LEADER 03902nam 22005535 450 001 9910789214903321 005 20200920133143.0 010 $a3-642-57748-2 024 7 $a10.1007/978-3-642-57748-2 035 $a(CKB)3400000000104310 035 $a(SSID)ssj0000805267 035 $a(PQKBManifestationID)11504528 035 $a(PQKBTitleCode)TC0000805267 035 $a(PQKBWorkID)10842170 035 $a(PQKB)11521016 035 $a(DE-He213)978-3-642-57748-2 035 $a(MiAaPQ)EBC3089524 035 $a(EXLCZ)993400000000104310 100 $a20121227d1995 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aBasic Geometry of Voting$b[electronic resource] /$fby Donald G. Saari 205 $a1st ed. 1995. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1995. 215 $a1 online resource (XII, 300 p.) 300 $a"With 102 Figures." 311 $a3-540-60064-7 320 $aIncludes bibliographical references and index. 327 $aI. From an Election Fable to Election Procedures -- 1.1 An Electoral Fable -- 1.2 The Moral of the Tale -- 1.3 From Aristotle to ?Fast Eddie? -- 1.4 What Kind of Geometry? -- II. Geometry for Positional And Pairwise Voting -- 2.1 Ranking Regions -- 2.2 Profiles and Election Mappings -- III. The Problem With Condorcet -- 3.1 Why Can?t an Organization Be More Like a Person? -- 3.2 Geometry of Pairwise Voting -- 3.3 Black?s Single-Peakedness -- 3.4 Arrow?s Theorem -- IV. Positional Voting And the BC -- 4.1 Positional Voting Methods -- 4.2 What a Difference a Procedure Makes; Several Different Outcomes -- 4.3 Positional Versus Pairwise Voting -- 4.4 Profile Decomposition -- 4.5 From Aggregating Pairwise Votes to the Borda Count -- 4.6 The Other Positional Voting Methods -- 4.7 Multiple Voting Schemes -- 4.8 Other Election Procedures -- V. Other Voting Issues -- 5.1 Weak Consistency: The Sum of the Parts -- 5.2 From Involvement and Monotonicity to Manipulation -- 5.3 Gibbard-Satterthwaite and Manipulable Procedures -- 5.4 Proportional Representation -- 5.5 House Monotone Methods -- VI. Notes -- VII. References. 330 $aA surprise is how the complexities of voting theory can be explained and resolved with the comfortable geometry of our three-dimensional world. This book is directed toward students and others wishing to learn about voting, experts will discover previously unpublished results. As an example, a new profile decomposition quickly resolves two centuries old controversies of Condorcet and Borda, demonstrates, that the rankings of pairwise and other methods differ because they rely on different information, casts series doubt on the reliability of a Condorcet winner as a standard for the field, makes the famous Arrow`s Theorem predictable, and simplifies the construction of examples. The geometry unifies seemingly disparate topics as manipulation, monotonicity, and even the apportionment issues of the US Supreme Court. 606 $aOperations research 606 $aDecision making 606 $aEconomic theory 606 $aOperations Research/Decision Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/521000 606 $aEconomic Theory/Quantitative Economics/Mathematical Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/W29000 615 0$aOperations research. 615 0$aDecision making. 615 0$aEconomic theory. 615 14$aOperations Research/Decision Theory. 615 24$aEconomic Theory/Quantitative Economics/Mathematical Methods. 676 $a324/.01/516 700 $aSaari$b Donald G$4aut$4http://id.loc.gov/vocabulary/relators/aut$057216 906 $aBOOK 912 $a9910789214903321 996 $aBasic geometry of voting$9911738 997 $aUNINA LEADER 01224nas 2200421 c 450 001 9910894900503321 005 20260218112937.0 024 7 $aurn:nbn:de:bsz:14-ppn2929733578 035 $a(CKB)3790000000118247 035 $a(DE-599)ZDB2471272-3 035 $a(OCoLC)300115015 035 $a(DE-101)991868749 035 $a(DE-599)2471272-3 035 $a(EXLCZ)993790000000118247 100 $a20081217b18781890 |y | 101 0 $ager 135 $aur||||||||a|| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aDingler's polytechnisches Journal$h[...]$iAtlas zu Dingler's polytechnischem Journal 210 31$aStuttgart$cCotta$d1878-1890 210 21$aAugsburg$cCotta$danfangs 215 $aOnline-Ressource 517 1 $aDingler's polytechnisches Journal / Atlas 517 3 $aAtlas zu Dingler's polytechnischem Journal 517 3 $aPolytechnisches Journal 608 $aZeitschrift$2gnd-content 676 $a600 676 $a500 686 $a19,2$2ssgn 801 0$b0014 801 1$bDE-101 801 2$b9999 906 $aJOURNAL 912 $a9910894900503321 996 $aDinglers Polytechnisches Journal$9797738 997 $aUNINA