ABSTRACT
In the event that three or more alternatives are under consideration, the voting problem turns out to be fraught with a variety of complexities. Because of these complexities, and because at the same time voting is a common phenomenon used by groups ranging from small committees to mass electorates, an extensive theoretical literature has developed on the subject. This chapter surveys the concepts, analytical techniques, and results of that portion of this literature that deals specifically with committee voting. Since Black revived the subject, many economists and political scientists, as well as some philosophers, mathematicians, and others, have made important contributions to the theory of committee voting, which has evolved in a cumulative fashion. The simplest voting problem arises when there are just two alternatives — call them x and y — on the agenda. In this case, voting by simple majority rule strikes most people as fair and reasonable.
