This book was written to teach an accessible and authentic mathematics course to a general audience. Games and elections are ideal topics for such a course. The motivating examples are familiar and engaging: from the 2000 U.S. presidential election, to economic pricing wars, to gambling games such as Poker and Blackjack. The elementary theory of these topics involves manageable computations and emphasizes analytic reasoning skills. Most important, the study of games and elections has produced a wealth of beautiful theorems, many within the last century. Games and elections offer a wide selection of elegant results that can be approached without extensive technical background. A course on these topics provides a view of mathematics as a powerful and thriving modern discipline.

There are excellent texts covering aspects of the theory of games and elections, such as those of Straffin [48] and Taylor and Pacelli [49]. The topics are also frequently covered as chapters in liberal arts mathematics texts. This text is pitched at a level between these two types of treatments. The book is designed to be more mathematically ambitious than the general textbook but to allow for a less demanding course than one offered using a more specialized text.

A novelty of this book is the integrative approach taken to the three subjects: probability theory, game theory, and social choice theory. This approach highlights the mix of ideas occurring in seminal results on games and elections such as the Jury Theorem, the Minimax Theorem, and the Gibbard-Satterthwaite Theorem. On a practical level, the integrative approach allows for a more gradual development of material. Rather than taking a steep descent in one area, the chapters follow a spiraling path from chance to strategy to social choice and back again, exploring examples and developing techniques and intuitions in all areas while delving deeper into the theory of games and elections.

Structure of the Book

This book is divided into three parts. Part I introduces the main devices used in the text.