Fair Voting System Design: A Game Theory Project
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Fair Voting System Design: A Game Theory Project

Grade 12Math3 days
In this project, students design a fair and manipulation-resistant voting system using game theory. They model, analyze, and optimize the system's fairness and efficiency, translating voter preferences into representative outcomes. The project involves quantifying fairness, analyzing strategic voting incentives, and using mathematical models to assess and compare different voting methods, ensuring a fair outcome for all voters.
Game TheoryVoting SystemsFairnessStrategic VotingMathematical ModelsManipulation Resistance
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Inquiry Framework

Question Framework

Driving Question

The overarching question that guides the entire project.How can we design a fair and manipulation-resistant voting system that effectively translates voter preferences into representative outcomes, using game theory to model, analyze, and optimize its fairness and efficiency?

Essential Questions

Supporting questions that break down major concepts.
  • How can game theory be used to model different voting systems?
  • What are the key properties of a fair voting system?
  • How can we quantify fairness in voting systems?
  • How do different voting systems incentivize strategic voting?
  • What are the possible outcomes of different voting systems, and how do they relate to the preferences of the voters?
  • How can we use mathematical models to analyze the fairness and efficiency of different voting systems?
  • How can we design a voting system that is resistant to manipulation and ensures a fair outcome for all voters?

Standards & Learning Goals

Learning Goals

By the end of this project, students will be able to:
  • Understand and apply game theory concepts to voting systems.
  • Identify and evaluate the properties of a fair voting system.
  • Quantify fairness in voting systems using mathematical models.
  • Analyze strategic voting incentives in different voting systems.
  • Predict outcomes of voting systems based on voter preferences.
  • Design a manipulation-resistant voting system.
  • Use mathematical models to assess voting system fairness and efficiency.
  • Effectively translate voter preferences into representative outcomes.
  • Optimize voting systems for fairness and efficiency.
  • Model voting systems using game theory principles.
  • Analyze the fairness and efficiency of different voting systems.
  • Ensure a fair outcome for all voters

Math

MIII.S-1C.A1
Primary
Apply probability concepts to analyze and interpret data.Reason: This standard aligns with the project's need to analyze and interpret data related to voting outcomes and fairness metrics.
MIII.S-1C.A2
Primary
Use statistical reasoning to draw conclusions and make predictions.Reason: This standard supports the project by enabling students to use statistical reasoning to predict outcomes and draw conclusions about the fairness of different voting systems.
MIII.S-1C.B3
Primary
Model and solve problems using mathematical concepts related to fair division.Reason: Directly relevant as the project involves designing a fair voting system, which is fundamentally a fair division problem.
MIII.S-1C.B4
Primary
Apply game theory principles to analyze strategic interactions and decision-making.Reason: Core to the project, as game theory is used to model and analyze voting systems and strategic voter behavior.
MIII.S-1C.B5
Primary
Evaluate and compare different voting methods using mathematical criteria.Reason: Essential for the project, requiring students to assess and compare voting systems based on fairness and efficiency.
MIII.S-1C.B6
Primary
Design and analyze algorithms for fair resource allocation.Reason: Relevant as voting can be seen as a resource allocation problem, where votes are resources allocated to candidates.

Entry Events

Events that will be used to introduce the project to students

The Unexpected Election Twist

A local election produces unexpected results, sparking a school-wide debate on the fairness of the current voting method; students analyze the results and propose alternative systems.
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Portfolio Activities

Portfolio Activities

These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.
Activity 1

Probability in Politics: Analyzing Voting Outcomes

Students will explore basic probability concepts and their application in understanding the likelihood of different voting outcomes. They will calculate probabilities related to voter preferences and election results.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Research basic probability concepts: Students will start by researching and understanding basic concepts of probability, such as sample space, events, and probability calculation.
2. Apply probability to voting scenarios: Students will apply these concepts to voting scenarios, calculating the probability of a specific candidate winning based on different voter preferences.
3. Create a report: Students will create a report summarizing their findings, including example calculations and explanations of how probability applies to voting.

