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.

COS Examples

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
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