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Band 3

Geometry of Voting

Aus der Reihe Studies in Economic Theory

98,99 €

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Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

18.04.2012

Verlag

Springer Berlin

Seitenzahl

372

Maße (L/B/H)

24,4/17/2,2 cm

Gewicht

681 g

Auflage

Softcover reprint of the original 1st ed. 1994

Sprache

Englisch

ISBN

978-3-642-48646-3

Beschreibung

Produktdetails

Einband

Taschenbuch

Erscheinungsdatum

18.04.2012

Verlag

Springer Berlin

Seitenzahl

372

Maße (L/B/H)

24,4/17/2,2 cm

Gewicht

681 g

Auflage

Softcover reprint of the original 1st ed. 1994

Sprache

Englisch

ISBN

978-3-642-48646-3

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Geometry of Voting
  • Produktbild: Geometry of Voting
  • I. From an Election Fable to Election Procedures.- 1.1 An Electoral Fable.- 1.1.1 Time for the Dean.- 1.1.2 The Departmental Election.- 1.2 The Moral of the Tale.- 1.2.1 The Basic Goal.- 1.2.2 Other Political Issues.- 1.2.3 Strategic Behavior.- 1.2.4 Some Procedures Are Better than Others.- 1.3 From Aristotle to “Fast Eddie”.- 1.3.1 Selecting a Pope.- 1.3.2 Procedure Versus Process.- 1.3.3 Jean-Charles Borda.- 1.3.4 Beyond Borda.- 1.4 What Kind of Geometry.- 1.4.1 Convexity and Linear Mappings.- 1.4.2 Convex Hulls.- II. Geometry for Positional and Pairwise Voting.- 2.1 Ranking Regions.- 2.1.1 Normalized Election Tally.- 2.1.2 Ranking Regions.- 2.1.3 Exercises.- 2.2 Profiles and Election Mappings.- 2.2.1 The Election Mapping.- 2.2.2 The Geometry of Election Outcomes.- 2.2.3 Exercises.- 2.3 Positional Voting Methods.- 2.3.1 The Difference a Procedure Makes.- 2.3.2 An Equivalence Relationship for Voting Vectors.- 2.3.3 The Geometry of w
    s
    Outcomes.- 2.3.4 Exercises.- 2.4 What a Difference a Procedure Makes; Several Different Outcomes.- 2.4.1 How Bad It Can Get.- 2.4.2 Properties of Sup(p).- 2.4.3 The Procedure Line.- 2.4.4 Using the Procedure Line.- 2.4.5 From Procedure Lines to Scoring Shells.- 2.4.6 Scoring Shell Geometry.- 2.4.7 Robustness of the Paradoxical Assertions.- 2.4.8 Proofs.- 2.4.9 Exercises.- 2.5 Why Can’t an Organization Be More Like a Person?.- 2.5.1 Pairs and the Irrational Behavior of Organizations.- 2.5.2 Confused, Irrational Voters.- 2.5.3 Information Lost from Pairwise Majority Voting.- 2.5.4 Geometry of Pairwise Voting.- 2.5.5 The Geometry of Cycles.- 2.5.6 From Group Coordinates to Profile Restrictions.- 2.5.7 Black’s Conditions for Avoiding Cycles.- 2.5.8 Spatial Voting.- 2.5.9 Extensions of Black’s Condition.- 2.5.10 Condorcet Winners and Losers.- 2.5.11 A Condorcet Improvement.- 2.5.12 Exercises.- 2.6 Positional Versus Pairwise Voting.- 2.6.1 Comparing Votes with a Fat Triangle.- 2.6.2 Positional Group Coordinates.- 2.6.3 Profile Sets.- 2.6.4 Some Comparisons.- 2.6.5 How Likely Is It?.- 2.6.6 How Varied Does It Get?.- 2.6.7 Procedures Lines and Cyclic Coordinates.- 2.6.8 Exercises.- III. From Symmetry to the Borda Count and Other Procedures.