UPC: 9783030147679 | Compact Textbooks in Mathematics: The Mathematics of Voting and Apportionment (Paperback)

UPC lookup results for: 9783030147679 | Compact Textbooks in Mathematics: The Mathematics of Voting and Apportionment (Paperback)

This textbook contains a rigorous exposition of the mathematical foundations of two of the most important topics in politics and economics: voting and apportionment at the level of upper undergraduate and beginning graduate students. It stands out among comparable books by providing in one volume an extensive and mathematically rigorous treatment of these two topics. The text s three chapters cover social choice yes-no voting and apportionment respectively and can be covered in any order allowing teachers ample flexibility. Each chapter begins with an elementary introduction and several examples to motivate the concepts and to gradually lead to more advanced material. Landmark theorems are presented with detailed and streamlined proofs; those requiring more complex proofs such as Arrow s theorems on dictatorship Gibbard s theorem on oligarchy and Gärdenfors theorem on manipulation are broken down into propositions and lemmas in order to make them easier to grasp. Simple and intuitive notations are emphasized over non-standard overly complicated symbols. Additionally each chapter ends with exercises that vary from computational to prove or disprove types. The Mathematics of Voting and Apportionment will be particularly well-suited for a course in the mathematics of voting and apportionment for upper-level undergraduate and beginning graduate students in economics political science or philosophy or for an elective course for math majors. In addition this book will be a suitable read for to any curious mathematician looking for an exposition to these unpublicized mathematical applications. No political science prerequisites are needed. Mathematical prerequisites (included in the book) are minimal: elementary concepts in combinatorics graph theory order relations and the harmonic and geometric means. What is needed most is the level of maturity that enables the student to think logically derive results from axioms and hypotheses and intuitively grasp logical notions such as contrapositive and counterexample.