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Voting Power

John Randolph

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Outline

  1. A simple voting game
  2. The electoral college
  3. Tree structure
  4. Examples

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1 - A simple voting game

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Is this fair?

Total votes = 17. Votes needed to pass legislation = 9

Reps have equal power

County board

Winning coalitions:

  • A, B
  • B, C
  • A, C
  • A, B, C

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

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Voting power is deceptively complex

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2 - The electoral college

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3 - Tree structure

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We can have a hierarchy with any weights, quotas

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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

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4 - Applications

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Decision tree

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Parse tree