Post on 14-Dec-2015
1.3 Borda, Condorcet, Approval
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Borda, Condorcet, and Approval
Section 1.3
Stick animation
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The animation hints at another voting method. How does it work with this preference schedule? (Hint: C wins with 24 points)
6 3 2 Pts
A B C 3
C C D 2
B D A 1
D A B 0
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Borda CountAlgorithm
• Each is assigned a
.
• Calculate the total for each candidate
• Most wins
Method 4
Count Borda
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Borda (3 – 2 – 1 – 0) - Who Wins?
1. A
2. B
3. C
4. D
4 2 2 1 Pts
A B C C 3
B C D D 2
C D B A 1
D A A B 0
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Same Election (6 – 5 – 1 – 0) - Who Wins?
(Assign candidates to groups)
4 2 2 1Pts
A B C C 6
B C D D 5
C D B A 1
D A A B 0
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Same Election (20 – 5 – 2 – 1) - Who Wins?
(Answers on clicks)
4 2 2 1Pts
A B C C 20
B C D D 5
C D B A 2
D A A B 1
A 80 2 2 862
C 8 10 20 7840
D 4 4 5 2310
20 40 1 654B
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Borda Count - Advantages
1. All P L co
2. Increases V T
3. Fewer P A
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Who has a legitimate complaint with the outcome of this election?
1. K
2. C
3. L
4. D
5 2 2Pts
A B C 3
B C D 2
C D B 1
D A A 0
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Borda Count - Disadvantages
Rigging elections
1. May not
2. Different
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Who wins using Borda?
1. A
2. B
3. C
4. D
20 19 15 10 PtsA B C D 3D D B C 2C C D B 1B A A A 0
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P.S. - Recall a big theme of this chapter
Plurality =
Runoff =
Hare =
Now Borda =
20 19 15 10A B C DD D B CC C D BB A A A
We saw the preference schedule on the last slide in Section 1.2. Winners were
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Borda Count
• Heisman winner in football, Academy Awards
• Not used in public elections
• Roman Senate - 105 A.D
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Another method due to a French nobleman
Animation
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The Hillary, Barack, John, and Joe animation hints at another new voting method. Explain how it works with this preference schedule. (Hint: C wins)
9 8 7
A B C
C C A
B A B
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Condorcet - Who wins?
1. A
2. B
3. C
4. D
9 8 7 2
A B C D
C C A C
D D D A
B A B B
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There are 3 candidates A, B, C in an election. Suppose A defeats B and B
defeats C. Then
1. A defeats C
2. A may defeat C
3. A can’t defeat C
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Condorcet Algorithm
Form of
candidates
Determine the of each pairing
The candidate who defeats is the Condorcet winner
Method 5
Condorcet
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Condorcet - Advantage
1. No
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Condorcet - Disadvantages
1. A
2. B
3. C
4. Other
4 6 9
A C B
B A C
C B A
1. May not
2. Fairly comp
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Suppose that A beats B, C beats B, and A loses to C. Who could be the Condorcet winner?
1. A
2. C
3. Can’t tell
4. No one
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If candidate A has a majority of the votes A will always win using the Condorcet method
1. True
2. False
3. Can’t tell
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Last (and most contemporary ) voting method
Smurf Animation
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The Smurf animation hints at a final voting method. Explain how it works
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ApprovalAlgorithm
Method 6
Each voter votes .
The candidate with wins
Brams, Weber
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Who wins using Approval voting?
Assume voters approve of the candidates in RED type
1. A
2. B
3. C
4. D
9 8 7 2
A B C D
C A D BD A D C
B C B A
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Who wins using Approval voting?
Assume voters approves of the candidates in RED type
1. A
2. B
3. C
4. D
6 8 7 1
D B C D
C D B C
A C D A
B A A B
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If candidate A has a majority of the votes A will always win using the Approval method
1. True
2. False
3. Can’t tell
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“Vote Splitting”
1992 (Democrats Benefit)
George Bush
Republican
Bill Clinton
Democrat
H. Ross Perot
Independent
2000 (Republicans Benefit)
George W. Bush
Republican
Al Gore Democrat
Ralph NaderIndependent
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Approval - Advantages
• Avoids vote splitting
• Feasible
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• Reduce negative campaigning
• Increases voter turnout
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Approval - Disadvantage
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Dis - Approval Voting
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Presidential Elections – Approval method to reduce a field of 15 to 2. Then plurality.
13th c. by the Venetians to elect magistrates
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End of 1.3
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A
B C
D
3
2103
210
3
210
Voters
Candidates
Points
A B C D
Point totals
2 763
BCDA
DBAC
DABC
Points
Points
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True Story
• Female colleague of mine started working for a Hartford insurance company in 1972
• First job was to determine a formula for best salesperson based on points for Most Sales, Most New Customers, Least complaints,…
• Winner was a woman (for first time)
• Colleague was ordered to revise point counts so that a man would win
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Monsieur Borda
• Jean-Charles Borda (1733-1799) French mathematician, scientist, expert in military weaponry
• Played a role in the American War of Independence
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Marie Jean Antoine Nicolas Caritat (Marquis de) Condorcet
(1743-94)
• French mathematician and political leader
• Passionate in his hatred of injustice and took part in the French Revolution
• Close friend of Thomas Jefferson
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Dr. Steven J. Brams NYU
Dr. Robert J. Weber Northwestern University
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The Winner
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The Winner
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0 0 0 0
‘08 Smurf Election1 11 2 13 2 234
Smurffet Wins
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