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 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 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 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 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
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 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