Political and Related Models

Front Cover
W.F. Lucas, S.J. Brams, P.D. Jr. Straffin
Springer Science & Business Media, Mar 13, 2013 - Business & Economics - 396 pages
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.
 

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Contents

The Process of Applied Mathematics
1
Saaty 2 Five Natutical Models Roberts L Baker
2
An Optimal Inventory Policy Model Oswaldo Marrero
3
An Arithmetic Model of Gravity Donald Greenspan
4
FourWay Stop or Traffic Lights? An Illustration of the Modeling
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
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About the author (2013)

Steven J. Brams is professor of politics at New York University.

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