The Plurality and Borda Count Methods
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1 The Plurality and Borda Count Methods Robb T. Koether Hampden-Sydney College Fri, Aug 29, 2014 Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
2 1 Assignment 2 Definitions 3 The Debate Club Election 4 The Plurality Method 5 The Borda Count Method 6 Icelandic Parliamentary Elections Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
3 Outline 1 Assignment 2 Definitions 3 The Debate Club Election 4 The Plurality Method 5 The Borda Count Method 6 Icelandic Parliamentary Elections Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
4 Assignment Assignment Page 28, Exercises 11, 13, 17, 19. Page 31: Exercises 21, 25, 27, 29. Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
5 Outline 1 Assignment 2 Definitions 3 The Debate Club Election 4 The Plurality Method 5 The Borda Count Method 6 Icelandic Parliamentary Elections Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
6 Definitions Definition (The Candidates) The candidates are the people running for office in an election. If we are choosing something other than people, we call them alternatives. Definition (The Voters) The voters are the people who have a say in the outcome of the election. All voters have equal say. Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
7 Definition (Single-choice Ballot) In a single-choice ballot, each voter selects one candidate. Definition (Preference Ballot) In a preference ballot, each voter ranks all the candidates from most preferred to least preferred. Definition (Truncated Preference Ballot) In a truncated preference ballot, each voter ranks some, but not all, the candidates by preference. Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
8 Outline 1 Assignment 2 Definitions 3 The Debate Club Election 4 The Plurality Method 5 The Borda Count Method 6 Icelandic Parliamentary Elections Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
9 The Debate Club Election Example There are four candidates for Debate Club president: A, B, C, and D. There are 37 voting members. Their preferences are shown on the next slide. Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
10 Voters Preferences Example st A B C D 2nd B D B C 3rd C C D B 4th D A A A Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
11 Who won? Example Who should be elected president? Who is more popular, A or B? Who is more popular, A or C? Who is more popular, A or D? Who is least popular? Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
12 Outline 1 Assignment 2 Definitions 3 The Debate Club Election 4 The Plurality Method 5 The Borda Count Method 6 Icelandic Parliamentary Elections Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
13 The Plurality Method Definition (The Plurality Method) By the plurality method, the candidate with the most first-place votes wins. Example In the Debate Club example, A wins by the plurality method. Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
14 Web Page Run the program Voting on the web: Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
15 The 2010 Republican Primary Example The 2010 Republican primary in Virginia s 5th district, there were 7 candidates: Robert Hurt Jim McKelvey Mike McPadden Kenneth Boyd Feda Morton Laurence Verga Ron Ferrin Robert Hurt was the establishment candidate. The other 6 were Tea Party candidates. Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
16 The 2010 Republican Primary Example Robert Hurt won 48.42% of the vote. Was he the most popular candidate? Could he have been the least popular candidate? (See Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
17 The 2012 Republican Primary Example The 2012 Republican primary for senator, there were 4 candidates: George Allen Jaime Radtke Bob Marshall E. W. Jackson George Allen was the establishment candidate. The other 3 were more conservative. George Allen won 65.45% of the vote. Was he the most popular candidate? Could he have been the least popular candidate? (See Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
18 Outline 1 Assignment 2 Definitions 3 The Debate Club Election 4 The Plurality Method 5 The Borda Count Method 6 Icelandic Parliamentary Elections Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
19 The Borda Count Method Definition (The Borda Count Method) By the Borda count method, the voters rank the candidates. Then each rank is assigned points, higher ranks receiving more points. The candidate with the most points wins. Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
20 The Debate Club Election Example (The Debate Club Election) Reconsider the Debate Club election with 4 points for 1st, 3 for 2nd, 2 for 3rd, and 1 for 4th st A B C D 2nd B D B C 3rd C C D B 4th D A A A Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
21 The Math Club Election Example (The Math Club Election) Which candidate wins? Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
22 The Math Club Election Example (The Math Club Election) Which candidate wins? Which candidate comes in last? Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
23 The Math Club Election Example (The Math Club Election) Which candidate wins? Which candidate comes in last? Would the outcome be different if the points were 3, 2, 1, 0? Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
24 The Math Club Election Example (The Math Club Election) Which candidate wins? Which candidate comes in last? Would the outcome be different if the points were 3, 2, 1, 0? What about 20, 15, 10, 5? Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
25 Outline 1 Assignment 2 Definitions 3 The Debate Club Election 4 The Plurality Method 5 The Borda Count Method 6 Icelandic Parliamentary Elections Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
26 Icelandic Parliamentary Elections Icelandic Parliamentary Elections Consider the Icelandic Parliamentary Elections, the method for apportionment of constituency seats. Robb T. Koether (Hampden-Sydney College) The Plurality and Borda Count Methods Fri, Aug 29, / 23
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