Social Choice: The Impossible Dream

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(No Transcript)
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This Presentation

• The Academy Award for Best Picture
• Looks for the best way to determine voters
  choice(s) among more than 2 options.
• Introduce different voting methods and their
  drawbacks
• The Hong Kong Legislative Council Election
  (Geographical Constituencies)

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The Academy Award

• The famous line And the Oscar goes to
• The Academy Award the biggest movie event of
  the year
• Since 1929 the oldest award ceremony in the
  media
• Voted by members of The Academy of Motion Picture
  Arts and Sciences
• Number of voters 5532
• (for the 83rd Annual Award)
• Currently 24 categories
• Best Director
• Best Actor
• Best Original Score
• The biggest award
• Best Picture.

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From 5 to 10

• Best Picture nominees increased from 5 to 10 from
  2010, for 2 reasons.
• First, rating price for a 30s commercial of this
  year 1.75 million US dollars.
• (1.75 2 60) / 42 5 USD/h Price for not
  letting an American to do anything for an hour
• 39,336 / 2,080 19 USD/h Price for
  letting an American to do something for an hour

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From 5 to 10 (contd)

• The second reason The Dark Knight.
• Video http//www.youtube.com/watch?vTerhj8mjPwY
  257 323

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Pick One From Ten
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Plurality, Majority

• Plurality
• The one that gets the largest number of
  votes wins
• Majority
• gt50

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Sequential Voting

• Determine the winner through multiple times of
  voting
• Pick the 3 strongest nominees to illustrate
• Simplify the number of voters to 100
• (a) The Kings Speech 40 Group A
• Actor-voters like experienced actors in a good
  film
• (b) True Grit 35 Group
  B
• A great film with experienced actors
• (c) The Social Network 25 Group C
• Other voters like the greatest film

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Sincere Voting vs. Strategic Voting
Sequential Voting (contd)

• Group X Y Z
• First choice a b
  c
• Second choice b a b
• Third choice c c
  a
• Percent 40 35
  25
• One kind of Runoff randomly pick 2 remaining
  nominees to vote each time
• Sincere Voting vs.
  Strategic Voting
• Strategic Voting Group A strategically votes (c)
  in the first round to eliminate (b).
• Alternative Elimination Runoff
• Vote for all remaining nominees eliminate the
  nominee with fewest number of votes vote again
  until majority. But voters might change their
  decisions each time!

75
25
35
65
b
b
c
c
40
60
75
25
a
c
b
a
a
c
b
a
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Preferential Voting

• Voters can vote for multiple nominees at the same
  time
• One kind of Preferential Voting Score
• Lets add Toy Story 3 (d) to the previous group
• Assuming voters are all closed-minded, and wont
  let an animated film to win so still 3 groups
• Group X Y Z
• First choice a b
  c
• Second choice b a b
• Third choice c c
  a
• Fourth choice d d d
  
• Percent 40 35
  25
• (a) The Kings Speech (40)(3) (35)(2)
  (25)(1) 215
• (b) True Grit (40)(2) (35)(3)
  (25)(2) 235 - winner
• (c) The Social Network (40)(1) (35)(1)
  (25)(3) 150
• (d) Toy Story 3 (40)(0) (35)(0)
  (25)(0) 0
• Strategic Voting, again
• Group A strategically switch (b) and (d), then
  (b) (40)(0) (35)(3) (25)(2) 155 - loser

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How They Do It - Rank
Preferential Voting (contd)
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How They Do It

• Number of voters 5532
• Assume the distribution of voters first choices
  is
• 1. Inception 1000
• 2. The Kings Speech 1000
• 3. Winters Bone 900
• 4. 127 Hours 800
• 5. The Kids Are All Right 500
• 6. Black Swan 400
• 7. The Fighter 382
• 8. Toy Story 3 250
• 9. True Grit 200
• 10. The Social Network 100

We eliminate The Social Network and
redistribute the 100 votes to the remaining nine
according to their preference of the 100 voters
second choice.
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How They Do It (contd)

• Assume 50 of them vote Toy Story 3 as their
  second place and 50 vote True Grit as their
  second place.
• Then it becomes
• 1. Inception 1000
• 2. The Kings Speech 1000
• 3. Winters Bone 900
• 4. 127 Hours 800
• 5. The Kids Are All Right 500
• 6. Black Swan 400
• 7. The Fighter 382
• 8. Toy Story 3 300
• 9. True Grit 250

50 TSN TG WB
150 TG TKS
50 TG TSN TS3
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How They Do It (contd)

• After assigning 150 to TKS, 50 to WB, and 50 to
  TS3, we have
• 1. The Kings Speech 1150
• 2. Inception 1000
• 3. Winters Bone 950
• 4. 127 Hours 800
• 5. The Kids Are All Right 500
• 6. Black Swan 400
• 7. The Fighter 382
• 8. Toy Story 3 350

Eliminate one by one until one nominee gets 2766
votes.
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Pick More Than One?

• Seats 6
• to get a seat100/616.667
• First Tanya Chan (26.4)
• 26.4 -16.667 9.733
• Second Regina Ip (19.5)
• 19.5 -16.667 2.833
• Third Jasper Tsang (19.3)
• Fourth Kam Nai-wai (12.7)
• Fifth Cyd Ho (9.9)
• Sixth Lo Wing-lok (6.5)
• The New Sixth Audrey Eu (9.733)

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• Time For You

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Real Life Example

• content

LG1 LG5 LG7
Leo 1 3 2
Vivian 1 2 3
Prof. Li 3 1 2
Yung 3 2 1
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Homework

• 1. If the following are the choices of 20 voters,
  which film will win the Best Picture Oscar?
  Please show steps.
• The numbers are voters, letters films.
• First choice -gt Seventh choice

1 A B C D E F G
2 A B D C E F G
3 A C D B E F G
4 B A C D E F G
5 G B C D A E F
6 F A B C D G E
7 B A C D E F G
8 F B A D C E G
9 D B A E F G C
10 B A C D E F G
11 A B C D E F G
12 A B D C E F G
13 A C D B E F G
14 G B C D E F G
15 G B C D A E F
16 G A B C D G F
17 B A C D E F G
18 D B A F C E G
19 D B C E F G A
20 B A C D E F G
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Homework (contd)

• 2. Based on our 4 voters preference on the 3
  canteens, please use at least method we
  introduced in the presentation to make each of
  the 3 canteens the winner. If you cannot find out
  a method, what you can add or change in order to
  get the desired result?
• Extra Can voters employ Strategic Voting in
  the current Best Picture Oscar voting method? Why
  or why not?

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Thank you.
Discussion