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(2-1) Weighted Voting Systems

“Each State shall appoint a Number of Electors equal to the whole Number of Senators and Representatives to which the state may be entitled in the Congress.”

-- Article II, Section 1

US Constitution

Weighted Voting System:

Motion:

The Players:

The Weights:

The Quota:

Notation:

Basic Concepts in Weighted Voting:

Weighted Voting in a Partnership: Consider a 4-way partnership. The partners P1, P2, P3, and P4 own 8, 7, 3, and 2 shares respectively. They agree that they will each have one vote per share and that two-thirds of the partners votes are needed to pass a motion. Describe the weighted voting system.

One Partner - One Vote: Consider the same partnership with the quota = 19. Describe the weighted voting system. Is there anything unusual about this system?

Size of the Quota: Consider [10:8, 7, 3, 2] and [21:8, 7, 3, 2]

Dictator or Dummy: Consider [11: 12, 5, 4], [30: 10, 10, 10, 9] and [6: 4, 3, 2, 1].

Power of the Veto: Consider [12: 9, 5, 4, 2].

Ex. 1: Consider the weighted voting system [14: 8, 7, 3, 2].

a. Find the total number of players:

b. Find the total number of votes:

c. The weight of P3:

d. The minimum percentage of votes needed to pass a motion (rounded to the nearest whole percent):

Ex. 2: Identify which players, if any, are (i) dictators, (ii) dummies, or (iii) have veto power in each of the following weighted voting systems:

a. [6: 4, 2, 1]

b.) [15: 16, 8, 4, 1]

c.) [10: 4, 3, 2, 1]

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