CMU 15-251 Social Choice Teachers: Anil Ada Ariel Procaccia (this time)
Social choice theory • • • • • 2
The voting model 𝑂 = {1, … , 𝑜} • 𝐵, |𝐵| = 𝑛 • • • 3
Voting rules • • o o o 4
More voting rules • 𝑛 − 𝑙 o 𝑙 o o o o 5
More voting rules • (𝑡 1 , … , 𝑡 𝑛 ) o (1,0, … , 0) (𝑛 − 1, 𝑛 − 2, … , 0) o • 𝑦 𝑧 𝑦 𝑧 • o o 6
More voting rules • 𝑛 − 1 o o o o 7
STV: example 8
Social choice axioms • • 𝑦 𝑦 • 9
Marquis de Condorcet • • • • 10
Condorcet winner 𝑦 𝑧 • 𝑦 𝑧 • • 11
Condorcet consistency • • 12
Condorcet consistency • ⇒ ⇒ 13
More voting rules • • 𝑦 = 𝑛 − 1 o < 𝑛 − 1 o 14
Dodgson’s Rule 𝑦 • 𝑦 • • 15
Awesome example 𝑏 • 𝑐 • • 𝑑 𝑒 • • 𝑓 16
Manipulation • 𝑐 • 𝑏 • • • 17
Strategyproofness • 𝑛 • 𝑛 = 1 1. 𝑛 = 2 2. 𝑛 = 3 3. 𝑛 = ∞ 4. 18
Strategyproofness • • • 19
Gibbard-Satterthwaite • • 𝑛 ≥ 3 • 20
Complexity of manipulation • • • 21
The computational problem • o 𝑞 o 𝑞 𝑞 = 𝑏 • 22
A greedy algorithm 𝑞 • • o 𝑞 o 23
Example: Borda 24
When does the alg work? • 𝑆 𝑆 ∈ { } • 25
Is social choice practical? • • • • 26
Computational social choice • o o • 27
What we have learned • o o o o o • o 28
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