MATH 275 Mathematics in Politics II
This course, intended for liberal arts students, explores the mathematics involved in political concepts and applications. We use an intuitive approach to social welfare theory including the concepts of independence of irrelevant alternatives, collective rationality, the axioms and the impossibility theorem of Kenneth Arrow, the possibility theorem of Duncan Black, and manipulation of social welfare functions; yes/no voting including a unified approach to Banzhaf and Shapley-Shubik power indices and dimension of a yes-no voting system; apportionment of the seats of the House of Representatives with a focus on the equity criteria of different apportionment procedures. Throughout the course, the presentation will be more intuitive than technical in order to suit liberal arts students. No background in algebra, calculus, statistics or geometry is required.