1. 1.4 Arrow’s Conditions and Approval Voting
Ms. Magne
Discrete Math

2. Arrow’s Conditions
We have talked about many different ways to rank voting preferences, but not all of them have been fair.
Kenneth Arrow came up with 5 conditions that are necessary for a fair group ranking

3. Arrow’s Conditions
1) Nondictatorship – one person’s votes should not be better then another person’s votes
2) Individual Sovereignty – everyone should
be allowed to order their choices in any
order they want
3) Unanimity – if everyone prefers one choice
to another, then the group ranking should
do the same

4. Arrow’s Conditions
4) Freedom from Irrelevant Alternatives – if a choice is removed, the order in which the others are ranked should not change
5) Uniqueness of Group Ranking – The
method of producing group ranking should
give same result whenever it is applied to a
given set of preferences. (not rolling a dice)

5. Approval Voting
Approval Voting – voters are allowed to vote for as many or as few choices as they like, but they do not rank them. Winner is whoever has the most votes.

6. Approval Voting
Ex. Find the winner if everyone approves of their first and third choices.
A B C D
B C B B
C D D C
D A A A C
The Approval Winner is _____.

7. Approval Voting Ex. Use the Approval Method to find the winner.
Voter 1
Voter 2
Voter 3
Voter 4
Voter 5 A X B C