The Mathematics of Elections and Voting [Paperback]

This title takes an in-depth look at?the mathematics in the context of voting and?electoral systems, with focus on simple ballots, complex elections, fairness,?approval?voting,?ties, fair?and unfair voting, and manipulation techniques. The exposition opens with a sketch of?the mathematics behind the various methods used in conducting elections.?The reader is lead to a comprehensive picture of the theoretical background of mathematics and elections through an analysis of Condorcets?Principle and Arrows Theorem?of conditions in electoral fairness.?Further detailed discussion of various related topics include: methods of manipulating the outcome of an election, amendments, and voting on small committees.

In recent years, electoral theory has been introduced into lower-level mathematics courses, as a way to illustrate the role of mathematics in our everyday life.?Few books have studied voting and elections from a more formal mathematical viewpoint.?This text will be useful to those who teach lower level courses or special topics courses and aims to inspire students to understand the more advanced mathematics of the topic. The exercises in this text are?ideal for upper undergraduate and early graduate students, as well as those with a keen interest in?the mathematics behind voting and elections.

1.Introduction.- 2.Simple Elections I.- 3. Simple Elections II - Condorcet's Method.- 4. Fair Elections; Polls; Amendments.- 5. Arrows Theorem and the Gibbard-Satterthwaite Theorem.- 6. Complex Elections.- 7. Cardinal Systems.- 8. Weighted Voting. References.

From the book reviews:

This concise volume is an introduction to various voting schemes and electoral systems. & the book gives a good picture of the range of voting systems that exist and some of the reasons they are used in certain situations. It is most suitable for undergraduates with some knowledge of combinatorics and proof, who are bel;