000890837 000__ 04645cam\a2200481Ki\4500
000890837 001__ 890837
000890837 005__ 20230306150124.0
000890837 006__ m\\\\\o\\d\\\\\\\\
000890837 007__ cr\cn\nnnunnun
000890837 008__ 190606s2019\\\\sz\\\\\\ob\\\\001\0\eng\d
000890837 019__ $$a1103467505$$a1105623165
000890837 020__ $$a9783030147686$$q(electronic book)
000890837 020__ $$a3030147681$$q(electronic book)
000890837 020__ $$z3030147673
000890837 020__ $$z9783030147679
000890837 0247_ $$a10.1007/978-3-030-14$$2doi
000890837 035__ $$aSP(OCoLC)on1105179295
000890837 035__ $$aSP(OCoLC)1105179295$$z(OCoLC)1103467505$$z(OCoLC)1105623165
000890837 040__ $$aLQU$$beng$$erda$$epn$$cLQU$$dGW5XE$$dYDX$$dSTF$$dYDXIT$$dGZM$$dOCLCF$$dYDXIT$$dUKMGB
000890837 049__ $$aISEA
000890837 050_4 $$aJF1001$$b.E44 2019
000890837 08204 $$a324.650151$$223
000890837 1001_ $$aEl-Helaly, Sherif,$$eauthor.
000890837 24514 $$aThe mathematics of voting and apportionment :$$ban introduction /$$cSherif El-Helaly.
000890837 264_1 $$aCham, Switzerland :$$bBirkhäuser,$$c[2019]
000890837 300__ $$a1 online resource :$$billustrations
000890837 336__ $$atext$$btxt$$2rdacontent
000890837 337__ $$acomputer$$bc$$2rdamedia
000890837 338__ $$aonline resource$$bcr$$2rdacarrier
000890837 4901_ $$aCompact Textbooks in Mathematics
000890837 504__ $$aIncludes bibliographical references and index.
000890837 5050_ $$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.
000890837 506__ $$aAccess limited to authorized users.
000890837 520__ $$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 texts 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 Arrows theorems on dictatorship, Gibbards 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, an d intuitively grasp logical notions such as "contrapositive" and "counterexample."
000890837 588__ $$aDescription based on online resource; title from digital title page (viewed on June 28, 2019).
000890837 650_0 $$aVoting$$xMathematics.
000890837 650_0 $$aApportionment (Election law)$$xMathematics.
000890837 77608 $$iPrint version$$z3030147673$$z9783030147679$$w(OCoLC)1084331879
000890837 830_0 $$aCompact textbooks in mathematics.
000890837 85280 $$bebk$$hSpringerLink
000890837 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-030-14768-6$$zOnline Access$$91397441.1
000890837 909CO $$ooai:library.usi.edu:890837$$pGLOBAL_SET
000890837 980__ $$aEBOOK
000890837 980__ $$aBIB
000890837 982__ $$aEbook
000890837 983__ $$aOnline
000890837 994__ $$a92$$bISE