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

开始时间: 04/22/2022 持续时间: 7 weeks

所在平台: CourseraArchive

课程类别: 经济与金融

大学或机构: University of Maryland, College Park(马里兰大学学院园分校)

授课老师: Eric Pacuit

课程主页: https://www.coursera.org/course/votingfairdiv

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课程详情

Much of our daily lives 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? 

课程大纲

Week 1: Introduction to Voting
    The Voting Problem
    Introduction to Voting Procedures (e.g., Plurality Rule, Borda Count,  
          Plurality with Runoff, The Hare System, Approval Voting)    
    Representing Preferences (including an introduction to relations)
    The Condorcet Paradox
    Condorcet Consistent Voting Methods
    Should the Condorcet Winner be Elected?
    Finding a Social Ranking vs. Finding a Winner
    Voting as Grading: Majoritarian Judgement
    Advanced Track: Dodgson's Method and the Smith Set 

Week 2: Comparing Voting Methods 
    Introduction to Comparing Voting Methods
    Condorcet's Other Paradox
    Monotonicity of Voting Rules (No-Show Paradox)
    Multiple-Districts Paradox
    Characterizing Majority Rule: May's Theorem
    Characterizing Scoring Rules (Fishburn's Theorem)
    Characterizing Approval Voting
    Independence of Irrelevant Alternatives
    Universal Domain and Non-Dictatorship
    Arrow's Impossibility Theorem
    Muller-Satterthwaite Theorem
    Advanced Track: Proof of Arrow's Theorem

Week 3: Topics in Voting Theory 
    Strategic Voting
    Manipulating the agenda
    Gibbard-Satterthwaite Theorem
    Random Dictator Model: Gibbard's Theorem
    Advanced Track: Proof of Gibbard's Theorem
    Circumventing Impossibility Results Part 1 of 2: Single-Peaked Preferences
    Circumventing Impossibility Results Part 2 of 2: Sen's Theorem
    Geometry of Voting: Explaining all Voting Paradoxes

Week 4: Aggregating Expert Opinions
   Anscombe's Paradox
   Multiple Elections Paradox
   From Voting to Aggregating Judgements
   Introduction to the Judgement Aggregation Model
   Discursive Dilemma and the Doctrinal Paradox
   Impossibility Results in Judgement Aggregation
   Advanced Track: Proof of the Impossibility Theorem(s)
   Voting to Track the Truth
   Aggregating Probability Judgements
   Condorcet Jury Theorem

Week 5: Introduction to Fair Division
    Introduction to Fair Division
    Fairness and Efficiency Criteria (Envy-Freeness, Proportionality, Equitability)
    Paradoxes of Fair Division part 
    Fairly Dividing Indivisible Goods
    Allocating indivisible goods: Help the Worst-off or Avoid envy?
    The Adjusted Winner Procedure
    Advanced Track: Proof that Adjusted Winner is Envy Free, Efficient and Equitable

Week 6: Cake-Cutting Algorithms and other Methods of Fair Division
    Introduction to Cake-Cutting Algorithms
   Advanced Track: Why do Envy-Free Divisions Exist?
   Cut and Choose 
   Even-Paz Divide and Conquer Algorithm
   Surplus Procedure
   Dubins-Spanier Moving Knife Procedure
   Banach-Knaster Procedure
   Selfridge-Conway Procedure
   Stromquist Procedure
   From Cake Cutting to Cutting a Pie
   Advanced Track: Complexity of Cake-Cutting Algorithms

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课程简介

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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马里兰大学帕克分校

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