Wulf Gaertner provides a comprehensive account of an important and complex issue within social choice theory: how to establish a social welfare function while restricting the spectrum of individual preferences in a sensible way. Gaertner's starting point is K. J. Arrow's famous 'Impossibility Theorem', which showed that no welfare function could exist if an unrestricted domain of preferences is to be satisfied together with some other appealing conditions. A number of leading economists have tried to provide avenues out of this 'impossibility' by restricting the variety of preferences: here, Gaertner provides a clear and detailed account, using standardized mathematical notation, of well over forty theorems associated with domain conditions. Domain Conditions in Social Choice Theory will be an essential addition to the library of social choice theory for scholars and their advanced graduate students.
• A most comprehensive survey of literature, covering over 100 theorems • Uses standardized mathematical notation • Work quoted by Amartya Sen in his Nobel Prize acceptance speech
Preface and acknowledgements; 1. Introduction; 2. Notation, definitions and two fundamental theorems; 3. The existence of collective choice rules under exclusion conditions for finite sets of discrete alternatives; 4. Arrovian social welfare functions, nonmanipulable voting procedures and stable group decision functions; 5. Restrictions on the distribution of individuals' preferences; 6. The existence of social choice rules in n-dimensional continuous space; 7. Concluding remarks; 8. References; Indexes.
'The domain conditions in social choice theory have a history of about half a century, going back to the classic paper of Duncan Black published in 1948. Over this period, a large number of writers have explored various aspects of the subject. Gaertner's survey provides an exceptionally lucid and comprehensive account of this diverse literature. Gaertner's exposition brings out the major intuitive themes in a very clear fashion, while paying meticulous attention to the technical details of individual results. Readers in search of an introduction to the literature, as well as researchers looking for an authoritative book of reference on the subject, should find the book very helpful.' Prasanta K. Pattanaik, University of California, Riverside
'Wulf Gaertner's monograph surveys the wide-ranging literature on domain restrictions in social choice theory. In a field where impossibility theorems abound, it is a refreshing change to see Gaertner's focus on what is possible if there are limits to the heterogeneity of individual preferences. Specialists will find this volume to be a handy compendium of what is known about the subject. By eschewing proofs, Gaertner has also made a rather technical subject accessible to the non-specialist.' John A. Weymark, Vanderbilt University
'The author had to encompass a very large number of results, coming from very diverse sources, and using a wide variety of techniques. He has managed to do this beautifully.' Journal of Economics
'… a perfect guide for any researcher who needs to know more about the preferences restriction in social choice theory … Although this field is considered as a difficult area in social choice theory, Gaertner made a wonderful job at presenting and illustrating the main results …' Social Choice and Welfare
'Domain Conditions in Social Choice Theory is an interesting and valuable book. It will be an essential addition to the library of social choice theory scholars and their graduate students. The most relevant results and theorems on the subject are included an proofs are easy to follow. This well-written monograph will be an excellent reference for researchers interested in domain restrictions in social choice theory.' Public Choice