as responsible moral agents and as holders of limited rights and legal personhood. I will further suggest that regulators should permit the use of autonomous artificial systems in high-stakes settings only if they are engineered to function as moral (not just intentional) agents and/or there is some liability-transfer arrangement in place. I will finally raise the possibility that if artificial systems ever became phenomenally conscious, there might be a case for extending a stronger moral status to them, but argue that, as of now, this remains very hypothetical. (shrink)

Many think that sentences about what metaphysically explains what are true iff there exist grounding relations. This suggests that sceptics about grounding should be error theorists about metaphysical explanation. We think there is a better option: a theory of metaphysical explanation which offers truth conditions for claims about what metaphysically explains what that are not couched in terms of grounding relations, but are instead couched in terms of, inter alia, psychological facts. We do not argue that our account is superior (...) to grounding-based accounts. Rather, we offer it to those already ill-disposed towards grounding. (shrink)

According to Sosa, knowledge is apt belief, where a belief is apt when accurate because adroit. Sosa :465–475, 2010; Judgment and agency, Oxford University Press, Oxford, 2015) adds to his triple-A analysis of knowledge, a triple-S analysis of competence, where a complete competence combines its seat, shape and situation. Much of Sosa’s influential work assumes that epistemic agents are individuals who acquire knowledge when they hit the truth through exercising their own individual skills in appropriate shapes and situations. This paper (...) explores an extension of Sosa’s framework to a social setting in which groups constitute epistemic agents over and above their individual members. The claim is that groups can be ascribed knowledge in virtue of hitting the truth through exercising their competences in appropriate shapes and situations. While knowledge at the collective level may diverge from knowledge at the individual level, the competences of groups are nothing over and above the combined competences of their members. The ensuing view thus has implications for the debate over reduction and supervenience in collective epistemology. (shrink)

This paper offers a comparison of three different kinds of collective attitudes: aggregate, common, and corporate attitudes. They differ not only in their relationship to individual attitudes—e.g., whether they are “reducible” to individual attitudes—but also in the roles they play in relation to the collectives to which they are ascribed. The failure to distinguish them can lead to confusion, in informal talk as well as in the social sciences. So, the paper’s message is an appeal for disambiguation.

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 analyse the incentives of individuals to misrepresent their truthful judgments when engaged in collective decision-making. Our focus is on scenarios in which individuals reason about the incentives of others before choosing which judgments to report themselves. To this end, we introduce a formal model of strategic behaviour in logic-based judgment aggregation that accounts for such higher-level reasoning as well as the fact that individuals may only have partial information about the truthful judgments and preferences of their peers. We find (...) that every aggregation rule must belong to exactly one of three possible categories: it is either (i) immune to strategic manipulation for every level of reasoning, or (ii) manipulable for every level of reasoning, or (iii) immune to manipulation only for everykth level of reasoning, for some natural number kgreater than 1. (shrink)

Group beliefs in social networks are often construed as arising from individual beliefs through processes of update and aggregation. In this paper, we explore an alternative ‘arational’ perspective. More specifically, we focus on group attitudes as neutral tendencies toward alignment of opinions driven by influence patterns among agents modeled in a Markov dynamics. In addition, we investigate logical patterns in the resulting potential group beliefs or, in more neutral arational terminology: collective opinion structures.

BackgroundPublic involvement activities are promoted as measures for ensuring good governance in challenging fields, such as biomedical research and innovation. Proponents of public involvement activities include individual researchers as well as non-governmental and governmental organizations. However, the concept of ‘public’ in public involvement deserves more attention by researchers because it is not purely theoretical: it has important practical functions in the guidance, evaluation and translation of public involvement activities.DiscussionThis article focuses on collective agency as one property a public as a (...) small group of participants in a public involvement activity could exhibit. It introduces a prominent theoretical approach to collective agents as one specific kind of social entities and demonstrates how this approach can be applied to current practice in public involvement activities. A brief discussion of different types of representation as they are used in the existing literature on this topic is also included because representation and collective agency can be closely related to each other. Suggestions and ideas that are derived from this reasoning include the proposal to use a ‘validity check’ for the generation of collective agents as a regular element of certain types of public involvement activities, the consequences of combining collective agency and representativeness as a further property a public could exhibit, and standards for reporting the content of public involvement activities in scientific publications.SummaryThis article discusses the importance of the concept of ‘public’ in public involvement activities, with a focus on biomedical research and innovation. It introduces various practically relevant ideas that are based on a theoretical analysis of collective agency as an important property a public can possess. (shrink)

