Collective Decisions and Voting

This book is about collective decisions, and one special way of making them, namely voting. It is divided into two parts, the first dealing with collective decisions and the second with voting procedures.The first part of the book is concerned with defining a collective decision, and then with classifying and evaluating the modes by which collective decisions are made. The theme of the second part of the book is that possible ways of voting are much more varied than one might expect, so that voting has a much greater potential than is generally realized. But to get as much as possible from voting, it is important first to understand what voting cannot do. The limitations of voting are developed through discussions of voting cycles, the Arrow theorem and the Gibbard-Satterthwaite theorem. The range of possibilities that voting offers is presented through a four-dimensional classification of voting procedures. This framework serves to organize discussions of three types of voting situations.The first type involves electing one candidate from many, using equally weighted votes. The second type involves electing more than one candidate through equally weighted votes. The third type involves responding to the intensities of voters' preferences. An important theme of both parts of the book is that no method of voting and no other way of making collective decisions can be guaranteed to yield indisputable results. A central concern for inquiry into collective decisions and voting is to identify procedures with the least serious faults, and then to give them the support they deserve without becoming blind to their faults.