Plurality, Instant Runoff, and

Hare

Section 1.2

1.2 Plurality, IRV, and Hare 2

Who should win?

10 9 5 1A B C DD C B CC D D AB A A B

1. A

2. B

3. C

4. D

1.2 Plurality, IRV, and Hare 3

Ideas 10 9 5 1A B C DD C B CC D D AB A A B

1.2 Plurality, IRV, and Hare 4

Plurality

Most Votes Wins

Voting Method 1

1.2 Plurality, IRV, and Hare 5

• “Plurality” = More votes than anyone else

• Plurality is the only voting method that

may elect someone disliked by

of the voters

• Plurality Winner is .

(Simply look along the top row)

35 33 32

A C B

B B C

C A A

• Is there a majority winner?

1.2 Plurality, IRV, and Hare 6

Who wins using Plurality?

1. A

2. B

3. C

4. D

5. E

1 1 1

A C E

B B C

C A B

1 1 1

D B B

B A C

C C A

1 1 1

D C B

B B C

C A A

1 1

E A

B B

A E

D D C

E E D

E E E

A D D

A D E

E E D

D C

C D

1.2 Plurality, IRV, and Hare 7

• Plurality is also known as “Winner-Take-All”

• In presidential elections all the electoral votes in 48/50 states are awarded to the Plurality winner

“Chads”

1.2 Plurality, IRV, and Hare 8

Which is correct?

1. If you have a majority of the votes then you have a plurality

2. If you have a plurality then you have a majority of the votes

3. Both statements are true

4. Both statements are false

1.2 Plurality, IRV, and Hare 9

Who wins using Plurality?

1. A

2. B

3. C

4. D

8 9 6 4

B A C C

C D B D

A C A B

D B D A

An extreme case

1.2 Plurality, IRV, and Hare 10

Plurality High School Class Rank

A school ranks its students by the number of A’s they receive

Who would be ranked higher?

Hortense:

Hildegard:

1.2 Plurality, IRV, and Hare 11

Plurality - For Better or Worse

• Most researchers believe that Plurality does the . job of picking a winner

• It is still widely used for important elections in the United States, Canada, the United Kingdom, and India

• And by the faculty in our College of Arts and Sciences

1.2 Plurality, IRV, and Hare 12

Plurality - Advantages

1. Easy to

2. Easy to

1.2 Plurality, IRV, and Hare 13

Plurality - Disadvantages

Why bother? My guy (C) hasn’t got a chance. I’m outta here

8 7 3

B A C

C C A

A B B

1. Sm Cli

2. Vo Ap

1.2 Plurality, IRV, and Hare 14

First disadvantage is the big problem with Plurality. How can we prevent a small clique from winning?

Animation

1. Keep having elections until someone gets a majority

2. Reduce the field to 2 candidates

3. You can’t prevent it

4. Other

1.2 Plurality, IRV, and Hare 15

Animation showed Traditional Runoff Election

Very common - Two separate elections separated by weeks/months

Drawbacks •Expensive•Longer campaigns•Different voting group for 2nd

election

1.2 Plurality, IRV, and Hare 16

How could we conduct a Runoff “instantly” - using only this

preference schedule?

20 19 15 10

A B C D

D D B C

C C D B

B A A A

1.2 Plurality, IRV, and Hare 17

Instant Runoff Voting (IRV)Algorithm

• all candidates . ..

• “Re-tally” the .

• The candidate with votes wins

Voting Method 2

1.2 Plurality, IRV, and Hare 18

What is an “algorithm”?

• Arabic for “calculate”

• Definition: A precise set of rules specifying how to solve some problem

• Examples

– Divide 232 by 17

– Shampoo

 

1.2 Plurality, IRV, and Hare 19

15 9 4

A B C

B E E

C A B

3 2

D E

B A

C C

D D A

E C D

E B

A D

First Tally

Re-Tally

Eliminate

wins to .

Animation of the IRV algorithm

1.2 Plurality, IRV, and Hare 20

Who wins using IRV(and how many votes did the winner

get?)

10 7 5 5

B D C A

A C A C

D A D D

C B B B

1. A – 102. A – 153. B – 104. B – 125. C – 106. C – 157. D – 128. D – 17

1.2 Plurality, IRV, and Hare 21

Different voting methods can produce different winners in the same

election

1. True

2. False

1.2 Plurality, IRV, and Hare 22

Important Theme #1

IRV winner .

Plurality winner .

10 7 5 5

B D C A

A C A C

D A D D

C B B B

1.2 Plurality, IRV, and Hare 23

If candidate A has a majority of the first-place votes, A will

always win using IRV

1. True

2. False

3. Can’t tell

1.2 Plurality, IRV, and Hare 24

Instant Runoff - Advantages 10

098 3

A B C

B C B

C A A1. Ma W

2. Ch er

3. L L P

4. Fewer Per Att

5.

1.2 Plurality, IRV, and Hare 25

Which candidate has a legitimate complaint with IRV?

100

98 97

2

A B C D

C C A C

D D D A

B A B B

1. A

2. B

3. C

4. D

5. No one

1.2 Plurality, IRV, and Hare 26

IRV – Disadvantage

1.

