“The arithmetic of the electoral reforms” served as the subject of the third public lecture in the series Frontiere jointly organized this year by ICTP, Immaginario Scientifico and the Department of Mathematics and Informatics at the University of Trieste. Marco Li Calzi, professor of mathematics at the University Ca’ Foscari in Venice, spoke on the crucial role played by mathematics in determining the number of seats that would likely be available for representatives of congress and parliament based on a nation’s population and the way in which a government chooses to divide its political districts. He focused on the situation in both the United States and in Italy. The lecture took place at the University of Trieste.