Iterative Judgment Aggregation

Judgment aggregation is a field in which individuals are required to vote for or against a certain decision (the conclusion) while providing reasons for their choice. The reasons and the conclusion are logically connected propositions. The problem is how a collective judgment on logically interconnected propositions can be defined from individual judgments on the same propositions. It turns out that, despite the fact that the individuals are logically consistent, the aggregation of their judgments may lead to an inconsistent group outcome, where the reasons do not support the conclusion. However, in this paper we claim that collective irrationality should not be the only worry of judgment aggregation. For example, judgment aggregation would not reject a consistent combination of reasons and conclusion that no member voted for. In our view this may not be a desirable solution. This motivates our research about when a social outcome is `compatible' with the individuals' judgments. The key notion that we want to capture is that any individual member has to be able to defend the collective decision. This is guaranteed when the group outcome is compatible with its members views. Judgment aggregation problems are usually studied using classical propositional logic. However, for our analysis we use an argumentation approach to judgment aggregation problems. Indeed the question of how individual evaluations can be combined into a collective one can also be addressed in abstract argumentation. We introduce three aggregation operators that satisfy the condition above, and we offer two definitions of compatibility. Not only does our proposal satisfy a good number of standard judgment aggregation postulates, but it also avoids the problem of individual members of a group having to become committed to a group judgment that is in conflict with their own individual positions.

Computational social choice is a new interdisciplinary research area at the intersection of social choice theory and computer science that studies computational aspects of social choice mechanisms as well as applications of social choice ideas in the design and analysis of computing systems. Research on computational social choice now encompasses a variety of topics, including the algorithmic aspects of voting rules, computational barriers to strategic behaviour, collective decision-making in multi-agent systems, preference elicitation and communication issues in voting, fair division, computational aspects of weighted voting games, collective decision-making in combinatorial domains, logic-based formalisms for social choice problems, belief and judgement aggregation, and social software. The aim of this special issue is to build on the spectacular success of two workshops on computational social choice (COMSOC’06, Amsterdam and COMSOC’08, Liverpool), and provide a forum for reseachers in the area to present their ideas on a variety of topics. This special issue is composed of nine research articles and a short note that span a fairly wide range of issues, including voting, mechanism design, judgment aggregation, and fairness, and a similarly wide range of techniques, such as logic, experiments, and computational complexity. The paper by Agotnes, van der Hoek and Wooldridge defines a new modal logic for representing and reasoning about preference and judgment aggregation. The authors show that their logic can be used to express a variety of concepts and results from the social choice domain, including majority voting, the discursive paradox, Arrow’s theorem and Condorcet’s paradox. Baharad, Goldberger, Koppel and Nitzan propose a maximum likelihood estimation-based approach for aggregating voters’ opinions over several issues. They argue that their method is vastly superior to simple majority voting, and use both analytical and empirical evaluation to support their argument. Balan, Richards and Luke deal with the problem of selecting a sequence of actions when the actions have multiple beneficiaries. Their goal is to select the actions according to a lexicographic fairness criterion. The explore the complexity of this problem for both finite and infinite sequences of actions and present both algorithms and intractability results for this problem. The paper by Caminada and Pigozzi applies argumentation theory to judgment aggregation, and proposes aggregation operators satisfying not only the usual property of collective rationality, but another highly desirable property,

Preference aggregation and judgment aggregation are two basic research models of group decision making. And preference aggregation has been deeply studied in social choice theory. However, researches of social choice theory gradually focus on judgment aggregation which appears recently. Judgment aggregation focuses on how to aggregate many consistent logical formulas into one, from the perspective of logic. We try to start with judgment aggregation model based on logic and then explore different solutions to problem of judgment aggregation.

