Graph Aggregation: Extended Abstract
Ulle Endriss, Umberto Grandi
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). Other potential applications include belief merging, data integration, and social network analysis. In this short paper, we review a recently introduced formal framework for graph aggregation that is 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. Our main result is a powerful impossibility theorem that generalises Arrow's seminal result regarding the aggregation of preference orders to a large collection of different types of graphs. We also provide a discussion of existing and potential applications of graph aggregation.