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CMU 15-251
Computational
Social choice
Teachers:
Victor Adamchik
Ariel Procaccia (this time)
Social choice theory
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The voting model
• 𝑁 = {1, … , 𝑛}
• 𝐴, |𝐴| = 𝑚
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Voting rules
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o
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o
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More voting rules
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o 𝑚 − 𝑘
𝑘
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o
o
o
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More voting rules
• 𝑥 𝑦𝑥 𝑦
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o
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More voting rules
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o 𝑚 − 1
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o
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STV: example
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Social choice axioms
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𝑥 𝑥
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Marquis de Condorcet
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Condorcet winner
• 𝑥 𝑦
𝑥 𝑦
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Condorcet consistency
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Condorcet consistency
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⇒
⇒
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More voting rules
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o 𝑥 = 𝑚 − 1
o < 𝑚 − 1
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Awesome example
• 𝑎
• 𝑏
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𝑐
• 𝑑
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𝑒
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Manipulation
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• 𝑏
• 𝑎
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Strategyproofness
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• 𝑚
1. 𝑚 = 1
2. 𝑚 = 2
3. 𝑚 = 3
4. 𝑚 = ∞
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Gibbard-Satterthwaite
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• 𝑚 ≥ 3
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Complexity of manipulation
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The computational problem
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𝑝
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𝑝
• 𝑝 = 𝑎
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A greedy algorithm
• 𝑝
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𝑝
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Example: Borda
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When does the alg work?
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What we have learned
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