Computational Social Choice
- or -
Political Science meets Computer Science
Ron K. Cytron
http://www.cs.wustl.edu/~cytron/
Joint work with
Lorrie Cranor (Wash U Ph.D. student, now at CMU)
Rob LeGrand (Wash U Ph.D. student, now at Angelo State)
16 May 2014
Some voting results are difficult to compute
• Voters say yes or no to each of k candidates
• Elect a subset of the candidates so that
– Least pleased voter is as happy as possible
– Bring as many people “forward” as possible
Computational Political Science
Electing a committee from approval ballots
[ Brams, NYU ]
k = 5 candidates
11110
approves of
candidates
4 and 5
00011
n = 6 ballots
01111
00111
10111
00001
•What’s the best committee of size m = 2?
Computational Political Science
Sum of Hamming distances
11110
m = 2 winners
00011
2
01111
4
4
How happy?
5
11000
4
10111
3
00001
Computational Political Science
00111
sum = 22
Fixed-size minisum
11110
m = 2 winners
00011
4
01111
2
0
How happy?
1
00011
2
10111
1
00111
sum = 10
00001
•Minisum elects winner set with smallest sumscore
•Easy to compute (pick candidates with most approvals)
Computational Political Science
Maximum Hamming distance
11110
m = 2 winners
00011
4
01111
2
0
1
00011
2
10111
1
00001
Computational Political Science
00111
sum = 10
max = 4
Fixed-size minimax
[Brams, Kilgour & Sanver ’04]
11110
m = 2 winners
00011
2
01111
2
2
1
00110
2
10111
3
00111
sum = 12
max = 3
00001
•Minimax elects winner set with smallest maxscore
•Hard to compute! Currently have to try all outcomes
Computational Political Science