The 2000 election and what it should teach us
A team project for MA279, Fall 2013
Team members: S. Butts, H. Guo, D. Koishybayev, S. Lemmon
Voting Methods
In chapter 1 we have learned several voting methods. Although all these methods look fair, they may produce completely different results in some situation. Therefore, the study of these methods can help us better understand the result of presidential election of 2000.
The plurality method
The plurality method is the most commonly used method to find a winner. In plurality method, only the first-place vote is considered, and the candidate with most first-place votes wins. The plurality method is actually the method used in the presidential election in the United States. The major advantage for plurality method is that it satisfies the majority criterion, which claims that the majority candidate (the candidate winning majority of first-place votes) should be the winner of the election.
However, the plurality method does have drawback. Since the plurality method never takes the voter’s preference on all other candidates into account, it violates Condorcet criterion, which means that even if the candidate is preferred over each of the other candidates in the head-to-head comparison, this candidate may still not win in the election.
The Borda count method
The Borda count method, unlike the plurality method, utilizes more information from the ballot by assigning points to each place on a ballot. In an election with n candidates, we give 1 point for the last place, 2 points for second last place, and so on, so each first-place vote earns the candidate N points. Eventually, the candidate with the highest points becomes the winner. This method looks like a perfectly fair method, for it takes into account all the information on the ballot, and the winner is the candidate with the highest average ranking. However, the method violates both the majority criterion and Condorcet criterion.
The plurality-with-elimination method
The plurality-with-elimination method, also known as instant runoff method, is an efficient way to conduct a runoff election. To apply this method, we need to use preference ballots instead of just the first-place vote. After the first-place votes for each candidate is determined, the candidate with the fewest votes will be eliminated from the election, as well as all from the preference schedules. This process will continue until there is only one candidate remaining, who becomes the winner of this election. ,
Although the plurality-with-elimination method satisfies the majority criterion, it violates the Condorcet criterion, as well as monotonicity criterion, which states that the winner of the election should remain the same as the long as the changes of the ballots still favors the winner. However, despite its flaws, the plurality-with-elimination method is a popular method and is used in many elections.
The method of pairwise comparisons One method that does not violate Condorcet criterion is the method of pairwise comparisons. In a pairwise comparison, which is a head-to-head match between two candidates, each votes goes to one candidate if this candidate ranked higher than another one on this vote. The candidate with more votes is the winner of this pairwise comparison. The winner gets one point and the loser gets none, and both gets 1/2 points if there is a tie. Once all the pairwise comparisons are done, the candidates with the most points wins. Besides Condorcet criterion, this method also preserves majority criterion, as well as monotonicity criterion. However, it violates the independence-of-irrelevant-alternatives criterion, which asserts that the winner should not change while a non-winning candidate withdraws.
Extended Ranking methods and recursive ranking methods
Each of the above methods has a corresponding extended ranking method and a recursive ranking method. The extended ranking method will just run the corresponding method once and rank each candidate based on points earned. The recursive ranking method, in the contrast, first run the corresponding method to determine winner as the first place, and eliminate the winner from the election, and run this method again to get another winner to be the second place, and so on, until all the candidates are ranked.
