The course aims to illustrate the mathematical theory of electoral processes and apportioment systems.
Course Prerequisites
Main concepts of the basic courses of the Undergraduate program in Mathematics.
Teaching Methods
Lezioni in aula
Assessment Methods
Written and oral exam. The written exam is aimed to test the knowledge of the main voting systems and apportionment methods by solving problems. The written exams explores the critical understanding by the student of the techniques employed in proving the theorems proved during the course
Texts
D.G. Saari: "The Geometry of Voting". Springer (1994) S. El-Helaly: "The Mathematics of Voting and Apportionment". Birkhauser (2019) Teacher's Lecture Notes
Contents
Social choice functions. Axiomatic systems for elections. Arrow's theorem. Gibbard-Satterrtwaite's theorem and the manipulability of elections. Voting paradoxes and their geometric analysis. Basic properties of the main voting systems: plurality vote, Condorcet's tournaments, Borda's method. Ballots. Axioms for apportionment and related paradoxes: Alabama paradox, population paradox. Double-proportional apportionments. Voting methods and gerrymandering.
