Distance rationalization of anonymous and homogeneous voting rules

Abstract

The concept of distance rationalizability of voting rules has been explored in recent years by several authors, particularly Elkind, Faliszewski and Slinko. We study in detail the commonly occurring case of anonymous and homogeneous rules, which allows for a more succinct representation. We first translate the theory to this compressed representation and unify and extend previous work. The new framework allows a geometric interpretation in terms of finite-dimensional Banach spaces that is new to the distance rationalizability framework and that suggests several conjectures about Voronoi theory in these spaces. We present both positive and negative results, focusing on the case of l¹.