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

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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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o

𝑝

o

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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