Judgment aggregation is a mathematical theory of collective decision-making. It concerns the methods whereby individual opinions about logically interconnected issues of interest can, or cannot, be aggregated into one collective stance. Aggregation problems have traditionally been of interest for disciplines like economics and the political sciences, as well as philosophy, where judgment aggregation itself originates from, but have recently captured the attention of disciplines like computer science, artificial intelligence and multi-agent systems. Judgment aggregation has emerged in the last decade as a unifying paradigm for the formalization and understanding of aggregation problems. Still, no comprehensive presentation of the theory is available to date. This Synthesis Lecture aims at filling this gap presenting the key motivations, results, abstractions and techniques underpinning it.

When the group denies individual nutritional wisdom

There are two different fundamental conceptions of the task of social aggregation: interest aggregation and judgment aggregation. While the former aims at the fair and efficient trade-off of personal interests, the latter aims the best resolution of disagreement. Both are possible interpretations of the standard preference aggregation and preference-based voting problems. This note makes two broad points. First, the judgment aggregation conception is not yet well understood and remains undertheorized. Second, the difference between the two conceptions matters; it is a difference that makes a difference. To substantiate the first point, we argue that judgment aggregation as resolution of disagreement cannot be subsumed under statistical aggregation in the manner of Condorcet’s jury theorem, and sketch a more specific articulation as “reflexive consensus under arguable disagreement”. To substantiate the second point, we illustrate the difference in the context of two important voting rules, the Kemeny rule and Majority Judgment.

Judgment aggregation is a recent theory that combines aggregation problems previously studied by social choice theory with logic. Social choice theory is a vast subject, including not only the study of preference aggregation and voting theory but also topics like social welfare and justice. Given the tight links between judgment aggregation and preference aggregation, in this first chapter we give a concise survey on some historical aspects of preference aggregation and then introduce and motivate the more recent field of judgment aggregation. The chapter builds on [Sen99, Sen86, Bla58] for the historical overview on social choice theory, and on [KS93, Kor92] for the informal introduction to judgment aggregation.

BackgroundThe role of clinician educators has expanded to encompass diverse responsibilities alongside providing competent care and engaging in scholarly activities. Faculty development (FD) programs have emerged as vital tools for equipping educators with teaching skills and career advancement opportunities. However, assessing faculty development programs’ impact on organizational culture remains challenging due to their multifaceted nature. This study explores this gap to understand how faculty development influences organizational culture.MethodsThis qualitative study used a constructivist approach to explore faculty perspectives on the Uniformed Services University of the Health Sciences (USU) Faculty Development Program’s influence on organizational culture. Forty-three faculty members participated in nine semi-structured focus groups, selected for diversity across roles and locations. Interviews were recorded, transcribed, and anonymized to ensure accuracy and participant confidentiality.Data analysisTranscripts were analyzed using thematic analysis. A multidisciplinary team independently reviewed transcripts, identified preliminary codes, and refined themes through iterative consensus building. Coding was organized using memos and grouped into themes. Using information power principles, the team determined that nine focus groups provided sufficient data richness to meet the study’s aims.ResultsThe research team identified and refined four central themes: professionalization, legitimization, the value of community, and leadership impact. The participants reported a greater sense of professionalization through enhanced teaching skills, increased awareness of educational literature, and heightened confidence in their educator roles. The faculty development program fostered a strong community, promoting collaboration, knowledge sharing, and mutual support across specialties and locations. Leadership impact was evident at individual and institutional levels, increasing confidence, mentorship, and organizational support.ConclusionsThis study provides valuable insights into the organizational impact of faculty development programs, shedding light on how such initiatives influence faculty experiences and organizational culture. Future research should explore leadership values, faculty retention, burnout prevention, and the broader value of education within academic institutions.

Judgment aggregation is a collective decision making framework where the opinions of a group of agents is combined into a collective opinion. This can be done using many different judgment aggregation procedures. We study the computational complexity of computing the group opinion for several of the most prominent judgment aggregation procedures. In particular, we show that the complexity of this winner determination problem for analogues of the Kemeny rule, the Slater rule and the Young rule lies at the Θp2-level of the Polynomial Hierarchy (PH). Moreover, we show that the problem has a complexity at the Δp2-level of the PH for the analogue of Tideman's procedure with a fixed tie-breaking rule, and at the Σp2-level of the PH for the analogue of Tideman's procedure without a fixed tie-breaking rule.

