Is Democracy Fair?

The Mathematics of Voting and Apportionment

Use Elections to Explore Mathematics
How do you know if an election result is fair? Or if the result truly represents the choice of the people? In this unique activity book, students are given a fascinating opportunity to learn and experiment with mathematical methods to explore different kinds of ballots, election decision procedures, and apportionment methods. And you have a golden chance to team with teachers in history, civics, and other social studies to demystify and bring to life the realities and responsibilities of living in a democracy.

Students Explore the Math and the History of Political Representation
In the first half of Is Democracy Fair?, students are introduced to a variety of alternatives to the "winner take all" strategy used in many elections. Determining which strategy is the fairest is usually a very difficult question to answer, and many times the strategy chosen determines the winner.

In the second part of the book, students investigate different methods of apportionment. How many representatives from each state will there be in the United States House of Representatives? How do countries using a proportional representation system decide on the number of representatives from each political party to be seated in their government bodies? It this a political or a mathematical decision? Or, is it both?

Enrich Your Students with a Host of Activities
The book does an exemplary job of integrating historical material, including historical events and the famous figures involved in them, into the mathematical coverage. Throughout the book, students encounter research questions related to voting, apportionment, and historical figures. Although all activities can be done with a four-function or scientific calculator, the book provides calculator extensions and programs for graphing calculators, plus computer techniques. An outline for a long-term student research project about voting and apportionment in another country also is included.

A Mathematics Adventure Inspired by Recent Historical Events
Michael de Villiers, co-author of Is Democracy Fair?, was inspired to draft this book by recent events in his home country of South Africa, where he teaches mathematics at the University of Durban-Westville. As he watched his country emerge from apartheid and, in its formative democratic stage, struggle with deciding on the "best" systems of voting and apportionment, de Villiers gave great thought to the many options that exist and to the role mathematics plays in political representation. The book that resulted from these firsthand observations has three objectives:

  • To demonstrate to secondary school students how mathematics applies to the analysis of problems in the seemingly non-mathematical areas of social and political science
  • To challenge the stereotype that mathematics is of value only in certain applied sciences, such as physics, chemistry, and computer science
  • To raise students' voter education awareness by exposing them to a variety of election decision procedures and their strengths and weaknesses

De Villiers' co-author, Leslie Johnson Nielsen, developed the book further, bringing to it another broad perspective. Experienced in teaching mathematics to both high school and middle school students in the United States, Nielsen now teaches elementary school in Denmark.

Grades 7-12


Is Democracy Fair? The Mathematics of Voting and Apportionment, 120 pp





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