Weighted Voting
Systems
Chapter 2
Objective: Recognize the notation for weighted voting system
and be able to define quota, player, dictator, dummy and veto
power.

Analyze two different weighted
voting scenarios & identify the
quota and players in proper
notation. In addition, identify
which player(s) is the dictator,
dummy and has the veto power.
Closing Product
Exit Ticket

Any formal voting arrangement in which
voters are not necessarily equal in terms
of number of votes they control.
Weighted Voting Systems
Examples
 Players
– the voters; denoted P1
, P 2 , P 3 , . . . . , Pn
 Weights - the number of votes
each player controls; denoted w1
, w 2 , w 3 , . . . . , wn
 Quota – the minimum number of
votes needed to pass a motion;
notated by q.
Characteristics
# of votes of P1
[ q; w1 , w2 , w3 , . . . . , wn ]
# of votes of P2
Quota
Weights are written in descending order
Weighted Voting System Notation
50% < q ≤ 100%
Quota Criteria
Consider the weighted voting system
[13: 7, 4, 3, 3, 2, 1]. Find the following:
6
a)
The total number of players
b)
The total number of votes
c)
The weight of P2
d)
The minimum number of votes needed to pass a
motion
13
Example #1
20
4
Consider the weighted voting system [q: 10, 6, 5, 4, 2]
a)
What is the smallest value that the quota q can take?
b)
What is the largest value that the quota q can take?
c)
What is the value of the quota if at least two-thirds
votes is needed to pass a motion?
d)
What is the value of the quota if more than two-thirds
of the votes are required to pass a motion?
Example #2

A committee has four members (P1, P2,
P3, and P4). In this committee P1 has
twice as many votes as P2; P2 has twice
as many votes as P3; P3 has twice as
many votes as P4. Describe the
committee as a weighted voting system
when the requirements to pass a motion
are
Example #3
a) At least two-thirds of the votes.
b) More than two-thirds of the votes.
c)
At least 80% of the votes.
d) More than 80 % of the votes
Example #3
[6: 7, 3, 1]

Dictator – a player
who’s weight is
greater than the
quota.

Dummy – a player
who has no power
(influence over the
outcome).
Consider the following …..
[q:4, 2, 1]
Veto Power – a player who is
not the dictator has this
power if a motion cannot pass
without his votes.
Consider the following ….
[19: 9, 7, 5, 3, 1]
[15: 16, 8, 4, 1]

Dictator?

Dictator?

Dummy?

Dummy?

Veto Power?

Veto Power?
Example # 4