Final Product

What students will submit as the final product of the activityA report summarizing basic probability concepts and their application to voting scenarios, including example calculations.

Alignment

How this activity aligns with the learning objectives & standardsAligns with MIII.S-1C.A1 (Apply probability concepts to analyze and interpret data) and Learning Goal: Understand and apply game theory concepts to voting systems.
Activity 2

Predicting the Future: Statistical Analysis of Elections

Students will use statistical reasoning to analyze voter preferences and predict election outcomes. This involves understanding different statistical methods and their application in predicting results.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Learn statistical methods: Students will learn about different statistical methods, such as regression analysis or hypothesis testing, and how they can be used to predict outcomes.
2. Analyze voter preference data: Students will analyze provided voter preference data using statistical methods to identify trends and patterns.
3. Predict election outcomes: Based on their analysis, students will predict the election outcomes and write a report explaining their reasoning and findings.

Final Product

What students will submit as the final product of the activityA statistical analysis report predicting election outcomes based on provided voter preference data.

Alignment

How this activity aligns with the learning objectives & standardsAligns with MIII.S-1C.A2 (Use statistical reasoning to draw conclusions and make predictions) and Learning Goal: Predict outcomes of voting systems based on voter preferences.
Activity 3

Justice League: Exploring Fair Division in Voting

Students will explore the concept of fair division and its relevance to designing a fair voting system. They will identify and evaluate the key properties of a fair voting system, understanding how these properties contribute to overall fairness.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Research fair division: Students will research the concept of fair division and its applications, understanding how it relates to voting systems.
2. Identify key properties: Students will identify and define the key properties of a fair voting system, such as anonymity, neutrality, and monotonicity.
3. Create a presentation: Students will create a presentation explaining these properties and their importance in ensuring a fair voting system.

Final Product

What students will submit as the final product of the activityA presentation defining and explaining the key properties of a fair voting system.

Alignment

How this activity aligns with the learning objectives & standardsAligns with MIII.S-1C.B3 (Model and solve problems using mathematical concepts related to fair division) and Learning Goal: Identify and evaluate the properties of a fair voting system.
Activity 4

Game of Votes: Strategic Voting Analysis

Students will apply game theory principles to analyze strategic interactions and decision-making in voting systems. They will understand how different voting systems incentivize strategic voting and how this can affect election outcomes.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Learn game theory principles: Students will start by learning about game theory principles, such as Nash equilibrium and dominant strategies.
2. Apply to voting systems: Students will apply these principles to analyze strategic voting in a specific voting system, identifying potential incentives for voters to vote strategically.
3. Create a game theory model: Students will create a game theory model analyzing strategic voting in that system, considering factors such as voter preferences and potential outcomes.

Final Product

What students will submit as the final product of the activityA game theory model analyzing strategic voting in a specific voting system.

Alignment

How this activity aligns with the learning objectives & standardsAligns with MIII.S-1C.B4 (Apply game theory principles to analyze strategic interactions and decision-making) and Learning Goal: Analyze strategic voting incentives in different voting systems.
Activity 5

The Math of Democracy: Comparing Voting Methods

Students will evaluate and compare different voting methods using mathematical criteria. They will learn how to quantify fairness in voting systems using mathematical models and metrics.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Learn evaluation criteria: Students will learn about different mathematical criteria for evaluating voting methods, such as Condorcet criterion and independence of irrelevant alternatives.
2. Apply criteria to methods: Students will apply these criteria to different voting methods, evaluating their strengths and weaknesses based on mathematical analysis.
3. Write a comparative analysis: Students will write a comparative analysis report, evaluating different voting methods using mathematical criteria and fairness metrics.

Final Product

What students will submit as the final product of the activityA comparative analysis report evaluating different voting methods using mathematical criteria and fairness metrics.

