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CMU 15-251
Social Choice
Teachers: Anil Ada Ariel Procaccia (this time)
Social choice theory
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CMU 15-251 Social Choice Teachers: Anil Ada Ariel Procaccia (this - - PowerPoint PPT Presentation
CMU 15-251 Social Choice Teachers: Anil Ada Ariel Procaccia (this - - PowerPoint PPT Presentation
CMU 15-251 Social Choice Teachers: Anil Ada Ariel Procaccia (this time) Social choice theory 2 The voting model = {1, , } , || = 3 Voting rules o o o 4
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The voting model
- π = {1, β¦ , π}
- π΅, |π΅| = π
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Voting rules
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More voting rules
- π β π
π
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More voting rules
- (π‘1, β¦ , π‘π)
- (1,0, β¦ , 0)
(π β 1, π β 2, β¦ , 0)
- π¦
π§ π¦ π§
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More voting rules
- π β 1
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STV: example
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Social choice axioms
- π¦
π¦
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Marquis de Condorcet
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Condorcet winner
- π¦
π§ π¦ π§
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Condorcet consistency
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Condorcet consistency
- β
β
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More voting rules
- π¦
= π β 1
- < π β 1
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Dodgsonβs Rule
- π¦
π¦
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Awesome example
- π
- π
- π
- π
- π
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Manipulation
- π
- π
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Strategyproofness
- π
1.
π = 1
2.
π = 2
3.
π = 3
4.
π = β
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Strategyproofness
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Gibbard-Satterthwaite
- π β₯ 3
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Complexity of manipulation
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The computational problem
- π
- π
- π = π
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A greedy algorithm
- π
- π
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Example: Borda
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When does the alg work?
- π
π β { }
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Is social choice practical?
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Computational social choice
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What we have learned
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