- 3.1 Symmetry.- 3.1.1 Partial Orbits and Intensity of Comparisons.- 3.1.2 Neutrality.- 3.1.3 Reversal of Fortune.- 3.1.4 Reversal Geometry.- 3.1.5 Back to the Procedure Line.- 3.1.6 Reversal Bias Paradoxes.- 3.1.7 Borda Symmetry.- 3.1.8 Exercises.- 3.2 From Aggregating Pairwise Votes to the Borda Count.- 3.2.1 Borda and Aggregated Pairwise Votes.- 3.2.2 Geometric Representation.- 3.2.3 The Borda Dictionary.- 3.2.4 Borda Cross-Sections.- 3.2.5 The BC Cyclic Coordinates.- 3.2.6 The Borda Vector Space.- 3.2.7 Exercises.- 3.3 The Other Positional Voting Methods.- 3.3.1 What Can Accompany a F3 Tie Vote?.- 3.3.2 A Profile Coordinate Representation Approach.- 3.3.3 What Pairwise Outcomes Can Accompany a w
    s
    Tally?.- 3.3.4 Probability Computations.- 3.3.5 Exercises.- 3.4 Multiple Voting Schemes.- 3.4.1 From Multiple Methods to Approval Voting.- 3.4.2 No Good Deed Goes Unpunished.- 3.4.3 Comparisons.- 3.4.4 Averaged Multiple Voting Systems.- 3.4.5 Procedure Strips.- 3.4.6 Exercises.- 3.5 Other Election Procedures.- 3.5.1 Other Procedures.- 3.5.2 Ordinal Procedures.- 3.5.3 Scoring Runoffs.- 3.5.4 Comparisons of Positional Outcomes.- 3.5.5 Plurality or a Runoff?.- 3.5.6 Cardinal Procedures.- 3.5.7 Exercises.- IV. Many Profiles; Many New Paradoxes.- 4.1 Weak Consistency: The Sum of the Parts.- 4.1.1 Other Uses of Convexity.- 4.1.2 An L of an Agenda.- 4.1.3 Condorcet Extensions.- 4.1.4 Other Pairwise Procedures.- 4.1.5 Maybe “if’s ” and “and’s”, but no “or’s” or “but’s”.- 4.1.6 A General Theorem.- 4.1.7 Exercises.- 4.2 From Involvement and Monotonicity to Manipulation.- 4.2.1 A Profile Angle.- 4.2.2 Positively Involved.- 4.2.3 Monotonicity.- 4.2.4 A General Theorem Using Profiles.- 4.2.5 Other Admissible Directions.- 4.2.6 Gibbard-Satterthwaite and Manipulable Procedures.- 4.2.7 Measuring Suspectibility to Manipulation.- 4.2.8 Exercises.- 4.3 Proportional Representation.- 4.3.1 Hare and Single Transferable Vote.- 4.3.2 The Apportionment Problem.- 4.3.3 Something Must Go Wrong — Alabama Paradox.- 4.3.4 A Better Improved Method?.- 4.3.5 More Surprises, but not Problems.- 4.3.6 House Monotone Methods.- 4.3.7 Unworkable Methods.- 4.3.8 Who Cares About Quota?.- 4.3.9 Big States, Small States.- 4.3.10 The Translation Bias.- 4.3.11 Sliding Bias.- 4.3.12 If the State of Washington Had Only 836 More People.- 4.3.13 A Solution.- 4.3.14 Exercises.- 4.4 Arrow’s Theorem.- 4.4.1 A Sen Type Theorem.- 4.4.2 Universal Domain and IIA.- 4.4.3 Involvement and Voter Responsiveness.- 4.4.4 Arrow’s Theorem.- 4.4.5 A Dictatorship or an Informational Problem?.- 4.4.6 Elementary Algebra.- 4.4.7 The $${F_{{c_i},{c_j}}}$$ Level Sets.- 4.4.8 Some Existence Theorems.- 4.4.9 Intensity IIA.- 4.4.10 Exercises.- 4.5 Characterizations of Scoring, Positional and Borda.- 4.5.1 Strong and Weak Consistency.- 4.5.2 Characterization of Scoring Rules.- 4.5.3 Positional Voting Methods.- 4.5.4 Axiomatic Characterizations of the BC.- 4.5.5 Generalized Positional Voting.- 4.5.6 Exercises.- Notes.- References.