Group decision making over multidimensional objects of choice

Abstract

Recent work in social choice theory has suggested very pessimistic results about the way in which majority rule voting procedures (a) reflect (or fail to reflect) the will of the majority and (b) are subject to manipulation. We briefly review this work but focus on more recent results that make use of the concept of the “yolk” (McKelvey, 1986, American Journal of Political Science, 30(2), 283–315). This recent literature (e.g., Feld, Grofman, & Miller, 1989, Mathematical and Computer Modeling 12(4/5), 405–416) shows that, when groups are voting over a set of objects that can be characterized as points in a multidimensional space under a simple sequential procedure of single elimination, alternatives that are centrally located within the pareto set are almost certain to be chosen. Moreover, the structure of majority rule in the spatial context imposes a natural “fuzzy ordering” on alternatives. We also look at how supramajoritarian decision rules can give rise to cores in spatial voting games.