Amartya Sen is the Thomas W. Lamont University Professor and Professor of Economics and Philosophy at Harvard University. In 1998, he was awarded the Nobel Memorial Prize in Economic Sciences, and in 1999, he was awarded the Bharat Ratna, Indias highest civilian award. He is also a senior fellow at the Harvard Society of Fellows, distinguished fellow of All Souls College, Oxford, and a Fellow of Trinity College, Cambridge. His books have been translated into more than thirty languages. Eric Maskin is an Adams University Professor at Harvard University. He received the 2007 Nobel Memorial Prize in Economics (with L. Hurwicz and R. Myerson) for laying the foundations of mechanism design theory. He has also made contributions to game theory, contract theory, social choice theory, political economy, and other areas of economics.

AcknowledgmentsIntroduction, by Prasanta K. PattanaikPart 1: The Lectures Opening Remarks, by Joseph E. StiglitzArrow and the Impossibility Theorem, by Amartya SenThe Arrow Impossibility Theorem: Where Do We Go From Here?, by Eric MaskinCommentary, by Kenneth J. ArrowPart II: Supplemental Materials The Informational Basis of Social Choice, by Amartya SenOn The Robustness of Majority Rule, by Partha Dasgupta and Eric MaskinThe Origins of the Impossibility Theorem, by Kenneth J. ArrowNotes on Contributors

Kenneth Arrow's pathbreaking impossibility theorem was a watershed in the history of welfare economics, voting theory, and collective choice, demonstrating that there is no voting rule that satisfies the four desirable axioms of decisiveness, consensus, nondictatorship, and independence. In this book, Amartya Sen and Eric Maskin explore the implications of Arrows theorem. Sen considers its ongoing utility, exploring the theorems value and limitations in relation to recent research on social reasoning, while Maskin discusses how to design a voting rule that gets us closer to the ideal - given that achieving the ideal is impossible. The volume also contains a contextual introduction by social choice scholar Prasanta K. Pattanaik and commentaries from Joseph E. Stiglitz and Kenneth Arrow himself, as well as essays by Sen and Maskin outlining the mathematical proof and framework behind their assertions.