Title
Where will the Denver Broncos play? (October Crowell)
Goals
1. Students will employ and justify a method for a consensual weighted voting system and apply Arrow's Conditions to their method.
2. Students will expand their knowledge of approval voting and weighted voting.
Abstract
This activity asks students to design a fair weighted voting system to determine the location of a new Denver Broncos stadium somewhere in the metro area. It is intended to be used after students have been introduced to the concepts of approval voting, coalitions and power indices.
Problem Statement
Let students know that the decision to place a new stadium can be very controversial and is struggled with by businesspersons as well as citizens in Denver. Discuss with students that they will be examining different ways to arrive at a decision for the location of the stadium with the fairness of the voting system at the focus of the activity.
Instructor Suggestions
1. Introduce the activity by discussing the "Problem statement" (see above) with the students.
2. Distribute the "Where will the Denver Broncos play" activity sheet (see attachments) and allow the students to read and review it.
3. Have the students form small groups and devise a weighted voting system that they believe is fair, and be able to explain and justify this system to the class.
4. When the groups are finished, have a spokesperson for each group present their system and explain its fairness.
5. Discuss the commonalties and differences of the systems in terms of approval voting concepts and Arrow's Conditions.
Materials
"Where will the Denver Broncos play?" activity sheet, chalk or overhead projector.
Time
Activity Introduction (5 minutes), Small group work (20 minutes), Group presentations and large group reflection (20 minutes)
Mathematics Concepts
Discrete Mathematics Concepts
Fairness, Approval Voting, Arrow's Conditions, Weighted Voting, Winning Coalitions, Power Index.
Related Mathematics Concepts
Ratio, Percent, Matrices, Permutations and Combinations.
NCTM Standards Addressed
Problem Solving, Communications, Reasoning, Connections, Algebra, Discrete Mathematics.
Colorado Model Content Standards Addressed
Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be integrated into an Algebra class when the topics ratio or matrices are examined. It could also be used in and Advanced Algebra class as a connected activity to permutations and combinations related to listing the winning coalitions.
Further Investigation
This activity can be extended by pinpointing a specific location for the stadium through an investigation into election theory within a particular city.
Variations/Comments
Other factors in the demographics could be included such as area, age factors, and sports preferences. In addition this activity could be used in conjunction with an internet project to search for demographic information and area maps.
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics across the curriculum, K-12. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
Census data for Colorado, 4/1/1990, by town