Pareto Optimality and Strategy Proofness in Group Argument Evaluation (Extended Version)

An inconsistent knowledge base can be abstracted as a set of arguments and a defeat relation among them. There can be more than one consistent way to evaluate such an argumentation graph. Collective argument evaluation is the problem of aggregating the opinions of multiple agents on how a given set of arguments should be evaluated. It is crucial not only to ensure that the outcome is logically consistent, but also satisfies measures of social optimality and immunity to strategic manipulation. This is because agents have their individual preferences about what the outcome ought to be. In the current paper, we analyze three previously introduced argument-based aggregation operators with respect to Pareto optimality and strategy proofness under different general classes of agent preferences. We highlight fundamental trade-offs between strategic manipulability and social optimality on one hand, and classical logical criteria on the other. Our results motivate further investigation into the relationship between social choice and argumentation theory. The results are also relevant for choosing an appropriate aggregation operator given the criteria that are considered more important, as well as the nature of agents' preferences

Manipulation in Group Argument Evaluation.

Given an argumentation framework and a group of agents, the individuals may have divergent opinions on the status of the arguments. If the group needsto reach a common position on the argumentation framework, the question is how the individual evaluations can be mapped into a collective one. Thisproblem has been recently investigated by Caminada and Pigozzi. In this paper, we investigate the behaviour of two of such operators from a socialchoice-theoretic point of view. In particular, we study under which conditions these operators are Pareto optimal and whether they are manipulable.Social choice theory; Judgment aggregation; Argumentation; Collective decision making;

Manipulation in group argument evaluation.

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.Collective decision making; Argumentation; Judgment aggregation; Social choice theory;

Paretian argumentation frameworks for Pareto optimal arguments

Argument-based reasoning offers promising interaction and computation mechanisms for multi-agent negotiation and deliberation. Arguments in this context are typically statements of beliefs or actions related to agents' subjective values, preferences and so on. Consequences of such arguments can and should be evaluated using various criteria, and therefore it is desirable that semantics supports these criteria as principles for accepting arguments. This article gives an instance of Dung's abstract argumentation framework to deal with Pareto optimality, i.e. a fundamental criterion for social welfare. We show that the instance allows Dung's acceptability semantics to interpret Pareto optimal arguments, without loss of generality. We discuss the prospects of justified Pareto optimal arguments and Pareto optimal extensions

How to Make Institutional Economics Policy-Relevant: Theoretical Considerations and an Application to Rural Credit Markets in Developing Countries

Welfare economics as the traditional, prescriptive theory framework used in agricultural economics has been criticised by institutional economists as being largely irrelevant to real-world policy issues. We therefore ask how normative statements are possible within an economic theory framework that does recognise the importance of institutional arrangements. Instead of applying established outcome-oriented criteria of social welfare, we examine whether the rules of economic interaction allow the acquisition of gains from cooperation. We suggest to reconstruct any interaction as an existing or repealed social dilemma. This approach helps to identify common rule interests which create room for improvement of all parties involved, and to suggest desirable institutional reforms. An application to credit markets in developing countries demonstrates the insufficiency of welfare economic arguments and the potential insights generated by a social dilemma heuristic. The latter sheds new light on the role of various forms of collateral and informal arrangements to overcome credit rationing.Agricultural Finance, Institutional and Behavioral Economics, D02, D63, D74, Q14,

A Framework for Data-Driven Explainability in Mathematical Optimization

Advancements in mathematical programming have made it possible to efficiently tackle large-scale real-world problems that were deemed intractable just a few decades ago. However, provably optimal solutions may not be accepted due to the perception of optimization software as a black box. Although well understood by scientists, this lacks easy accessibility for practitioners. Hence, we advocate for introducing the explainability of a solution as another evaluation criterion, next to its objective value, which enables us to find trade-off solutions between these two criteria. Explainability is attained by comparing against (not necessarily optimal) solutions that were implemented in similar situations in the past. Thus, solutions are preferred that exhibit similar features. Although we prove that already in simple cases the explainable model is NP-hard, we characterize relevant polynomially solvable cases such as the explainable shortest-path problem. Our numerical experiments on both artificial as well as real-world road networks show the resulting Pareto front. It turns out that the cost of enforcing explainability can be very small