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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