Since the publication of Ekins’ The Nature of Legislative Intent, significant attention has been paid to common attitude models of legislative intention, that is, models that require unanimity among its group members. A common interpretation of Ekins is that these common attitudes are to be preferred over aggregated attitudes. I argue that any feasible theory of legislative attitudes will require non-trivial aggregation (ie. not based on unanimity rules alone). Two arguments are put forward in this regard: first, that non-trivial aggregation (...) better explains uncooperative legislative behaviour and second, that mathematical problems with aggregation apply to common attitudes as well since they involve trivial aggregation. These arguments generalise to theories of common attitudes other than Ekins’. (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)

In this study, we propose a new direction of research on the axiomatic analysis of approval voting, which is a common democratic decision method. Its novelty is to examine an infinite population setting, which includes an application to intergenerational problems. In particular, we assume that the set of the population is countably infinite. We provide several extensions of the method of approval voting for this setting. As our main result, axiomatic characterizations of the extensions are offered by revealing a direct (...) link between approval voting and the Borda rule. The characterized methods are natural extensions of the standard approval voting method for the finite-population case and are regarded as minimum requirements for other possible infinite-population extensions, which are reasonably democratic. (shrink)

Development of decision-support and intelligent agent systems necessitates mathematical descriptions of uncertainty and fuzziness in order to model vagueness. This paper seeks to present an outline of Peirce’s triadic logic as a practical new way to model vagueness in the context of artificial intelligence. Charles Sanders Peirce was an American scientist–philosopher and a great logician whose triadic logic is a culmination of the study of semiotics and the mathematical study of anti-Cantorean model of continuity and infinitesimals. After presenting Peircean semiotics (...) within AI perspective, a mathematical formulation of a Peircean triadic set is given in relationship with classical and fuzzy sets. Using basic logical operators, all possible respective implication operators, bi-equivalence operators, valid rules of inference, and associative, distributive and commutative logical properties are derived and verified through the truth function approach. In order to suggest practical directions, aggregation operators for Peirce’s triadic logic have been formulated. A mathematical formulation of a medical diagnostic problem and ER diagram of a library management system using Peirce’s triadic relation show potential for further applications of the proposed triadic set and triadic logic. Alongside, a classical AI game—The Wumpus World—is implemented to show practical efficacy in comparison with binary implementation. Besides giving some preliminary formulations for trichotomous set theory and definition of finite automaton, development of hybrid architectures for intelligent agents and evolutionary computations are discussed as potential practical avenues for Peirce’s triadic logic. (shrink)

When scientists are asked to give expert advice on risk-related questions, such as the authorization of medical drugs, deliberation often does not eliminate all disagreements. I propose to model these remaining discrepancies as differences in risk assessments and/or in risk acceptability thresholds. The normative question I consider, then, is how the individual expert views should best be aggregated. I discuss what “best” could mean, with an eye to some robustness considerations. I argue that the majority rule, which is currently often (...) used in expert panels, has significant drawbacks. (shrink)

In this paper, we investigate the problem of truth approximation via belief merging, i.e., we ask whether, and under what conditions, a group of inquirers merging together their beliefs makes progress toward the truth about the underlying domain. We answer this question by proving some formal results on how belief merging operators perform with respect to the task of truth approximation, construed as increasing verisimilitude or truthlikeness. Our results shed new light on the issue of how rational (dis)agreement affects the (...) inquirers’ quest for truth. In particular, they vindicate the intuition that scientific inquiry, and rational discussion in general, benefits from some heterogeneity in opinion and interaction among different viewpoints. The links between our approach and related analyses of truth tracking, judgment aggregation, and opinion dynamics, are also highlighted. (shrink)