On the Equivalence of Some Solution Concepts in Spatial Voting Theory
We prove that, for a spatial voting setting with convex preferences, the locally uncovered set, proposed by Schofield (1999), is closely related to the dimension-bydimension median of Shepsle (1979). It is shown that every point in the interior of the locally uncovered set can be supported as a dimension-by-dimension median by some set of basis vectors for the space of alternatives. Moreover, for a two-dimensional policy space, the locally uncovered set and the set of dimension-by-dimension medians coincide. We also introduce a measure that allows to differentiate locally uncovered alternatives and chose the best one.