Collective rationality in Graph aggregation

Abstract

Suppose a number of agents each provide us with a directed graph over a common set of vertices. Graph aggregation is the problem of computing a single collective graph that best represents the information inherent in this profile of individual graphs. We consider this aggregation problem from the point of view of social choice theory and ask what properties shared by the individual graphs will transfer to the graph computed by a given aggregation procedure. Our main result is a general impossibility theorem that applies to a wide range of graph properties.