1.4 Arrow’s Conditions and Approval Voting

Ms. Magne

Discrete Math

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

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

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)

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.

Approval Voting

Ex. Find the winner if everyone approves of their first and third choices.

A B C DB C B BC D D CD A A A8 5 6 6

The Approval Winner is _____.C

Approval Voting

Ex. Use the Approval Method to find the winner.

Voter 1 Voter 2 Voter 3 Voter 4 Voter 5

A X X X

B X X X X

C X X