Stirling Numbers and a Geometric Structure from Voting Theory

Abstract In the spatial theory of voting, m candidates are each represented by a point in a p-dimensional Euclidean “attribute” space. The hyperplanes bisecting the line segments joining pairs of these points divide the space into regions, and each region corresponds to a definite ranking of the distances to the candidates. This paper discusses the combinatorics of such a structure and shows that the Stirling numbers have a geometrical significance.