When one thinks about how collective decisions are made, voting is the method that comes naturally to mind. But other methods such as random process and consensus are also used. This book explores just what a collective decision is, classifies the methods of making collective decisions, and identifies the advantages and disadvantages of each method. Classification is the prelude to evaluation. What are the characteristics of a method of making collective decisions, the book asks, that permit us to describe a collective decision as good? The second part of the book is detailed exploration of voting: the dimensions in which voting situations differ, the origins and logic of majority rule, the frequency of cycles in voting, the Arrow and Gibbard-Satterthwaite theorems, criteria for ways of cutting through cycles and the application of these criteria to a variety of rules, voting over continuums, proportional representation, and voting rules that take account of intensities of preferences. Relatively unknown methods of voting give voting a much greater potential than is generally recognized. Collective Decisions and Voting is essential reading for everyone with an interest in voting theory and in how public choices might be made.

Every day thousands of decisions are made by all kinds of committees, parliaments, councils and boards by a 'yes-no' voting process. Sometimes a committee can only accept or reject the proposals submitted to it for a decision. On other occasions, committee members have the possibility of modifying the proposal and bargaining an agreement prior to the vote. In either case, what rule should be used if each member acts on behalf of a different-sized group? It seems intuitively clear that if the groups are of different sizes then a symmetric rule (e.g. the simple majority or unanimity) is not suitable. The question then arises of what voting rule should be used. Voting and Collective Decision-Making addresses this and other issues through a study of the theory of bargaining and voting power, showing how it applies to real decision-making contexts.

A study of the classical aggregation problems that arise in social choice theory, voting theory, and group decision-making under uncertainty.

Harrie de Swart is a Dutch logician and mathematician with a great and open int- est in applications of logic. After being confronted with Arrow’s Theorem, Harrie became very interested in social choice theory. In 1986 he took the initiative to start up a group of Dutch scientists for the study of social choice theory. This initiative grew out to a research group and a series of colloquia, which were held approximately every month at the University of Tilburg in The Netherlands. The organization of the colloquia was in the hands of Harrie and under his guidance they became more and more internationally known. Many international scholars liked visiting the social choice colloquia in Tilburg and enjoyed giving one or more presentations about their work. They liked Harrie’s kindness and hospitality, and the openness of the group for anything and everything in the eld of social choice. The Social Choice Theory Group started up by Harrie consisted, and still c- sists, of scholars from several disciplines; mostly economics, mathematics, and (mathematical) psychology. It was set up for the study of and discussion about anything that had to do with social choice theory including, and not in the least, the supervision of PhD students in the theory. Members of the group were, among o- ers, Thom Bezembinder (psychologist), Hans Peters (mathematician), Pieter Ruys (economist), Stef Tijs (mathematician and game theorist) and, of course, Harrie de Swart (logician and mathematician).

Individual decision making can often be wrong due to misinformation, impulses, or biases. Collective decision making, on the other hand, can be surprisingly accurate. In Democratic Reason, Hélène Landemore demonstrates that the very factors behind the superiority of collective decision making add up to a strong case for democracy. She shows that the processes and procedures of democratic decision making form a cognitive system that ensures that decisions taken by the many are more likely to be right than decisions taken by the few. Democracy as a form of government is therefore valuable not only because it is legitimate and just, but also because it is smart. Landemore considers how the argument plays out with respect to two main mechanisms of democratic politics: inclusive deliberation and majority rule. In deliberative settings, the truth-tracking properties of deliberation are enhanced more by inclusiveness than by individual competence. Landemore explores this idea in the contexts of representative democracy and the selection of representatives. She also discusses several models for the "wisdom of crowds" channeled by majority rule, examining the trade-offs between inclusiveness and individual competence in voting. When inclusive deliberation and majority rule are combined, they beat less inclusive methods, in which one person or a small group decide. Democratic Reason thus establishes the superiority of democracy as a way of making decisions for the common good.