Graph aggregation

Abstract

Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of situations, e.g., when applying a voting rule (graphs as preference orders), when consolidating conflicting views regarding the relationships between arguments in a debate (graphs as abstract argumentation frameworks), or when computing a consensus between several alternative clusterings of a given dataset (graphs as equivalence relations). In this paper, we introduce a formal framework for graph aggregation grounded in social choice theory. Our focus is on understanding which properties shared by the individual input graphs will transfer to the output graph returned by a given aggregation rule. We consider both common properties of graphs, such as transitivity and reflexivity, and arbitrary properties expressible in certain fragments of modal logic. Our results establish several connections between the types of properties preserved under aggregation and the choice-theoretic axioms satisfied by the rules used. The most important of these results is a powerful impossibility theorem that generalises Arrow's seminal result for the aggregation of preference orders to a large collection of different types of graphs. * This work refines and extends papers presented at COMSOC-

Preservation of Semantic Properties during the Aggregation of Abstract Argumentation Frameworks

“…In the remainder of this section, we first define a number of specific aggregation rules and review their properties. We focus on simple rules that are adaptations of well-known rules used in the social choice literature, particularly in judgment aggregation [17] and graph aggregation [14]. We then adapt several standard properties of aggregation rules, known as axioms in that same literature, to our setting.…”

“…This is true under any of the four semantics. To prove this result-and some of those that follow-we are going to use a technique developed by Endriss and Grandi [14] for the more general framework of graph aggregation, which in turn has been inspired by the seminal work on preference aggregation of Arrow [3]. It amounts to showing that, under certain assumptions, the collection of coalitions of agents that are sufficiently powerful to force collective acceptance of an attack must form an ultrafilter.…”

“…Our approach uses techniques originating in social choice theory, the study of collective decision making [2,16], the relevance of which to collective argumentation has previously been noted by several of the aforementioned authors, starting with Tohmé et al [25]. In particular, we make use of recent results on graph aggregation [14]. Besides the formulation of a clear and simple model for the axiomatic study of the preservation of semantic properties during aggregation, our contribution consists in delineating how fundamental axiomatic properties of aggregation rules interact with such preservation requirements.…”

Social Choice Methods for Database Aggregation

“…The corresponding versions of these results have been proved to hold in judgment and graph aggregation [13,18]. We now show the following equivalence between majority and the distance-based rule in the absence of integrity constrains: Lemma 3.…”

Aggregation in Value-Based Argumentation Frameworks

“…The second approach to this problem is to aggregate directly the agents' attack graphs, searching for a collective justification in the form of an ordering over the values a posteriori. Techniques in graph aggregation [18] and belief merging [19] have already proven useful in various settings related to argumentation [9,10,7].…”