Although Kenneth Arrow is probably best known for his contributions to methods of direct decision making and the theory of ideal market decentralization, he laid much of the groundwork for subsequent discussion on alternative methods of organization. By pointing out and developing the relationships between the competitive allocation mechanism and other planning procedures, he caused us to focus on issues such as information gathering, communication efficiency, and transmission costs in deciding among forms of economic organization.

We think it is fair to say that he set an agenda for the future in his presidential address to the American Economic Association in 1974 and in his Fels lectures (The limits to organization) published at roughly the same time. He pointed out the need for a better understanding of information costs and how they should be measured; he suggested that many of the problems faced in understanding the structure and operation of large organizations could be analyzed only by bringing information and communication channels more directly into the agenda of economists; and he advanced the view that the correct boundaries between internal and market allocations should be analyzed in those terms.

The contributions in this section explore various aspects of this agenda. Oniki addresses directly the question of how to measure the costs of communication. Drawing on ideas and concepts from information theory, he is able to quantify these costs and perform some suggestive comparisons between centralized and market mechanisms. Gorman motivates a view of the scope of the firm in terms of similarity of purpose and type of operation among production units. Making use of parallels with the theory of aggregation, he demonstrates the “information-saving” features of certain pseudomarket organizational forms.

The impact of Kenneth Arrow's work on twentieth century economics has been to change fundamentally economists' understanding of their discipline and their view of several major classes of problems. Arrow was a leader in the post-World War II push to bring the full power of mathematics and statistics to bear on economic analysis. The fields of general equilibrium, social choice and welfare economics, mathematical programming, and economics of uncertainty have been fundamentally altered by his contributions. In addition, Arrow is a man of wide learning, refreshing spontaneity, personal warmth, and remarkable absence of pretension.

Born in 1921 to Harry and Lillian Arrow of New York City, Kenneth Arrow was raised in and around New York. He pursued his undergraduate studies at City College of New York. On graduation from CCNY in 1940, he was awarded the Gold Pell Medal for highest grades in the graduating class. He studied then at Columbia, in particular with Harold Hotelling, and received an M.A. in mathematics in 1941.

Arrow's studies were interrupted by World War II. He served with the Weather Division of the Army Air Force and there wrote his first scientific paper (“On the use of winds in flight planning”). However, his other professional activities in the division almost prevented this line of research. The new young group of statisticians in the Weather Division subjected the prevailing prediction techniques to statistical test against a simple null hypothesis based on historical averages for the date in question.

Arrow is the creator of the field of social choice. Naturally, there were precursors, but the leap from previous literature to Social choice and individual values (1951) was as great as any in the postwar period in economics. Arrow showed that it was impossible to find a reasonable and consistent procedure for any society to choose among conflicting alternatives. The basic properties a procedure had to satisfy to be “reasonable” were these: that all rankings (including the social ranking) be transitive, that any preferences are possible (universal domain); that the social ordering put alternative a ahead of alternative b if everybody prefers a to b (Pareto principle); that, in choosing between two alternatives, society only need consult people's preferences over those two alternatives (independence of irrelevant alternatives), and finally, that no person is a dictator.

All literature that followed had to grapple with, in some way, the basic facts behind Arrow's theorem. Indeed, much of the subsequent literature is devoted to weakening one or more of Arrow's conditions in attempting to escape from the impossibility theorem.

Hammond reexamines two attempts to escape from Arrow impossibility from the viewpoint of “consequentialism,” that is, all decisions should be based solely on their feasible consequences. He finds that relaxation of either the independence of irrelevant alternatives or the ordinality of the social choice function violates consequentialism.

The study of “market failure” had a long history before Arrow. Most of this work involved identifying areas in which decentralized markets would not reach the first best (monopolies, public goods, externalities) and discussing appropriate modifications for those situations. For example, Lindahl shares could be used to allocate public goods, and Pigovian taxes could be used to correct for externality. Subsequently, Arrow was a significant contributor to this literature; he developed a general model that showed that virtually every type of nonmarket interaction could be corrected in principle through the use of appropriate “extended” markets. However, he pointed out very clearly the limitations of this approach, arguing that the information requirements and/or monopoly incentives inherent in extended markets would render them unworkable in many circumstances.

If we concede the impossibility of first-best pseudomarket procedures, then public sector planning must move in one of two directions. On the one hand, we can back away from “markets” and think about planning problems in an institution-free setting. Arrow contributed to this approach in a series of papers and a book (coauthored with M. Kurz) analyzing intertemporal consumption and public investment problems. Two chapters in this section deal with this approach. Scarf looks at planning problems in the presence of indivisibilities, which render market approaches unworkable. He discusses computational procedures that will “solve” a restricted class of such problems.

This three-volume work is composed of essays written by many of Kenneth Arrow's students and collaborators. Although it is impossible to cover the entire range of his contributions to economics, we have organized the presentation around the major topics of his research career: Volume I treats “Social Choice and Public Decision Making,” Volume II covers “Equilibrium Analysis,” and Volume III deals with “Uncertainty, Information, and Communication.”

We would like to thank all contributors to these volumes not only for their cooperation in helping expedite on-time production but also for voluntary efforts contributed in reading and commenting on each other's essays. In addition, we acknowledge with thanks the help of the following outside referees: Chuck Blackorby, Mark Johnson, Mark Machina, John McMillan, and Joel Sobel.

Special thanks go to Deborah Bailey who coordinated our (sometimes chaotic) correspondence among authors, editors, and publisher; she cheerfully dealt with potential disasters and enabled us to deliver the completed manuscript as scheduled. Also, we would like to thank Colin Day and his staff at Cambridge University Press for a highly professional effort at their end.

Finally, and most importantly, we speak for all contributors in thanking Kenneth Arrow for being an inspirational teacher and colleague over the years. The intellectual standards he set and the enthusiasm with which he approaches our subject are surely part of all of us. We can only hope that these essays convey some sense of our appreciation and esteem.