Index

Discrete Mathematics Project
Election Theory Activity

Title

How Will You Be Evaluated? (Dominic D. Peressini)

Goals

  1. Students will begin to explore the concept of group-ranking as it relates to election theory.
  2. Students will work in small groups in order to arrive at a consensual group-ranking and be able to explain, and justify, how they arrived at this group-ranking to the rest of the class

Abstract

This activity, which is set in the context of having students vote on how their performance will be evaluated for a particular class, focuses on group-ranking. Students are asked to individually determine a rank-ordering of how the five requirements for their class should be weighted. These individual preferences are then tallied, and the students are asked to determine one rank-ordering for the entire class. This activity could be used to introduce Election Theory, and in particular, group-ranking.

Problem Statement

Let students know that as you planned for a class, you thought that it would be nice to come to a group consensus regarding how students' performance in the class would be evaluated. Consequently, you have not yet determined the weighting of the course requirements (assignments). Now as a class, you need to determine the importance of each requirement and weight it accordingly. The first step in determining these weights will be to vote on the rank-order of the assignments.

Instructor Suggestions

  1. Set the stage by discussing the "Problem Statement" (see above) with your students.
  2. Distribute the "How Will You Be Evaluated?" activity sheet and allow the students to individually read and complete the first part of the activity.
  3. When all of the students are finished, have each students write their preference on the board.
  4. After all of the preferences have been recorded, have the students form small-groups and determine a class ranking based on the individual rankings.
  5. When the small-groups are finished, have a spokesperson for each group share their preference and explain their method and reasoning involved in arriving at their ranking.
  6. Discuss the students work as it relates to rank-ordering.

Materials

"How Will You Be Evaluated?" activity sheet, chalk- or dry-erase board.

Time

Introduction of Problem Statement (5 min.), individual work (5 min.), small-group work (20 min.), presentation of small-group work and large-group discussion (15 min.)

Mathematics Concepts

Discrete Mathematics Concepts

Group-Ranking, Plurality Winner, Majority Winner, Borda Method, Runoff Method, Sequential Runoff Method, Condorcet Method (paradox), Arrow's Conditions, Recurrence Relations

Related Mathematics Concepts

Matrices, Sequences and Series

NCTM Standards Addressed

Problem Solving, Communication, Reasoning, Connections (within mathematics and across disciplines), Algebra, Geometry, Discrete Mathematics

Colorado Model Content Standards Addressed

Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

This activity could be integrated
  1. into a traditional Advanced Algebra or Pre-Calculus class when the topics of sequences and series are examined--the focus would be on sequences and series as recurrence relations and how these relations can be used to represent possible preference schedules. The activity could also be integrated
  2. into an Algebra or Geometry class as the topic of Matrices, and their related operations, are examined--this integration would be bridged by the application of matrix modeling in order to apply Borda's method.

Further Investigation

This activity could also be extended by asking students to determine the actual weights of each assignment after the class preference has been determined.

Variations/Comments:

The students could form small groups before they put their preferences on the board -- this would allow one person from each group to tally their groups' preferences and then put them on the board.
Send your variations and comments to this Web page's editor

References and Related Web Links:

Brams, S. J. (1983). Approval voting. Boston: Birkhauser.

Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W. H. Freeman and Company.

Kenney, M. J., & Hirsch, C. R. (Eds.). (1991). Discrete mathematics across the curriculum, K-12. Reston. VA: National Council of Teachers of Mathematics.

Lum, L., & Kurtz, D. C. (1989). Voting made easy: A mathematical theory of election procedures. Greensboro, NC: Guilford Press.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

Last updated November 22, 1996