We introduce a new approach for designing rules for participatory budgeting, the problem of deciding on the use of public funds based directly on the views expressed by the citizens concerned. The core idea is to embed instances of the participatory budgeting problem into judgment aggregation, a powerful general-purpose framework for modelling collective decision making. Taking advantage of the possibilities offered by judgment aggregation, we enrich the familiar setting of participatory budgeting with additional constraints, namely dependencies between projects and quotas regarding different types of projects. We analyse the rules obtained in both algorithmic and axiomatic terms.

Developing a straightforward approach for group decision making based on determining weights of decision makers

John Broome has argued that there are distinct requirements of rationality and reason. Niko Kolodny has defended an error theory about requirements of rationality, arguing that requirements of rationality fall out of the requirements of reason, not in the straightforward sense that one has a reason to be rational as such, but in the sense that requirements of rationality are a byproduct of requirements of reason. Recent work in the theory of group agency and the problem of judgment aggregation raises a difficulty for applying Kolodny's error theory to the case of requirements of group rationality and group reason. This chapter explores ways in which the conflict between the proposed error theory in the group case and the results concerning judgment aggregation might be resolved. The chapter also considers what bearing the group case has on the success of the error theory in the individual case.

Trail network systems among ants have received a lot of scientific attention because of their various applications in problem solving of networks. Recent studies have shown that ants select the fastest available path when facing different velocities on different substrates, rather than the shortest distance. The progress of decision making by these ants is determined by pheromone-based maintenance of paths, which is a collective decision. However, path optimization through individual decision making remains mostly unexplored. Here, we present the first study of time-optimized path selection via individual decision making by scout ants. Megaponera analis scouts search for termite-foraging sites and lead highly organized raid columns to them. The path of the scout determines the path of the column. Through installation of artificial roads around M. analis nests, we were able to influence the pathway choice of the raids. After road installation, 59% of all recorded raids took place completely or partly on the road, instead of the direct, i.e. distance-optimized, path through grass from the nest to the termites. The raid velocity on the road was more than double that on the grass, and the detour thus saved 34.77±23.01% of the travel time compared with a hypothetical direct path. The pathway choice of the ants was similar to a mathematical model of least time, allowing us to hypothesize the underlying mechanisms regulating the behavior. Our results highlight the importance of individual decision making in the foraging behavior of ants and show a new procedure of pathway optimization.

Collective decision making is the process of mapping the individual views of several individual agents into a joint decision. The need for collective decision making mechanisms is abundant, not just in the realm of politics, but also for a wide range of scientific and technological applications. These include, for instance, logistics, grid computing, and recommender systems. The alternatives to be decided upon often have a combinatorial structure: an alternative is characterised by a tuple of variables, each ranging over a finite domain. Classical approaches to collective decision making, developed in social choice theory, do not take the computational limitations induced by the combinatorial nature of the problem into account. For instance, if we are asked to elect a committee consisting of k representatives, choosing from a pool of n candidates, then we are in fact faced with a social choice problem with $(^n_k)$ alternatives. Asking each voter for their full preferences over these $(^n_k)$ alternatives may not be feasible in practice. Similarly, if we have to choose between accepting or rejecting each of n different propositions, then we are dealing with a social choice problem with 2 n possible outcomes. In this talk I will report on a number of recent developments in the area of collective decision making in combinatorial domains. This includes the study of languages for the compact representation of preferences [2,4], the design of voting rules for multi-issue elections [1], and the analysis of the computational complexity of decision problems arising in judgment aggregation [3].

Complexity of manipulation and bribery in premise-based judgment aggregation with simple formulas