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1.4 Arrow’s Conditions and Approval Voting

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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

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