Some foundations for empirical study in the Euclidean spatial model of social choice

Abstract

Recent results are surveyed, and some new results are given, that contribute towards a theoretical and computational basis for empirical study in the Euclidean spatial model. The results are of two types: asymptotic statistical consistency of sample estimators, and algorithmic methods for recovering spatial locations and computing various solution concepts. The new results are: the asymptotic consistency of the sample yolk center and epsilon- core; NP-completeness of the 1-dimensional spatial location recovery system; a modification of the Poole-Rosenthal heuristic for multidimensional recovery; and fast algorithms to compute Simpson-Cramer points and supermajority win sets in fixed dimension