Networks with Condorcet solutions (Q1058436)

A Condorcet point on a network is a point such that there is no other point closer to a strict majority of users which are located at the vertices of the network. A complete characterization is given of those networks on which no Condorcet paradox occurs, in the sense that for each distribution of users there exists at least one Condorcet point. Moreover, those networks are characterized on which Condorcet points and Weber points always coincide. A polynomial algorithm is obtained which decides whether a given network has Condorcet points for all distributions of users on the network.