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.
A similar situation may have occurred in the 2000 Presidential election in Florida. George Bush won the Presidency in spite of losing the nationwide popular vote because he had more electoral votes than Al Gore. After the votes were counted, George Bush had 271 electoral votes and Al Gore had 266 electoral votes. By winning Florida, Bush received 25 electoral votes which made the difference. In 2000, Ralph Nader was the Green Party candidate. What would have happened if Ralph Nader, who obviously did not win Florida, had been removed from the ballot a few months or even weeks before the election? Would that have made a difference in the very close Florida count? In fact, the Florida vote was decided by 537 votes in favor of Bush. Ralph Nader received 97,421 votes in Florida.
Would some of Ralph Nader’s 97,421 votes in Florida have gone to Al Gore if Nader had not been on the ballot? In his own book, Crashing the Party, Nader himself estimates that had he not been on the ballot, 38% of his supporters would have supported Gore. If that were true, that’s over 37,000 more votes for Al Gore. In defense of Ralph Nader though, the following should be noted: –There were 7 other third party candidates (besides Nader) in the 2000 election that received more votes in Florida than the 537 vote difference between Bush and Gore. Ever heard of Harry Browne? He got over 16,000 votes for President in Florida that year. –If Al Gore had won his home state of Tennessee, he would have had enough electoral votes to have won the Presidency.
There is a joke based on the failure of IIA in plurality voting: A waiter says to a customer “We have Apple, Blueberry and Rhubarb pie for desert.” To which the customer replies, “I’d like Apple pie, and please bring the check.” When the waiter returns he mentions that the Rhubarb pie was actually sold out anyway. “In that case”, says the customer, “I’ll take the Blueberry pie.”