Theory of choice

Abstract

Part 1 Choosing options: the problem of choosing options formal model. Part 2 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. Part 3 Examples of choice mechanisms: generalization of the concept multi-criteria choice mechanisms tournament choice concluding remarks proofs of theorems. Part 3 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. Part 5 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. Part 6 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 theorems concluding remarks.

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