Voting Power
John Randolph
Outline
1 - A simple voting game
Is this fair?
Total votes = 17. Votes needed to pass legislation = 9
Reps have equal power
County board
Winning coalitions:
Representative | Rep A | Rep B | Rep C |
Power | 1/3 | 1/3 | 1/3 |
Votes | 7 | 5 | 5 |
Population | 7,000 | 5,000 | 5,000 |
Voting power is deceptively complex
2 - The electoral college
3 - Tree structure
We can have a hierarchy with any weights, quotas
Calculating power
Players: {C, E, G, H, I, J, K, L, M}
(In general: n players)
Computation time: n^2 2^n
Computation time: n 2^s
s = branching factor
Instead, look at sub-games
4 - Applications
Decision tree
Parse tree