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# Making Better Group Decisions: Voting, Judgement Aggregation and Fair Division

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## Overview

Much of our daily life is spent taking part in various types of what we might call “political” procedures. Examples range from voting in a national election to deliberating with others in small committees. Many interesting philosophical and mathematical issues arise when we carefully examine our group decision-making processes.

There are two types of group decision making problems that we will discuss in this course. A voting problem: Suppose that a group of friends are deciding where to go for dinner. If everyone agrees on which restaurant is best, then it is obvious where to go. But, how should the friends decide where to go if they have different opinions about which restaurant is best? Can we always find a choice that is “fair” taking into account everyone’s opinions or must we choose one person from the group to act as a “dictator”? A fair division problem: Suppose that there is a cake and a group of hungry children. Naturally, you want to cut the cake and distribute the pieces to the children as fairly as possible. If the cake is homogeneous (e.g., a chocolate cake with vanilla icing evenly distributed), then it is easy to find a fair division: give each child a piece that is the same size. But, how do we find a “fair” division of the cake if it is heterogeneous (e.g., icing that is 1/3 chocolate, 1/3 vanilla and 1/3 strawberry) and the children each want different parts of the cake?

## Syllabus

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)
Preferences
How Likely is the Condorcet Paradox?
Condorcet Consistent Voting Methods
Approval Voting
Combining Approval and Preference

Choosing How to Choose
Should the Condorcet Winner be Elected?
Failures of Monotonicity
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

Week 5: Aggregating Judgements
Voting in Combinatorial Domains
The Condorcet Jury Theorem
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?

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

Eric Pacuit

## Reviews for Coursera's Making Better Group Decisions: Voting, Judgement Aggregation and Fair Division 3.5 Based on 2 reviews

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