On Some Concept Lattice of Social Choice Functions

Social choice function or voting procedure is one of the crucial concepts in the domain of political sciences. It maps individuals' preferences over a set of candidates to some subset (possibly one-element) of the candidates who can be thought as the winners of an election procedure. The paper is aimed at applications of formal concept analysis methods to study of social choice functions. We will construct concept lattices over selected set of social choice functions characterized by possessing some properties deemed as important from the point of view of political sciences. We will discuss issues connected with reducibility of both objects and attributes, irreducibility of object concepts as well as attribute concepts and attribute implications. We will discuss also the shape of the constructed concept lattice of social choice functions which in some part is exceptionally regular from the perspective of the lattice theory.