# The Plurality Method Fails The Independence of Irrelevant Alternatives Criterion.

## Presentation on theme: "The Plurality Method Fails The Independence of Irrelevant Alternatives Criterion."— Presentation transcript:

The Plurality Method Fails The Independence of Irrelevant Alternatives Criterion

The Independence of Irrelevant Alternatives criterion states: If a re-election is held and the only change is that some non-winning candidate drops out, the previous winner should still win the election. This is a condition of fairness in voting in the sense that it would seem unfair that a candidate that otherwise would have won, ends up losing in an election because some other losing candidate drops out of the election.

Suppose there are 9 faculty members in the math department at a community college and they have decided to vote on the choice of the next textbook for College Algebra. Suppose there are three choices for the textbook – books authored by Woodbury, Blitzer, and McKeague. Suppose all 9 faculty members have reviewed or used these books in the past and can rank their preferences as to which they favor 1 st, 2 nd, and 3 rd, in their own opinion.

The table below shows the preferences of the faculty Number of faculty 432 First choiceWoodburyBlitzerMcKeauge Second choiceBlitzerWoodburyBlitzer Third choiceMcKeague Woodbury

Based on these preferences, and using the Plurality method, the winner of the vote would be Woodbury. If the vote were held with these preferences, Woodbury wins because Woodbury has more votes than either of the other two candidates. Number of faculty 432 First choiceWoodburyBlitzerMcKeauge Second choice BlitzerWoodburyBlitzer Third choiceMcKeague Woodbury

Number of faculty 432 First choiceWoodburyBlitzerMcKeauge Second choice BlitzerWoodburyBlitzer Third choiceMcKeague Woodbury Suppose that the 2 faculty members that prefer McKeague as their first choice realize that the majority of the faculty dislike the McKeauge book. Suppose the other 7 faculty agree that they would never vote for McKeague and based on a concession from the 2 McKeauge supporters, a decision is made to remove McKeague from the ballot.

Number of faculty 432 First choiceWoodburyBlitzerMcKeauge Second choice BlitzerWoodburyBlitzer Third choiceMcKeague Woodbury Assuming everyone’s preferences remain the same, even if McKeague is removed, the table appears as follows…

Number of faculty 432 First choiceWoodburyBlitzer Second choice BlitzerWoodburyBlitzer Third choiceWoodbury Assuming everyone’s preferences remain the same, even if McKeague is removed, the table appears as follows…

Number of faculty 45 First choiceWoodburyBlitzer Second choice BlitzerWoodbury Third choice Now we can align those voters whose preferences are the same. And now the new winner of the election, still using the same method, is the Blitzer book.

Number of faculty 432 First choiceWoodburyBlitzerMcKeauge Second choice BlitzerWoodburyBlitzer Third choiceMcKeague Woodbury Perhaps those 2 faculty that were in the minority had an agenda! Perhaps they knew that the McKeague book could never win. Perhaps by suggesting the elimination of a choice that may have seemed irrelevant to the majority of voters, those 2 faculty got their second choice and avoided what would have been their last choice.

Number of faculty 45 First choiceWoodburyBlitzer Second choice BlitzerWoodbury Third choice By eliminating what might have seemed an irrelevant choice, because Mckeauge was not going to win, the results of the election have changed. The winner is now Blitzer. This illustrates how the Plurality method fails the independence of irrelevant alternatives criterion: Woodbury was going to win in the original vote. By removing a losing candidate, the results of the election have changed and Woodbury is no longer the winner.