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Home , Frank Hahn

Preface (1970)

The theory of collective choice belongs to several disciplines. Econom- ics is one of them but not the only one. While this book is part of a series in ‘ texts’, no attempt has been made to confine the treatment to economic problems exclusively. Indeed the approach of this book is based on the belief that the problem cannot be satisfactorily discussed within the confines of economics. While collective choice is a crucial aspect of economics (notably of welfare economics, planning theory and public economics), the subject relates closely to political science, in particular to the theory of the state and the theory of decision procedures. It also has important philosophical aspects, related to ethics and especially to the theory of justice. The book is divided into starred chapters which contain formal analyses, and unstarred ones which are quite informal. They alter- nate. A non-technical reader can get an intuitive idea of the main arguments from the unstarred chapters. However, for precise state- ment of results as well as proofs, the starred chapters have to be read. The partitioning of the book into formal and informal chapters is a stylistic experiment. Many problems of collective choice require a rigorous and formal treatment for definiteness, and informal argu- ments can indeed be treacherous, but, once the results are obtained, their meaning, significance and relevance can be discussed infor- mally. In fact, a purely formal discussion of significance would be unnecessarily narrow. The book attempts to cater to two distinct groups of readers, viz., those who are primarily interested in the rel- evance of the results rather than in their formal statement and technical derivation, and those who are also concerned with the

vii Preface (1970) latter. Thus, the partitioning of the book into starred and unstarred chapters does have some rationale, aside from reflecting the author’s incurable schizophrenia. The mathematics used in the book mainly involves the logic of relations. The main results of mathematical logic employed in prov- ing theorems on collective choice are stated, discussed and proved in Chapter 1*. The book is in this sense ­self-­contained. The field of collective choice is vast. It has not been possible to cover all the branches, and still less to discuss all of them equally thoroughly. While it is hoped that the book covers the major branches of the literature adequately, it must be recognized that the judgment of the relative importance of different branches represents the author’s own bias. For facilities of typing and duplication of two versions of this manuscript I am grateful to the Delhi School of Economics and to the Harvard Institute of Economic Research. The actual typing of the two versions was done very efficiently by Mr C. G. Devarajan and Mrs. Helen Bigelow, respectively. I must express my indebtedness to people who have influenced this book. My interest in the problem was first aroused by some stimulat- ing discussions with Maurice Dobb when I was an undergraduate at Trinity College, Cambridge, about a decade and a half ago, and I have had discussions with him intermittently ever since. My debt to is immense, not merely because his pioneering work has opened up several avenues of research in the field of collective choice, but, more personally, because he has gone through the entire manuscript and has suggested many important improvements. John Rawls read entirely the first version of the manuscript, which was pre- pared during ­1966–​7­, and has put me right on several questions, especially on the philosophical side of the problem. During 1­ 967–­​8, Tapas Majumdar, and Prasanta Pattanaik read the first draft of the manuscript and suggested numerous improvements both of substance and style, and the final version of the book reflects the impact of their comments. I have also benefited from the joint seminar on this subject that Arrow, Rawls and I conducted at during 1­968–­​9, in particular from the

viii Preface (1970) participation of Franklin Fisher, A. Gibbard, Stephen Marglin, How- ard Raiffa, Jerome Rothenberg, Ross Starr, David Starrett and Richard Zechhauser. I have also had useful discussions with, or helpful comments from, Dipak Banerjee, Robert Cassen, Partha Dasgupta, , Jan Graaff, Frank Hahn, Bengt Hansson, John Har- sanyi, Hans Herzberger, ­Ken-­Ichi Inada, , Abba Lerner, , Thomas Schelling, and Subramaniam Swamy. But I am, alas, reconciled to the fact that none of these gentlemen can be held responsible for the errors and shortcomings of this work.

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