The Results are in! Clinton wins? The election has been completed and the results recorded, but do we really have a majority winner? Newspaper headlines assail: The people have spoken. It’s time for change! But another side claims: I represent the 57% and look after their needs. What do we have here? How can both sides claim to represent the wishes of the majority of the population?
This is a classic case in election theory. The system of the election can actually determine the outcome of the election. Consider some of the “what if’s” and the results each would bring to this election.
Plurality • Simply stated, the one with the most votes wins. This election gives a plurality winner but that winner is not a majority winner. No candidate has more than 50% of the vote. Receiving at least 50% of the vote can be considered a criteria of fairness and can be violated under the plurality system. So is the plurality system the best method?
Preference Schedule • Other methods of voting have been developed in an attempt to solve the problem and provide a winner that is fair to the majority of people in the election. These methods require a different type of ballot. It is important not only to know which candidate is the first choice; but also the second, third and additional choices in order. When you have listed your choices in order, you have developed a preference schedule for the candidates in the election. This is a common method of voting used by business personnel, sportswriters and others whose jobs require the ranking of items, teams or policies.
The Set Up • By reading the results of pre-election surveys , the following assumptions have been made: • 1. If a voter choose Bush, then Perot would have been the second choice. • 2. If a voter choose Clinton, then Perot would have been the second choice. • 3. If a voter choose Perot, then 50% would chose Clinton second and the other 50% would choose Bush as the second choice.
Run-Off • Under this method the candidates with the highest two votes are paired against each other and the votes for any other candidate(s) are distributed to them according to the preference schedules. In the above election an additional 9,618,623 votes would be given to each Clinton and Perot.
The Final Results • Under this method you will always have a majority winner. _______ has more than 50% of the vote. • The runoff method satisfies the criteria of fairness that the winner of the election is the choice of the majority of the people.
Sequential Runoff Method • Under this method of election the lowest ranking candidate is eliminated first and he is eliminated from the preference schedules. • The process continues until you have two candidates and then the runoff method produces a winner. • In the election we are considering here, the other candidates would have been eliminated one at a time until we were left with Clinton, Bush and Perot. • Sequential Runoff will always have a majority winner.
The Borda Method • This method is named after Jean-Charles de Borda(1733-1799) a French Mathematician who was dissatisfied with the plurality method. Under this method a point total is given to each candidate according to the preference schedules. When n candidates are ranked, n points is given to the first place vote, (n-1) to the second place vote, etc. The Borda method allows for the preference opinions of the voters to be considered.
Think about it. • The Borda method produces a different winner than the previous procedures. While it considers all the elements in the preference schedules, it too has some potential problems. • It is easily swayed by insincere voting. The Borda method produces a ranking of the candidates from highest to lowest. In some cases this is an important attribute of the election process.
For example… • If we were to select a first team all conference volleyball team, then we are interested in not just the highest point total but the six highest totals. • The method has many applications, but as we see here it might have produced a different President had it been used in the national election to choose our President.
The Condoret Method • This method was proposed by Maquois de Condorcet(1743-1794) also a French mathematician and friend of Borda. He too felt the plurality method was unfair. The method he proposed suggested that you must consider every possible pair of candidates, and that if some candidate can defeat all others in a pair-wise race, then that candidate should win the election.
Problem • It is possible to have group rankings that violate the Transitive Property. • A defeats B and B defeats C but C defeats A. • Another problem is that we do not always have a winner.
Try all the methodsPlurality, Majority, Runoff, Sequential Runoff, Borda, Condorcet and Approval(1st and 2nd places are approved) Please complete the Election Theory Worksheet.