## Political and Related ModelsW.F. Lucas, S.J. Brams, P.D. Jr. Straffin The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modern mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of classroom settings, and all have undergone extensive peer review and revision. Illustrations and exercises are included in most chapters. Some units can be covered in one class, whereas others provide sufficient material for a few weeks of class time. Volume 1 contains 23 chapters and deals with differential equations and, in the last four chapters, problems leading to partial differential equations. Applications are taken from medicine, biology, traffic systems and several other fields. The 14 chapters in Volume 2 are devoted mostly to problems arising in political science, but they also address questions appearing in sociology and ecology. Topics covered include voting systems, weighted voting, proportional representation, coalitional values, and committees. The 14 chapters in Volume 3 emphasize discrete mathematical methods such as those which arise in graph theory, combinatorics, and networks. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

1 | |

2 | |

3 | |

4 | |

5 | |

Process Edward E Packel 6 A Model for Municipal Street Sweeping Operations A C Tucker | 6 |

Bodin 7 Finite Covering Problems Ronald E Prather | 7 |

Combat Models Courtney S Coleman | 8 |

Business Games | 91 |

Notes for the Instructor | 97 |

Environmental Impact StatementEcology | 104 |

Exercises | 132 |

References | 162 |

How To Ask Sensitive Questions without Getting | 169 |

Using the Randomized Response Method and the Unrelated | 177 |

Measuring Power in Weighted Voting Systems | 183 |

The Evolution of a Model | 9 |

Traffic Models 10 How Long Should a Traffic Light Remain Amber? Donald A Drew | 10 |

Queue Length at a Traffic Light via Flow Theory Donald A Drew | 11 |

CarFollowing Models Robert L Baker | 12 |

Equilibrium Speed Distributions Donald A Drew | 13 |

Traffic Flow Theory Donald A Drew | 14 |

Steady States of Nonlinear Systems 15 Why the Percentage of Sharks Caught in the Mediterranean Sea Rose | 15 |

References | 16 |

Courtney S Coleman 17 The Principle of Competitive Exclusion in Population Biology | 17 |

Martin Braun 18 Biological Cycles and the Fivefold Way Courtney S Coleman | 18 |

How Many Cycles? Courtney S Coleman | 19 |

Models Leading to Partial Differential Equations 20 Surge Tank Analysis Donald A Drew | 20 |

Shaking a Piece of String to Rest Robert L Borrelli | 21 |

Heat Transfer in Frozen Soil Gunter H Meyer | 22 |

Network Analysis of Steam Generator Flow T A Porsching | 23 |

6 | 28 |

Summary and Conclusions | 60 |

Modeling Coalitional Values | 66 |

Equitable Users Fees | 84 |

Additional Examples | 195 |

Computational Aids | 214 |

Notes for the Instructor | 224 |

To the Minimal Winning Victors Go the Equally | 239 |

References | 254 |

Appendix | 297 |

Solutions to Selected Exercises | 313 |

References | 319 |

Introduction | 321 |

The Barycenter Model | 329 |

An Example of an Experiment | 336 |

Notes for the Instructor | 345 |

The Apportionment Problem | 358 |

Some Traditional Methods | 367 |

Local Measures of Inequity | 375 |

The Axiomatic Approach | 383 |

The General Apportionment Problem | 389 |

### Other editions - View all

### Common terms and phrases

American Naturalist analysis applied apportionment approval voting assume assumption axioms bandwagon effect behavior binomial bloc Brams calculate candidates cast characteristic function column Condorcet winner consider contest cost cumulative voting denote described differential equations discussed distribution dominant strategy ecological economic election Electoral College environmental estimate example EXERCISES exponential distribution game theory given gives graph theory individual Journal of Theoretical Leslie matrix linear Markov chain Mathematical Models matrix method minimal winning module n-person negative voting number of votes optimal outcome pivots plant players plurality plurality voting Poisson Poisson distribution political pollution population positive vote power indices preference scale presidential probability problem question randomized response runoff Science Section Shapley Shapley value Shapley—Shubik index Shubik simple games situation Straffin subset Theorem Theoretical Biology tion total number undominated vector voters voting strategies voting systems weighted voting game winning coalitions York