Theory of choice
Author(s)
Bibliographic Information
Theory of choice
（Studies in mathematical and managerial economics, v. 38）
North-Holland, 1995
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Note
Bibliography: p. 307-314
Description and Table of Contents
Description
Choice theory forms the basis for many scientific fields, such as decision making, mathematical models of micro-economics, voting theory, theory of control in socio-economic systems, and some branches of psychology. This volume is a first monograph summing up major scientific results obtained during two decades. The studies presented in the book go beyond the classical approach with a new look at the mathematical theory of choice, taking into account the dependence of choice on the context. The book also provides a new approach to the voting theory, the basis of which forms the description of individual opinions and collective decision as choice functions. The classical approach is shown to be an important but particular case of the developed theory. Students and scientists in economic, social science, decision making and control theory, will find this book of value. The reader does not need special mathematical knowledge as the book uses mainly set-theoretic language.
Table of Contents
Choosing Options. The problem of choosing options. Formal model. Choice Mechanisms and Functions. Properties of choice functions. Pair-dominant mechanisms. Choice by preference relations. Criterion extremization algorithms. Various forms of pair-dominant choice mechanisms. Proofs of theorems. Examples of Choice Mechanisms. Generalization of the concept. Multi-criteria choice mechanisms. Tournament choice. Concluding remarks. Proofs of theorems. Classes of Choice Mechanisms. Non-classical structures (hyper relations). Choice rules on non-classical structures. Classes of choice mechanisms. Some special non-classic choice mechanisms. Proofs of theorems. Operations over Choice Functions. Problem outline. Basic definitions. Closedness of choice function space. Superposition of choice functions. Choice function approximation. Concluding remarks. Proofs of theorems. Voting Theory. Formal statement. Problem outline. Characteristic properties of L-operators. Closedness of domains. Mechanisms generating L-operators. Explicit definition of L-operators. List representation of L operators. Proof of the theorems. Concluding remarks.
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