There are some who, following Riker (1982), take Arrow’s theorem to show that democracy, conceived as government by the will of the people, is an incoherent illusion. Others argue that some conditions of the theorem are unreasonable, and from their point of view the prospects for collective choice look much brighter. After presenting the theorem itself, this entry will take up some main points of critical discussion. Section 4 considers the meaning and scope of Arrow’s conditions. Section 5 discusses aggregation procedures that are available when not all of Arrows conditions need be satisfied, or when different underlying assumptions are made about the nature of social choice. Section 6 concludes with an overview of proposals to study within Arrow’s technical framework certain aggregation problems other than the one that concerned him. 