Social choice theory is a natural subject for an economist with a background in mathematics. I first discovered the theory as an undergraduate, and it was the subject of my first published paper. In twenty years of study, social choice theory has not ceased to fascinate me, but I have become aware that it has not had its due influence on politics, economics or philosophy. This book is an attempt to bring together its main themes, to provide a framework in which the theory can have a greater influence.

There are many related themes, beginning with the famous impossibility theorem of Arrow (perhaps it is this title that keeps social choice theory away from the centre of debate), through the work on strategic manipulation, theories of rights, justice and utilitarianism. All of these are introduced here: though we do not go to the frontiers of research in any of them. The main purpose of this book is to provide an integrated way of looking at the problems raised in social choice theory, and proofs of the main propositions so that they are reasonably accessible to readers without a formal mathematical training.

This book has been long in the making. I first thought of writing it when I was a visitor at the University of Guelph in Canada in 1982/3.