We review several different languages for collective decision making problems, in which agents express their judgments, opinions, or beliefs over elements of a logically structured domain. Several such languages have been proposed in the literature to compactly represent the questions on which the agents are asked to give their views. In particular, the framework of judgment aggregation allows agents to vote directly on complex, logically related formulas, whereas the setting of binary aggregation asks agents to vote on propositional variables, over which dependencies are expressed by means of an integrity constraint. We compare these two languages and some of their variants according to their relative succinctness and according to the computational complexity of aggregating several individual views expressed in such languages into a collective judgment. Our main finding is that the formula-based language of judgment aggregation is more succinct than the constraint-based language of binary aggregation. In many (but not all) practically relevant situations, this increase in succinctness does not entail an increase in complexity of the corresponding problem of computing the outcome of an aggregation rule.

We provide a comprehensive analysis of the computational complexity of the outcome determination problem for the most important aggregation rules proposed in the literature on logic-based judgment aggregation. Judgment aggregation is a powerful and flexible framework for studying problems of collective decision making that has attracted interest in a range of disciplines, including Legal Theory, Philosophy, Economics, Political Science, and Artificial Intelligence. The problem of computing the outcome for a given list of individual judgments to be aggregated into a single collective judgment is the most fundamental algorithmic challenge arising in this context. Our analysis applies to several different variants of the basic framework of judgment aggregation that have been discussed in the literature, as well as to a new framework that encompasses all existing such frameworks in terms of expressive power and representational succinctness.

We study voting games on binary issues, where voters hold an objective over the outcome of the collective decision and are allowed, before the vote takes place, to negotiate their ballots with the other participants. We analyse the voters' rational behaviour in the resulting two-phase game when ballots are aggregated via non-manipulable rules and, more specifically, quota rules. We show under what conditions undesirable equilibria can be removed and desirable ones sustained as a consequence of the pre-vote phase.

Computational studies of voting are mostly motivated by two intended applications: the coordination of societies of artificial agents, and the study of human collective decisions whose complexity requires the use of computational techniques. Both research directions are too often confined to theoretical studies, with unrealistic assumptions constraining their significance for real-world situations. Most practical applications of these results are therefore confined to low-stakes decisions, which are of great importance in expanding the use of algorithms in society, but are far from high-stakes choices such as political elections, referenda, or parliamentary decisions, which societies still make using old-fashioned technologies like paper ballots. In this paper I argue in favour of conceiving "voting avatars", artificial agents that are able to act as proxies for voters in collective decisions at any level of society. Besides being an ideal test-bed for a large number of techniques developed in the field of multiagent systems and artificial intelligence in general, agent-mediated social choice may also suggests innovative solutions to the low voter participation that is endemic in most practical implementations of electronic decision processes.

We introduce a formal model of iterative judgment aggregation, enabling the analysis of scenarios in which agents repeatedly update their individual positions on a set of issues, before a final decision is made by applying an aggregation rule to these individual positions. Focusing on two popular aggregation rules, the premise-based rule and the plurality rule, we study under what circumstances convergence to an equilibrium can be guaranteed. We also analyse the quality, in social terms, of the final decisions obtained. Our results not only shed light on the parameters that determine whether iteration converges and is socially beneficial, but they also clarify important differences between iterative judgment aggregation and the related framework of iterative voting.

Different agents may have different points of view. Following a popular approach in the artificial intelligence literature, this can be modelled by means of different abstract argumentation frameworks, each consisting of a set of arguments the agent is contemplating and a binary attack-relation between them. A question arising in this context is whether the diversity of views observed in such a profile of argumentation frameworks is consistent with the assumption that every individual argumentation framework is induced by a combination of, first, some basic factual attack-relation between the arguments and, second, the personal preferences of the agent concerned regarding the moral or social values the arguments under scrutiny relate to. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. In doing so, we distinguish different constraints on admissible rationalisations, e.g., concerning the types of preferences used or the number of distinct values involved. We also distinguish two different semantics for rationalisability, which differ in the assumptions made on how agents treat attacks between arguments they do not report. This research agenda, bringing together ideas from abstract argumentation and social choice, is useful for understanding what types of profiles can reasonably be expected to occur in a multiagent system.

We review several different languages for collective decision making problems, in which agents express their judgments, opinions, or beliefs over elements of a logically structured domain. Several such languages have been proposed in the literature to compactly represent the questions on which the agents are asked to give their views. In particular, the framework of judgment aggregation allows agents to vote directly on complex, logically related formulas, whereas the setting of binary aggregation asks agents to vote on propositional variables, over which dependencies are expressed by means of an integrity constraint. We compare these two languages and some of their variants according to their relative succinctness and according to the computational complexity of aggregating several individual views expressed in such languages into a collective judgment. Our main finding is that the formula-based language of judgment aggregation is more succinct than the constraint-based language of binary aggregation. In many (but not all) practically relevant situations, this increase in succinctness does not entail an increase in complexity of the corresponding problem of computing the outcome of an aggregation rule.

We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the outcome of a judgment aggregation procedure in her favour by reporting insincere judgments (the strategic manipulation problem); and (3) deciding whether a given judgment aggregation scenario is guaranteed to result in a logically consistent outcome, independently from what the judgments supplied by the individuals are (the problem of the safety of the agenda). We provide results both for specific aggregation procedures (the quota rules, the premise-based procedure, and a distance-based procedure) and for classes of aggregation procedures characterised in terms of fundamental axioms.

Finally, explore possible methods for decision making in general, have received a lot uses of combinatorial aggregation in sequential voting, of attention in the AI community in recent years. The reasons and discuss theoretical generalisations to more complex logical for this focus are clear: SCT provides tools for the analysis of languages and practical applications. Particularly close to the interests of AI is the to study binary aggregation procedures, inspired by research problem of social choice in combinatorial domains (Chevaleyre in AI. As long as we do not know the intended application of et al., 2008), where the space of alternatives the individuals the model, there is no appropriate set of axioms to concentrate have to choose from has a combinatorial structure. Instead, we prove characterisation results concerning one Definition 1.

A multiagent system may be thought of as an artificial society of autonomous software agents and we can apply concepts borrowed from welfare economics and social choice theory to assess the social welfare of such an agent society. In this paper, we study an abstract negotiation framework where agents can agree on multilateral deals to exchange bundles of indivisible resources. We then analyse how these deals affect social welfare for different instances of the basic framework and different interpretations of the concept of social welfare itself. In particular, we show how certain classes of deals are both sufficient and necessary to guarantee that a socially optimal allocation of resources will be reached eventually.