Standards - Mathematics

2019 - Mathematics Course of Study Document
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.22

Analyze advantages and disadvantages of different types of ballot voting systems.

Unpacked Content

Knowledge

Students know:

  • Basic understanding of election methods.

Skills

Students are able to:

  • Discuss advantages and disadvantages of various voting methods.

Understanding

Students understand that:

  • There are a variety of voting systems other than those most frequently used systems and may provide advantages or disadvantages as compared to our current system.

Vocabulary

  • Ranked choice voting or preferential ballot voting
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.23

Apply a variety of methods for determining a winner using a preferential ballot voting system, including plurality, majority, run-off with majority, sequential run-off with majority, Borda count, pairwise comparison, Condorcet, and approval voting.

Unpacked Content

Knowledge

Students know:

  • Basic voting methods such as single choice ballots.

Skills

Students are able to:

  • Interpret data from ranked-choice voting ballots or summarized in preference schedules.
  • Use data to determine an election winner using a variety of methods.
  • Compare and contrast the methods and their results.

Understanding

Students understand that:

  • Various election methods can be used to achieve a group decision from the preferences of the individuals of the group.

Vocabulary

  • Ranked choice voting or preferential ballot voting
  • Plurality winner
  • Majority winner
  • Runoff method
  • Simple majority
  • Sequential runoff (instant runoff) method
  • Borda count
  • Condorcet method
  • Approval voting

Aligned Learning Resources

Racing Around
Rational and Radical Exponents
Rational Exponents and Solving Exponential Equations
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.24

Identify issues of fairness for different methods of determining a winner using a preferential voting ballot and other voting systems and identify paradoxes that can result.

Example: Arrow’s Theorem

Unpacked Content

Knowledge

Students know:

  • How to determine election winners using a variety of methods.

Skills

Students are able to:

  • Discuss the fairness of a voting method based on Arrow’s conditions (Identify how a method may violate one or more of Arrow’s conditions using specific voter preference data)

Understanding

Students understand that:

  • Commonly used group ranking methods are flawed.

Vocabulary

  • Arrow's fairness conditions
  • Arrow's Theorem
  • Condorcet Paradox
  • Paradox
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.25

Use methods of weighted voting and identify issues of fairness related to weighted voting.

Example: determine the power of voting bodies using the Banzhaf power index

Unpacked Content

Knowledge

Students know:

  • How to determine a simple majority.

Skills

Students are able to:

  • Determine each voting body’s power based on their voting weight using the Banzhaf power index.
  • Identify situations that result in unequal distribution of power among voters.

Understanding

Students understand that:

  • Power distribution can vary in weighted-voting situations.
  • High individual voting strength may not result in a high power index.

Vocabulary

  • Weighted voting
  • Power index
  • Voting Coalition
  • Winning coalition
  • Simple majority

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