Manipulation in group argument evaluation (Extended Abstract) Martin Caminada Individual and Collective Reasoning, University of Luxembourg martin.caminada@uni.lu Gabriella Pigozzi LAMSADE Université Paris-Dauphine France gabriella.pigozzi@dauphine.fr Mikolaj Podlaszewski Individual and Collective Reasoning, University of Luxembourg mikolaj.podlaszewski@gmail.com ABSTRACT Given an argumentation framework and a group of agents, the individuals may have divergent opinions on the status of the arguments. If the group needs to reach a common po- sition on the argumentation framework, the question is how the individual evaluations can be mapped into a collective one. This problem has been recently investigated in [1]. In this paper, we study under which conditions these operators are Pareto optimal and whether they are manipulable. Categories and Subject Descriptors I.2.11 [Artificial Intelligence]: Distributed Artificial In- telligence—multiagent systems General Terms Economics, Theory Keywords Collective decision making, Argumentation, Judgment ag- gregation, Social choice theory 1. INTRODUCTION Individuals can hold different reasonable positions on the information they share. In this paper we are interested in group decisions where members share the same infor- mation. One of the principles of argumentation theory is that an argumentation framework can have several exten- sions/labellings. If the information the group shares is rep- resented by an argumentation framework, and each agent’s reasonable position is an extension/labelling of that argu- mentation framework, the question is how to aggregate the individual positions into a collective one. Caminada and Pigozzi [1] have studied this issue in ab- stract argumentation and provided three aggregation opera- tors. The key property of these operators is that the collec- tive outcome is ‘compatible’ with each individual position. That is, an agent who has to defend the collective position in public will never have to argue directly against his own private position. Cite as: Manipulation in group argument evaluation (Extended Ab- stract), Martin Caminada, Gabriella Pigozzi and Mikolaj Podlaszewski, Proc. of 10th Int. Conf. on Autonomous Agents and Mul- tiagent Systems (AAMAS 2011), Tumer, Yolum, Sonenberg and Stone (eds.), May, 2–6, 2011, Taipei, Taiwan, pp. 1127-1128. Copyright c  2011, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved. In this paper we focus on the behaviour of two of the three aggregation operators of [1] and address the following research questions: (i) Are the social outcomes of the aggregation operators in [1] Pareto optimal if preferences between different outcomes are also taken into account? (ii) Do agents have an incentive to misrepresent their own opinion in order to obtain a more favourable outcome? And what are the effects from the perspective of social welfare? Due to page constraints, we refer the reader to [1] for an outline of abstract argumentation theory and for the defini- tions of the sceptical and credulous aggregation operators. 2. PREFERENCES In order to investigate Pareto optimality and strategy- proofness we need to assume that agents have preferences over the possible collective outcomes. We write L≥i L ′ to denote that agent i prefers labelling L to L ′ . We write L∼i L ′ , and say that i is indifferent between L and L ′ , iff L≥i L ′ and L ′ ≥i L. Finally, we write L >i L ′ (agent i strictly prefers L to L ′ ) iff L≥i L ′ and not L∼i L ′ . We assume that the labelling submitted by each agent is his most preferred one and, hence, the one he would like to see adopted by the whole group. The order over the other possible labellings is generated according to the distance from the most preferred one. For this purpose, we define Hamming sets and Hamming distance among labellings. Definition 1. Let L1 and L2 be two labellings of argu- mentation framework. We define the Hamming set between these labellings as L1 ⊖L2 = {A |L1(A) = L2(A)} and the Hamming distance as L1 |⊖| L2 = |L1 ⊖L2|. We are now ready to define an agent’s preference given by the Hamming set and the Hamming distance as follows. Definition 2. Let (Ar , def ) be an argumentation frame- work, Labellings the set of all its labellings and ≥i the pref- erence of agent i. We say that agent i’s preference is Ham- ming set based (written as ≥i,⊖) iff ∀L, L ′ ∈Labellings , L≥i L ′ ⇔L⊖Li ⊆L ′ ⊖Li where Li is the agent’s most pre- ferred labelling. Similarly, we say that agent i’s preference is Hamming distance based (written as ≥ i,|⊖| ) iff ∀L, L ′ ∈ Labellings , L≥i L ′ ⇔ L |⊖| Li ≤L ′ |⊖| Li where Li is the agent’s most preferred labelling. We now have the machinery to represent individual prefer- ences over the collective outcomes. We can now turn to the first research question of the paper, i.e., whether the scepti- cal and credulous aggregation operators are Pareto optimal. 1127