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assignment Level : Introductory
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timer 7 hours in total

About the content

Learn about different voting methods and fair division algorithms, and explore the problems that arise when a group of people need to make a decision.

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Week 1:  Voting Methods
    The Voting Problem
    A Quick Introduction to Voting Methods (e.g., Plurality Rule, Borda Count,  
          Plurality with Runoff, The Hare System, Approval Voting)    
    The Condorcet Paradox
    How Likely is the Condorcet Paradox?
    Condorcet Consistent Voting Methods
    Approval Voting
    Combining Approval and Preference
    Voting by Grading

Week 2: Voting Paradoxes
    Choosing How to Choose
    Condorcet's Other Paradox
    Should the Condorcet Winner be Elected?
    Failures of Monotonicity
    Multiple-Districts Paradox
    Spoiler Candidates and Failures of Independence
    Failures of Unanimity
    Optimal Decisions or Finding Compromise?
    Finding a Social Ranking vs. Finding a Winner

Week 3: Characterizing Voting Methods
    Classifying Voting Methods
    The Social Choice Model
    Anonymity, Neutrality and Unanimity
    Characterizing Majority Rule
    Characterizing Voting Methods
    Five Characterization Results
    Distance-Based Characterizations of Voting Methods
    Arrow's Theorem
    Proof of Arrow's Theorem
    Variants of Arrow's Theorem

Week 4: Topics in Social Choice Theory
    Introductory Remarks
    Domain Restrictions: Single-Peakedness
    Sen’s Value Restriction
    Strategic Voting
    Manipulating Voting Methods
    Lifting Preferences
    The Gibbard-Satterthwaite Theorem
    Sen's Liberal Paradox

Week 5: Aggregating Judgements
    Voting in Combinatorial Domains
    Anscombe's Paradox
    Multiple Elections Paradox
    The Condorcet Jury Theorem
    Paradoxes of Judgement Aggregation
    The Judgement Aggregation Model
    Properties of Aggregation Methods
    Impossibility Results in Judgement Aggregation
    Proof of the Impossibility Theorem(s)

Week 6: Fair Division 
    Introduction to Fair Division
    Fairness Criteria
    Efficient and Envy-Free Divisions
    Finding an Efficient and Envy Free Division
    Help the Worst Off or Avoid Envy?
    The Adjusted Winner Procedure
    Manipulating the Adjusted Winner Outcome

Week 7:  Cake-Cutting Algorithms
   The Cake Cutting Problem
   Cut and Choose
   Equitable and Envy-Free Proocedures
   Proportional Procedures
   The Stromquist Procedure
   The Selfridge-Conway Procedure
   Concluding Remarks


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