Title | Political and Related Models [electronic resource] / edited by Steven J. Brams, William F. Lucas, Philip D. Straffin |
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Imprint | New York, NY : Springer New York : Imprint: Springer, 1983 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5430-0 |
Descript | XX, 396 p. online resource |
1. The Process of Applied Mathematics -- 1. Introduction -- 2. Applied Mathematics as a Process -- 3. The Construction and Use of Mathematical Models -- 4. Planetary Motion: The Evolution of a Model -- 5. An Example from Psychology -- 6. Concluding Remarks -- References -- 2. Proportional Representation -- 1. Introduction -- 2. Cumulative Voting -- 3. Single Transferable Vote -- 4. Cumulative Voting with Transfer of Surplus -- 5. Cumulative Voting with Transfer of Surplus and Elimination of Low-Ranking Candidates -- 6. An Illustration of the Use of Cumulative Voting -- 7. STV versus CTV -- References -- Notes for the Instructor -- 3. Comparison Voting -- 1. Preview: Do the Rules of the Game Make a Difference? -- 2. Introduction -- 3. Negative Voting in Two-Candidate Contests -- 4. Negative Voting in Three-Candidate Contests without a Runoff -- 5. Negative Voting in Three-Candidate Contests with a Runoff -- 6. Advantages of Approval Voting -- 7. General Results for Approval Voting -- 8. The Possible Confounding Effects of a Poll -- 9. Approval Voting and Presidential Elections -- 10. Summary and Conclusions -- Solutions to Selected Exercises -- References -- Notes for the Instructor -- 4. Modeling Coalitional Values -- 1. Introduction -- 2. Basic Concepts -- 3. Some Experiments -- 4. Some Pollution Models -- 5. Equitable Userโs Fees -- 6. Economic Markets -- 7. Business Games -- References -- Notes for the Instructor -- 5. Urban Wastewater Management Planning -- 1. Introduction -- 2. Description of the Study Area and the Scenario -- 3. Environmental Engineering Design -- 4. Economic Analysis -- 5. Financial Analysis -- 6. Environmental Impact StatementโEcology -- 7. Public Participation -- 8. Political Science -- 9. Epilogue -- Notes for the Instructor -- 6. An Everyday Approach to Matrix Operations -- 1. Introduction to Vectors and Matrices -- 2. Vector Addition, Subtraction, and Multiplication by Scalars -- 3. Vector Inner Product -- 4. Multiplication of a Matrix and a Vector -- 5. Matrix Addition, Subtraction, and Multiplication -- 6. Properties of Matrix Operations and Special Matrices -- 7. Matrices and Profits -- Exercises -- Reference -- Notes for the Instructor -- 7. Sources of Applications of Mathematics in Ecological and Environmental Subject Areas, Suitable for Classroom Use -- 1. Introduction -- 2. Probability Theory -- 3. Matrix and Linear Algebra -- 4. Calculus -- 5. Differential Equations -- 6. Game Theory -- 7. Graph Theory -- 8. Optimal Control Theory -- 9. Miscellaneous -- References -- 8. How To Ask Sensitive Questions without Getting Punched in the Nose -- 1. Introduction -- 2. Definitions -- 3. The Randomized Response Method -- 4. Unrelated Question Model -- 5. Using the Randomized Response Method and the Unrelated Question Model -- 6. Classroom Suggestions -- 7. Complements and Problems -- Appendix: Randomized Response Survey -- References -- Notes for the Instructor -- 9. Measuring Power in Weighted Voting Systems -- 1. Introduction -- 2. Simple Examples -- 3. Measures in Voting Power -- 4. Additional Examples -- 5. Mini-Projects -- 6. Computational Aids -- 7. The Electoral College -- 8. Additional Voting Problems -- 9. Limits of the Mathematical Models -- References -- Notes for the Instructor -- 10. To the (Minimal Winning) Victors Go the (Equally Divided) Spoils: A New Power Index for Simple n-Person Games -- 1. Introduction -- 2. Power Index Definition and Examples -- 3. Characterization Axioms -- 4. Applications and Limitations -- 5. Concluding Remarks -- Exercises -- References -- Notes for the Instructor -- 11. Power Indices in Politics -- 1. Voting Games and Power Indices -- 2. Using the Power Indices -- 3. Characterizing the Power Indices -- Solutions to Selected Exercises -- References -- Notes for the Instructor -- 12. Committee Decision Making -- 1. Introduction -- 2. Committee Decision-Making Experiment -- 3. Geometric Representation of the Situation -- 4. Utility -- 5. Remarks on Models in Political Science -- 6. The Barycenter Model -- 7. The Pareto Model -- 8. The Core Model -- 9. General Discussion -- 10. The Arrow Theorem -- Appendix I: An Example of an Experiment -- Appendix II: Mathematical Notes -- Notes for the Instructor -- 13. Stochastic Difference Equations with Sociological Applications -- 1. Difference Equation Models -- 2. Review of Probability and Statistics -- 3. Stochastic Difference Equations -- Notes for the Instructor -- 14. The Apportionment Problem -- 1. The Basic Problem -- 2. Some Traditional Methods -- 3. Local Measures of Inequity -- 4. The Axiomatic Approach -- 5. The General Apportionment Problem -- 6. Conclusions -- References