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Unit 12A

Unit 12A. Voting: Does the Majority Always Rule?. Majority Rule. The simplest type of voting involves only two choices. With majority rule , the choice receiving more than 50% of the vote is the winner. Some properties of majority rule are listed below. Every vote has the same weight.

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Unit 12A

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  1. Unit 12A Voting: Does the Majority Always Rule?

  2. Majority Rule The simplest type of voting involves only two choices. With majority rule, the choice receiving more than 50% of the vote is the winner. Some properties of majority rule are listed below. • Every vote has the same weight. • There is symmetry between the candidates. • If a vote for the loser were changed to a vote for the winner, the outcome of the election would not be changed.

  3. Example 1 The table shows the 2000 presidential election official results. Describe the outcomes of the popular and electoral votes.

  4. Variations on Majority Rule In some cases, a candidate or issue must receive more than a majority of the vote to win─such as 60% of the vote, 75% of the vote, or a unanimous vote. In these cases, a super majority is required. • A 60% super majority is required to end a filibuster in the U.S. Senate. • A 2/3 super majority is required by both the House and Senate to amend the U.S. Constitution.

  5. Example 2 Evaluate the outcome in each of the following cases. a. Of the 100 senators in the U.S. Senate, 59 favor a new bill on campaign finance reform. The other 41 senators are adamantly opposed and start a filibuster. Will the bill pass? b. A criminal conviction in a particular state requires a vote by 3/4 of the jury members. On a nine-member jury, seven jurors vote to convict. Is the defendant convicted?

  6. Example 2(cont) c. A proposed amendment to the U.S. Constitution has passed both the House and the Senate with more than the required 2/3 super majority. Each state holds a vote on the amendment. The amendment garners a majority vote in 36 of the 50 states. Is the Constitution amended? d. A bill limiting the powers of the President has the support of 73 out of 100 senators and 270 out of 435 members of the House of Representatives. But the President promises to veto the bill if it is passed. Will it become law?

  7. Example 3 The table shows the results for the three major candidates in the 1992 U. S. presidential election. Analyze the outcome. Could Bush have won if Perot had not run?

  8. Preference Schedule Tabulating results from ballots requires a special type of table, called a preference schedule, that tells us how many voters chose each particular ranking order among the candidates.

  9. Example 4 Below are the results of a three-way governor race between Smith, Jones, and Wilson. Suppose that there were a total of 1000 voters, and their full preferences were as follows: • For 320 voters, Smith is their first choice and Jones is their second choice, leaving Wilson as their third choice. • For 330 voters, Jones is their first choice and Smith is their second choice, leaving Wilson as their third choice. • For 175 voters, Wilson is their first choice, Smith is their second choice, and Jones is their third choice. • For 175 voters, Wilson is their first choice, Jones is their second choice, and Smith is their third choice. Make a preference schedule for this election.

  10. Voting Methods withThree or More Choices Plurality method: The candidate with the most first-place votes wins. Single (top-two) runoff method: The two candidates with the most first-place votes have a runoff. The winner of this runoff is the winner of the election. Sequential runoff method: A series of runoffs is held, eliminating the candidate with the fewest first-place votes at each stage. Runoffs continue until one candidate has a majority of the first-place votes and is declared the winner.

  11. Voting Methods withThree or More Choices Point system (Borda count): Points are awarded according to the rank of each candidate on each ballot (first, second, third, …). The candidate with the most points wins. Method of pairwise comparisons (Condorcet method):The candidate who wins the most pairwise (one-on-one) contests is the winner of the election.

  12. Example 7 (similar) Consider the following three-candidate preference schedule for candidate A, B, and C. Use the five methods of voting for three or more candidates. Is there a clear winner? Explain.

  13. Example 8 Answer the following questions to be sure you understand the preference schedule. a. How many voters ranked candidates in the order E, B, D, C, A? b. How many voters had candidate E as their first choice? c. How many voters preferred candidate C over candidate A?

  14. Example 9 Using the chart below, use the five methods of voting for three or more candidates. Is there a clear winner? Explain.

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