Alignment

How this activity aligns with the learning objectives & standardsAligns with MIII.S-1C.B5 (Evaluate and compare different voting methods using mathematical criteria) and Learning Goal: Quantify fairness in voting systems using mathematical models.
Activity 6

Cracking the Code: Designing a Manipulation-Resistant Voting System

Students will design and analyze algorithms for fair resource allocation, focusing on creating a manipulation-resistant voting system. This involves understanding how different algorithms can be used to prevent strategic voting and ensure a fair outcome for all voters.

Steps

Here is some basic scaffolding to help students complete the activity.
1. Research algorithms: Students will research different algorithms for fair resource allocation and their applications in voting systems.
2. Design an algorithm: Students will design an algorithm for a manipulation-resistant voting system, considering factors such as voter preferences and potential outcomes.
3. Analyze effectiveness: Students will analyze the effectiveness of their algorithm, identifying potential vulnerabilities and areas for improvement.

Final Product

What students will submit as the final product of the activityAn algorithm for a manipulation-resistant voting system, along with an analysis of its effectiveness.

Alignment

How this activity aligns with the learning objectives & standardsAligns with MIII.S-1C.B6 (Design and analyze algorithms for fair resource allocation) and Learning Goal: Design a manipulation-resistant voting system.
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Rubric & Reflection

Portfolio Rubric

Grading criteria for assessing the overall project portfolio

Probability in Politics: Analyzing Voting Outcomes Rubric

Category 1

Probability Application and Report Quality

This category assesses the student's understanding and application of basic probability concepts in analyzing voting outcomes. It evaluates the accuracy of calculations, the clarity of explanations, and the overall presentation of the report.
Criterion 1

Probability Calculations and Explanations

Accuracy of probability calculations and explanations related to voting scenarios.

Exemplary
4 Points

Demonstrates precise and accurate probability calculations with thorough explanations, showcasing a deep understanding of probability concepts in the context of voting scenarios.

Proficient
3 Points

Demonstrates mostly accurate probability calculations with clear explanations, showing a good understanding of probability concepts in the context of voting scenarios.

Developing
2 Points

Demonstrates some accurate probability calculations with basic explanations, indicating an emerging understanding of probability concepts in the context of voting scenarios.

Beginning
1 Points

Demonstrates inaccurate probability calculations with unclear or missing explanations, indicating a limited understanding of probability concepts in the context of voting scenarios.

Criterion 2

Report Clarity and Organization

Clarity and organization of the report, including the effective use of examples to illustrate probability applications in voting.

Exemplary
4 Points

Presents a well-structured and exceptionally clear report with highly effective examples that significantly enhance the understanding of probability applications in voting.

Proficient
3 Points

Presents a well-structured and clear report with effective examples that enhance the understanding of probability applications in voting.

Developing
2 Points

Presents a somewhat structured report with examples that provide some understanding of probability applications in voting.

Beginning
1 Points

Presents a poorly structured report with unclear or missing examples, providing little to no understanding of probability applications in voting.

Reflection Prompts

End-of-project reflection questions to get students to think about their learning
Question 1

Reflecting on the entire project, what was the most surprising thing you learned about the challenges and complexities of designing a fair voting system?

Text
Required
Question 2

To what extent do you feel that the mathematical models and game theory principles you applied accurately captured the nuances of real-world voting scenarios?

Scale
Required
Question 3

If you could revisit one aspect of your voting system design, what would it be and why?

Text
Required
Question 4

Which portfolio activity (Probability in Politics, Predicting the Future, Justice League, Game of Votes, The Math of Democracy, Cracking the Code) contributed the most to your understanding of fair voting systems, and why?

Multiple choice
Required
Options
Probability in Politics: Analyzing Voting Outcomes
Predicting the Future: Statistical Analysis of Elections
Justice League: Exploring Fair Division in Voting
Game of Votes: Strategic Voting Analysis
The Math of Democracy: Comparing Voting Methods
Cracking the Code: Designing a Manipulation-Resistant Voting System