LEADER 05329nam 22006495 450 001 9910338247003321 005 20200704014327.0 010 $a3-030-14768-1 024 7 $a10.1007/978-3-030-14768-6 035 $a(CKB)4100000008280631 035 $a(DE-He213)978-3-030-14768-6 035 $a(MiAaPQ)EBC5919740 035 $a(PPN)236523805 035 $a(EXLCZ)994100000008280631 100 $a20190521d2019 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Mathematics of Voting and Apportionment $eAn Introduction /$fby Sherif El-Helaly 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2019. 215 $a1 online resource (XV, 264 p. 27 illus., 2 illus. in color.) 225 1 $aCompact Textbooks in Mathematics,$x2296-4568 311 $a3-030-14767-3 327 $aChapter 1: Social Choice -- Introduction -- Elimination Procedures -- Condorcet Ideas and Related Procedures -- Scoring Procedures: Borda Count -- A Glimpse into Social Welfare Theory -- Social Choice Procedures: Indifference and Ties Allowed -- Manipulability of Social Choice Procedures: Indifference and Ties Allowed -- Exercises -- Chapter 2: Yes-No Voting -- Introduction -- Quantification of Power in a Yes-No Voting System -- Some Combinatorics -- Banzhaf and Shapley-Shubik Indices in One View -- Weightable Yes-No Voting Systems -- Exercises -- Chapter 3: Apportionment -- Introduction -- Axioms of Apportionment -- Quota Procedures -- Divisor Procedures -- Equity Criteria -- Apportionment Paradoxes -- Applications of Priority Formulas -- Exercises. 330 $aThis 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.?. 410 0$aCompact Textbooks in Mathematics,$x2296-4568 606 $aMathematics 606 $aSocial sciences 606 $aGame theory 606 $aWelfare economics 606 $aElections 606 $aMathematics in the Humanities and Social Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M32000 606 $aGame Theory, Economics, Social and Behav. Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13011 606 $aSocial Choice/Welfare Economics/Public Choice/Political Economy$3https://scigraph.springernature.com/ontologies/product-market-codes/W31020 606 $aElectoral Politics$3https://scigraph.springernature.com/ontologies/product-market-codes/911070 615 0$aMathematics. 615 0$aSocial sciences. 615 0$aGame theory. 615 0$aWelfare economics. 615 0$aElections. 615 14$aMathematics in the Humanities and Social Sciences. 615 24$aGame Theory, Economics, Social and Behav. Sciences. 615 24$aSocial Choice/Welfare Economics/Public Choice/Political Economy. 615 24$aElectoral Politics. 676 $a515 676 $a324.650151 700 $aEl-Helaly$b Sherif$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781809 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910338247003321 996 $aThe Mathematics of Voting and Apportionment$92525716 997 $aUNINA