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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.