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Arrow Impossibility Theorems
1st Edition - January 1, 1978
Author: Jerry S. Kelly
Editor: Karl Shell
9 7 8 - 1 - 4 8 3 2 - 7 1 2 6 - 2
Arrow Impossibility Theorems is a 10-chapter text that describes existing impossibility theorems. This book explores a number of formalizations of ethical constraints of the… Read more
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Arrow Impossibility Theorems is a 10-chapter text that describes existing impossibility theorems. This book explores a number of formalizations of ethical constraints of the theorems. After an introduction to the framework and notation for Arrow impossibility theorems, this book goes on discussing some concepts and an apparatus of relations among those concepts which are important for the theorems. Other chapters present some impossibility results that serve to point out serious difficulties in some plausible escape routes from the theorems of earlier chapters. The final chapter describes important areas of research that have arisen in the collective choice field in the transition away from studying the conditions of Arrow's theorem alone to the totality of all impossibility theorems. This book is intended primarily for economists.
PrefaceAcknowledgmentsIntroduction1 Framework2 Decisiveness3 Simplicity: Conditions4 Simplicity: Impossibility Theorems5 Conditional Decisiveness6 Strategy-Proofness7 Domain: Part I8 Domain: Part II9 Rights Exercising10 Unsolved ProblemsMathematical Appendix A. Logic B. Sets C. Relations and Functions D. Integers E. Zorn's Lemma F. Notation NoteSelected Bibliography and ReferencesAuthor IndexSubject Index