Making Better Group Decisions: Voting, Judgement Aggregation and Fair Division
开始时间: 04/22/2022
持续时间: 7 weeks
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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