Various Condorcet consistent social choice functions based on majority rule (tournament solutions) are considered in the general case, when ties are allowed: the core, the weak and strong top cycle sets, versions of the uncovered and minimal weakly stable sets, the uncaptured set, the untrapped...

Based on the leximin and leximax preferences, we consider two threshold preference relations on the set X of alternatives, each of which is characterized by an n-dimensional vector (n ≥ 2) with integer components varying between 1 and m(m ≥ 2). We determine explicitly in terms of binomial...

A classically rational subject is a maximiser: he chooses the best alternative(s) according to some utility function, a paradigm going back to the eighteenth century. One of the ways to overcome its well-known deficiences is to extend it to take into account insenitivity threshold as well as the...

We study a problem of individual manipulation in an impartial culture (IC) framework using computer modeling. We estimate the degree of manipulability of ten positional voting rules in the case of multiple choice for 3 and 4 alternatives. -- manipulability ; positional voting rules ; multiple...

The utility maximization paradigm forms the basis of many economic, psychological, cognitive and behavioral models. However, numerous examples have revealed the deficiencies of the concept. This book helps to overcome those deficiencies by taking into account insensitivity of measurement...

Some Basic Concepts -- Vectors and Matrices -- Square Matrices and Determinants -- Inverse Matrix -- Systems of Linear Equations -- Linear Spaces -- Euclidean Spaces -- Linear Transformations -- Eigenvectors and Eigenvalues -- Linear Model of Production in a Classical Setting -- Linear...