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The strategy of social choice. (English) Zbl 0543.90002

Advanced Textbooks in Economics, Vol. 18. Amsterdam - New York - Oxford: North-Holland Publishing Company. XI, 214 p. $ 27.50; Dfl. 75.00 (1983).
The book is devoted to a relatively new field of group decision theory - strategic aspects of voting. The author made a nice job surveying the fast growing literature on strategy-proofness, implementation of the social choice rules, non-cooperative and cooperative stability of voting methods, etc. Many of the strategic notions for social choice appear in the monographic predecessors of the volume of P. Pattanaik [”Strategy and group choice” (1978; Zbl 0408.90003)] and B. Peleg [”Game theoretic analysis of voting in committees”, Inst. Math., Hebrew Univ. Jerusalem (1980)] however, the book under review is the most complete and modern thematically and presents a unified theory of strategic group decisions. Of course, a concentrate of traditional non- strategic social choice theory also appears in the book to make it self- contained.
The contents is as follows. In Chapter 1, ”Introduction”, problems of and literature on strategic group decisions is surveyed. Chapters 2 and 3, ”Social choice functions and correspondences”, and ”Monotonicity and the Arrow theorem”, concern the non-strategic social choice fundamental axioms and traditional or less traditional rules. Chapter 4 ”Strategy- proofness and monotonicity” introduces the game forms, strategy proofness, and the main existence theorems. The implementation mechanisms for the case of complete information and non-cooperative society are considered in Chapter 5, ”Sophisticated voting”. The case of cooperative mechanisms appear on the last two chapters. A few partial veto voting rules are studied in Chapter 6, ”Voting by veto”. Chapter 7, ”Cooperative voting”, is devoted to a general analysis of cooperative voting in which the voting by veto plays a substantial role. Here effectivity functions, cooperative stability, inclusion minimal strongly monotonicity and other notions are investigated.
The main text of the book contains rather general concepts and results, however, many interesting particular results appear as problems. The book seems most appropriate for use in a course on social choice theory and/or public choice for graduate students.
Reviewer: E.Vilkas

MSC:

91B14 Social choice
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
91A40 Other game-theoretic models

Citations:

Zbl 0408.90003