The power to elect officials is the power to change the world , but the mathematics of voting extends far beyond the notion of majorityrule.
This election year, use COMAP materials to explore this fascinating process with your students. The candidate with the most votes wins an election. Simple, right?
Wrong. The whole story has as much to do with voting methods as voting numbers.
This CDROM contain materials that help students address complex questions that are a very real part of our political system.
What is a good way for a group to make a democratic decision?
Mathematical modeling is essential in answering this question. In this unit, which is developed from COMAP’s Mathematics: Modeling Our World curriculum, students:
• Are introduced to mathematical modeling in the engaging context of elections;
• Develop their skills in number sense and percentages;
• Learn about new representations, including preference diagrams and digraphs, and current election reform topics such as instant runoffs and approval voting;
• Use software (for PC and Mac) to conduct their own elections and explore “what if” questions with election data.
A video adds historical (1992 election) and contemporary (Nielsen ratings) background. Supplemental material includes several articles from Consortium on elections and related topics.




Pick a Winner:
Decision
Making in a
Democracy
Student Material 
Teacher's Material 


LESSON ONE:
Two Current
Election Models
Mathematical Modeling
Plurality Models
Majority
Preference Diagram
Graph
Runoff Models

LESSON ONE:
Two Current
Election Models
Mathematical Modeling
Plurality Models
Majority
Preference Diagram
Graph
Runoff Models



LESSON TWO:
Two Alternative
Election Models
Instant Runoff Models
Approval Models

LESSON TWO:
Two Alternative
Election Models
Instant Runoff Models
Approval Models



Review 
Review 
Mathematical Summary 
Mathematical Summary 
Glossary 
Glossary 
Project: Point Models 
Project: Point Models 



Video Support 

Pick a Winner: Decision Making in a Democracy 



Software 

PC 
MAC OSX 
Election Machine 
Election Machine 


Preference Schedule 
Preference Schedule 
Supplemental Material
Apportionment: Measuring Unfairness
Every ten years when the census is taken, the federal government rearranges or reapportions the delegates in the House of Representatives. This reapportionment is designed to give equal representation by assuring that all districts with the same population get equal numbers of representatives. After the 2000 census, the state of Utah sued the federal government arguing that it should be given the delegate that went to the state of North Carolina. What mathematics is behind the apportionment of the House of Representatives, and did Utah have a case?
The Gerrymander Problem: Measuring Compactness
Every ten years, the U.S. House of Representatives is reconfigured according to the results of the U.S. Census. This reconfiguration comes in two distinct stages. The first is the reapportionment of the 435 seats in the House of Representatives. The Everybody’s Problems article “Apportionment: Measuring Unfairness” discussed the mathematical model on which this reapportionment is based.
The ABC's of Point Count Systems
When I have taught the unit on Social Choice, one of the questions that sometimes arises concerns the numbers used in the Borda Count. Everyone agrees that first place deserves more points than second, second more than third, and so forth. We shall call any such a monotone point count system. But, except for purely historical reasons, why do the numbers have to be 5, 4, 3, 2, 1 (or 4, 3, 2, 1, 0 as in more recent editions)?
Scenario: The Mathematics of Presidential Elections
Number notions underlying the election of the president of the United States can be the source of many “what if ” questions. Winning and losing outcomes invariably rest on a straightforward application of the counting process and resulting number comparisons. Such applications may suggest at first glance a simple procedure but on further reflection, this simplicity feature fades away. Is it the popular vote that elects the president, or does some other counting scheme apply? What if no candidate receives a majority of the votes cast? Who makes the decision if certain vote totals are in doubt?
Voting Power
In ordinary elections, each person has a single vote and everyone’s vote has the same power. However, in some situations, some voters have more votes than others.
The electoral college is one example. Presently, North Carolina has 14 votes and Alaska only 3 votes. Shareholders in a company often have the number of votes equal to the number of shares of stock they own.
Polling Pitfalls
In 1936, the famous magazine Literary Digest, distributed over 10 million mailin ballots to assess voter preference for either Franklin Roosevelt or Alfred Landon for President of the United States.
From this survey, the magazine found that 54% of the respondents preferred Alfred Landon and 41% favored Roosevelt. Millions read the prediction that Alfred Landon would defeat Franklin Roosevelt by a wide margin. Instead, Roosevelt won by a landslide, receiving 61% of the vote (Schlesinger). How could such a large survey by a major magazine be so wrong?


