Comparison of Condorcet and Weber solutions on a plane: Social choice versus centralization

This paper compares the quality of facility location resulting from voting and that of a centralized decision. The focus is on the quality of the Condorcet solution, which is measured by the ratio of the Condorcet solution value to the global Weber solution value. Prior work defined on networks showed that the ratio is bounded by 3. We attempt to reduce the impact of topology by investigating the problem on the plane. In this case, the ratio is smaller than $\sqrt{2}$ . The result suggests that, when reducing the impact of topology, although a solution originated via voting can be somewhat distant from the optimal solution obtained via a centralized system, it is much closer to optimality than previously suggested.