Aggregation of Argumentation Systems
Aim. The aim of this WP is to study how to aggregate different argumentation systems. Before designing deliberation protocols aiming at exchanging arguments between agents, we need to be able to say if the result of a deliberation is satisfying from a social point of view. In order to achieve this, we will rely on tools from social choice theory and from logical aggregation. The main research question of this WP is to study how to define an aggregation system that best represents a set of argument systems coming from different agents. The problem is challenging because agents may have different sets of arguments to start with, or different opinions as to what constitutes a contradiction between some of these arguments. Furthermore, argumentation is a reasoning model which typically allows conflicting “viewpoints” even if the agents agree on the underlying “background” theory: this means that aggregation of viewpoints may be necessary at different stages.
Background. The problem of how to aggregate individual argumentation systems into a collective one is a novel research question. There is some initial work, particularly from the members of this project [CDKLM07, CP11, CPP11]. Specifically, Coste-Marquis et al. [CDKLM07] have put forward the first proposal addressing the merging of argumentation systems, where the individual argumentation frameworks may be different. Conflicts between argumentation frameworks are solved using merging techniques [KP02]. On the other hand, the case of the aggregation of different viewpoints on a given argumentation framework has been investigated by Caminada and Pigozzi [CP11]. Three aggregation procedures suitable for small groups where agents wish to reach a collective position that is compatible with their individual views were proposed. Welfare properties and strategic issues of these operators have also been studied [CPP11]. The natural framework for studying the aggregation of individual argumentation systems is social choice. The study of the aggregation of individual preferences, and the properties that aggregation rules may satisfy can be used as a theoretical reference to the aggregation of individual attack relations [TBS08]. When preference relations over individual positions are considered, welfare properties of collective argument evaluation (like Pareto optimality) can also be explored, as done in [RL08]. There is also a line of work building on the similarity between judgment aggregation and argumentation aggregation [RT10]. Recently, Marquis and colleagues have investigated argument aggregation under an axiomatic perspective, and studied preliminary complexity results [DMW12].
Challenges/Subtasks. As we have seen in the background section, the study of the aggregation of individual argumentation frameworks into a collective one is promising but still in its infancy. Several steps need to be undertaken in order to provide the field with a solid ground.
The first issue to tackle is to define a set of desirable properties that one may wish an arguments aggregation procedure to satisfy, e.g. anonymity (i.e. all individuals count the same), unanimity (i.e. if all agents agree on the evaluation of one argument, the group position on that argument should reflect the unanimous view), and collective rationality (i.e. the collective outcome must be a permissible evaluation of the argumentation system). These are some standard properties employed in aggregation theories like social choice [Arrow51], belief merging [KP02, KG06] and judgment aggregation [LP09, LP10]. However, existing axioms may not simply be imported in the new framework. Unanimity, for example, is not a trivial axiom in arguments aggregation: arguments are connected by attack relations, and the evaluation of one argument affects the evaluation of arguments attacked by it. And it may happen that, even though there is a unanimous opinion on the status of one argument, such view cannot be preserved at the group level [CP11]. Thus, the aggregation of argumentation systems may call for specific axioms that are not common to other disciplines. Once a set of axioms suitable for the aggregation of argumentation systems is put forward, the next quest is for possibility and impossibility results to cast a light on which axioms are mutually consistent and which are not.
Given a profile of individual argumentation systems, there exist several ways to aggregate them into a group argumentation system [BF04]. The choice among different procedures depends - among other things - on the axioms that we want to be satisfied, on the particular properties we wish for the aggregation procedure, but also on the decision context. For example, anonymity is an intuitive desirable axiom, but when the agents participating to the decision have different competences, one may require a rule that takes this information into account. As far as it concerns the decision contexts, some require a majoritarian approach whereas others call for an egalitarian approach, when aiming at equally distributing the individual satisfaction seems to be more appropriate. One of the challenges of this WP will then be to propose a whole range of aggregation procedures.
In addition to the definition of several aggregation rules, we need to study what are the properties that we expect from these procedures. The aim here is to define what kind of properties one could expect from the aggregation of several argumentation systems. This is necessary to be able to distinguish between interesting aggregation procedures and the ones with bad behaviours, but also to classify them according to the specific decision contexts and to their respective behaviours. Examples are social welfare properties like Pareto optimality, and properties of the aggregation procedure, like its sensibility to manipulation. When a rule is manipulable, an agent (upon knowing the other participants’ votes) may cast an insincere input in order to obtain a social outcome that is better for him compared to the one he had obtained, had he voted sincerely. Clearly, a strategy-proof procedure is desirable, but unfortunately very unlikely [Gibbard73, Satterthwaite75]. But as the recent findings of computational social choice show [CELM07], even if an aggregation procedure is manipulable, its complexity may be so high that manipulation is practically difficult.
Another key issue is to clarify the relation between argumentation aggregation, voting procedures and judgment aggregation on the one hand, and belief merging on the other hand. The question of whether it is possible to embed the aggregation of argumentation systems into the judgment aggregation framework [LP10] seems particularly urgent, as already pointed out by [RT10, CP11]. The analogy (at least when the agents share the same argumentation system) is striking. Once this relation is clarified, results obtained in judgment aggregation may eventually be reformulated for the argumentation aggregation case (e.g. results that relate to the agendas and to the conditions that the aggregation rules need to satisfy in order to guarantee consistent group positions). But there are also differences between argumentation aggregation and judgment aggregation, most notably the fact that the underlying logic of judgment aggregation is usually a classical two-value propositional logic. For argument labelling [Caminada06, CG09], three values can be taken (in, out, undec). Recently, [DH10] have studied aggregation of non-binary evaluations, allowing for an extension of judgment aggregation problems using three values, thus providing a more suitable framework.
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