French Presidential Election - 2002

Election

1.2 Plurality, IRV, and Hare 27

How to prevent strong 3rd, 4th, … place candidates from being eliminated in

the first round?

1. Eliminate all but the top 3 vote getters and re-tally

2. Eliminate all but the top 4 vote getters and re-tally

3. Eliminate the lowest vote getter. Re-tally. Again, eliminate lowest vote-getter. Re-tally. Etc. etc.

4. You can’t prevent it

1.2 Plurality, IRV, and Hare 28

http://video.google.com/videoplay?docid=1385351542097864075&q=m

usical+chairs&hl=en

1.2 Plurality, IRV, and Hare 29

The video hints at a new voting method. Explain how it works with this preference schedule

20 19 15 10

A B C D

D D B C

C C D B

B A A A

1.2 Plurality, IRV, and Hare 30

HareAlgorithm

• the .

• Re-tally the . Repeat this process, each time eliminating the .

• Eventually there will be only .

• The one with the wins

Voting Method 3

1.2 Plurality, IRV, and Hare 31

Animation using Hare

8 9 6

B A C

C D B

A C A

3

D

C

B

D B D A

Tally 1

Re-Tally

Re-Tally

wins to .

1.2 Plurality, IRV, and Hare 32

Who wins using Hare? (and determine how many votes the

winner gets)

17

12

616

A B C D

C C A C

D D B A

B A D B

1. A – 23

2. A – 35

3. B – 18

4. B – 35

5. C – 34

6. C – 37

7. D – 28

8. D – 45

1.2 Plurality, IRV, and Hare 33

If there are 3 candidates IRV and Hare

1. Always choose the same winner

2. Never choose the same winner

3. Sometimes choose the same winner

4. Can’t tell

1.2 Plurality, IRV, and Hare 34

If A has a majority of the first-place votes, A will always win using Hare

1. True

2. False

3. Can’t tell

1.2 Plurality, IRV, and Hare 35

Hare Method – Advantages

1. M W

2. Co ve

3. Fewer P A

4. En V T

1.2 Plurality, IRV, and Hare 36

Hare Method – Disadvantages

1. D to E

1.2 Plurality, IRV, and Hare 37

Who wins using Plurality?

1. A

2. B

3. C

4. D

20 19 15 10A B C DD D B CC C D BB A A A

1.2 Plurality, IRV, and Hare 38

Who wins using IRV?

1. A

2. B

3. C

4. D

20 19 15 10A B C DD D B CC C D BB A A A

1.2 Plurality, IRV, and Hare 39

Who wins using Hare?

1. A

2. B

3. C

4. D

20 19 15 10A B C DD D B CC C D BB A A A

1.2 Plurality, IRV, and Hare 40

OK, who wins?(Sorry, no questions on this one)

1. A

2. B

3. C

4. I don’t know

35 33 32

A C B

B B C

C A A

1.2 Plurality, IRV, and Hare 41

If you wanted candidate A to win which voting method would you choose?

17 19 21 10A B C DD D B AC A A BB C D C1. Plurality

2. Run off

3. Hare

1.2 Plurality, IRV, and Hare 42

If you wanted candidate B to win which voting method would you choose?

17 19 21 10A B C DD D B AC A A BB C D C1. Plurality

2. Run off

3. Hare

1.2 Plurality, IRV, and Hare 43

If you wanted candidate C to win which voting method would you choose?

17 19 21 10A B C DD D B AC A A BB C D C

1. Plurality

2. Run off

3. Hare

End of 1.2

1.2 Plurality, IRV, and Hare 45

2000 Presidential Election Florida’s Famous “Hanging Chads”

1.Bush defeats Gore by

537 votes (out of

5,800,000 cast)

2.Wins ALL electoral

votes in the state

3.Bush becomes

President

1.2 Plurality, IRV, and Hare 46

Plurality - An Extreme Case

Mapai Ahdut Ha'avodah

Aguddat Israel

Arab Democratic Party

Arab Movement for Change

Ariel Sharon Forms New Political Party

The Center Party

Centrist Party Takes Shape

Citizen's Rights Movement

Degel Hattorah

Democratic Choice

Democratic Movement for Change

Gahal

General Zionists/Liberal PartyGesher

Hadash

Herut

The Israeli Communist Party

Kach

Kadima

The Labor Party

United Arab List

United Torah Judaism

The Likud Party

1.2 Plurality, IRV, and Hare 47

Election 1

A

10 9

B C

4

D

3

E

2

Election 2

1.2 Plurality, IRV, and Hare 48

Candidates Votes 1st round

% Votes 2nd round %

Jacques Chirac

5,665,855 19.88% 25,537,956 82.21%

Jean-Marie Le Pen

4,804,713 16.86% 5,525,032 17.79%

Lionel Jospin 4,610,113 16.18%

François Bayrou

1,949,170 6.84%

Arlette Laguiller

1,630,045 5.72%

Jean-Pierre Chevènement

1,518,528 5.33%

Noël Mamère

Olivier Besancenot

French Presidential Election 2002

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