Mathematics and elections, paradoxes and electoral problems

Mathematics has remarkable applications, not only in natural sciences, as well known, but also in social sciences. In this paper we shall analyze electoral and social choice systems from a mathematical point of view, paying particular attention to the paradoxical and inevitable aspects appearing in choice problems, which are emphasized by the use of mathematics. In the past these applications of mathematics in social sciences have led to Nobel prizes in economy. These subjects are an area of research which is nowadays still alive