Probabilistic opinion pooling generalized. Part one: general agendas

Agents that must reach agreements with other agents need to reason about how their preferences, judgments, and beliefs might be aggregated with those of others by the social choice mechanisms that govern their interactions. The emerging field of judgment aggregation studies aggregation from a logical perspective, and considers how multiple sets of logical formulae can be aggregated to a single consistent set. As a special case, judgment aggregation can be seen to subsume classical preference aggregation. We present a modal logic that is intended to support reasoning about judgment aggregation scenarios (and hence, as a special case, about preference aggregation): the logical language is interpreted directly in judgment aggregation rules. We present a sound and complete axiomatisation. We show that the logic can express aggregation rules such as majority voting; rule properties such as independence; and results such as the discursive paradox, Arrow's theorem and Condorcet's paradox--which are derivable as formal theorems of the logic. The logic is parameterised in such a way that it can be used as a general framework for comparing the logical properties of different types of aggregation--including classical preference aggregation. As a case study we present a logical study of, including a formal proof of, the neutrality lemma, the main ingredient in a well-known proof of Arrow's theorem.

Information retrieval on RDF data benefits greatly from additional provenance information attached to the individual pieces of information. Provenance information such as origin of data, certainty, and temporal information on RDF statements can be used to rank search results according to one of those dimensions. In this paper, we consider the problem of aggregating provenance information from different dimensions in order to obtain a joint ranking over all dimensions. We relate this to the problem of preference aggregation in social choice theory and translate different solutions for preference aggregation to the problem of aggregating provenance rankings. By exploiting the ranking orderings on the provenance dimensions, we characterize three different approaches for aggregating preferences, namely the lexicographical rule, the Borda rule and the plurality rule, in our framework of provenance aggregation.

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.

Agents that must reach agreements with other agents need to reason about how their preferences, judgments, and beliefs might be aggregated with those of others by the social choice mechanisms that govern their interactions. The recently emerging field of judgment aggregation studies aggregation from a logical perspective, and considers how multiple sets of logical formulae can be aggregated to a single consistent set. As a special case, judgment aggregation can be seen to subsume classical preference aggregation. We present a modal logic that is intended to support reasoning about judgment aggregation scenarios (and hence, as a special case, about preference aggregation): the logical language is interpreted directly in judgment aggregation rules. We present a sound and complete axiomatisation of such rules. We show that the logic can express aggregation rules such as majority voting; rule properties such as independence; and results such as the discursive paradox, Arrow's theorem and Condorcet's paradox - which are derivable as formal theorems of the logic. The logic is parameterised in such a way that it can be used as a general framework for comparing the logical properties of different types of aggregation - including classical preference aggregation.

In response to recent work on the aggregation of individual judgments on logically connected propositions into collective judgments, it is often asked whether judgment aggregation is a special case of Arrowian preference aggregation. We argue for the converse claim. After proving two impossibility theorems on judgment aggregation (using “systematicity” and “independence” conditions, respectively), we construct an embedding of preference aggregation into judgment aggregation and prove Arrow’s theorem (stated for strict preferences) as a corollary of our second result. Although we thereby provide a new proof of Arrow’s theorem, our main aim is to identify the analogue of Arrow’s theorem in judgment aggregation, to clarify the relation between judgment and preference aggregation, and to illustrate the generality of the judgment aggregation model.

Many areas of study, such as information retrieval, collaborative filtering, and social choice face the preference aggregation problem, in which multiple preferences over objects must be combined into a consensus ranking. Preferences over items can be expressed in a variety of forms, which makes the aggregation problem difficult. In this work we formulate a flexible probabilistic model over pairwise comparisons that can accommodate all these forms. Inference in the model is very fast, making it applicable to problems with hundreds of thousands of preferences. Experiments on benchmark datasets demonstrate superior performance to existing methods

We consider the problem of preference aggregation in group decision making. The role of the collaborative imperative used by the group in determining the form of the aggregation function is noted. We focus on one collaborative imperative, called the primal, deriving from participant autonomy, an agent doesn't have to accept a decision by the group it doesn't like. We showed that t-norms and more generally the class of uninorms having zero fixation provide appropriate aggregation operators to implement this primal collaborative imperative. We then discuss the possibility of an agent using a strategic manipulation of its preference information to get its preferred alternative. A mechanism based upon the use of an importance weighting is then suggested for modifying the construction of the group decision function to defend against strategic manipulation.

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.

My focus is on aggregation of individual value rankings of alternatives to a collective value ranking. This is compared with aggregation o individual prefrences to a collective preference. While in an individual preference ranking the alternatives are ordered in accordance with one’s preferences, the order in a value ranking expresses one’s comparative evaluation of the alternatives, from the best to the worst. I suggest that, despite their formal similarity as rankings, this difference in the nature of individual inputs in two aggregation scenarios has important implications: The kind of procedure that looks fine for aggregation of judgments is inappropriate for aggregation of preferences. The procedure I have in mind consists in similarity maximization, or – more precisely – in minimization of the average distance from individual inputs. When applied to judgment aggregation, this procedure can also be approached from the epistemic perspective: the questions are posed concerning its advantages as a truth-tracker. From that perspective, what matters is not only the probability of the outcome of the procedure being true, but also the expected verisimilitude of the outcome: its expected distance from truth.

Three practical criteria of comparison among ordinal preference aggregating rules

This paper clarifies, how a preference aggregation problem can be solved using the prioritized aggregation operators (PAO), where, a given group of candidates should be aggregated based upon their satisfaction for a collection of ranked places. The comparison results show that the proposed method can accurate aggregate a preference ranking system with less computation and without the need to solve any mathematical model. Also, a metasearch application shows the usefulness of applying the PAO for a preference aggregation. © 2010 Wiley Periodicals, Inc.

Group Recommendation (GR) is the task of suggesting relevant items/events for a group of users in online systems, whose major challenge is to aggregate the preferences of group members to infer the decision of a group. Prior group recommendation methods applied predefined static strategies for preference aggregation. However, these static strategies are insufficient to model the complicated decision making process of a group, especially for occasional groups which are formed adhoc. Compared to conventional individual recommendation task, GR is rather dynamic and each group member may contribute differently to the final group decision. Recent works argue that group members should have non-uniform weights in forming the decision of a group, and try to utilize a standard attention mechanism to aggregate the preferences of group members, but they do not model the interaction behavior among group members, and the decision making process is largely unexplored.In this work, we study GR in a more general scenario, that is Occasional Group Recommendation (OGR), and focus on solving the preference aggregation problem and the data sparsity issue of group-item interactions. Instead of exploring new heuristic or vanilla attention-based mechanism, we propose a new social self-attention based aggregation strategy by directly modeling the interactions among group members, namely Group Self-Attention (GroupSA). In GroupSA, we treat the group decision making process as multiple voting processes, and develop a stacked social self-attention network to simulate how a group consensus is reached. To overcome the data sparsity issue, we resort to the relatively abundant user-item and user-user interaction data, and enhance the representation of users by two types of aggregation methods. In the training process, we further propose a joint training method to learn the user/item embeddings in the group-item recommendation task and the user-item recommendation task simultaneously. Finally, we conduct extensive experiments on two real-world datasets. The experimental results demonstrate the superiority of our proposed GroupSA method compared to several state-of-the-art methods in terms of HR and NDCG.

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.

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,

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.