Transcript Social Choice: The Impossible Dream

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)
The Academy Award

The famous line – “And the Oscar goes to…”
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The Academy Award – the biggest movie event of the year
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Since 1929 – the oldest award ceremony in the media
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Voted by members of The Academy of Motion Picture Arts and Sciences
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Number of voters: 5532
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

(for the 83rd Annual Award)
Currently 24 categories
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Best Director
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Best Actor
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Best Original Score…
The biggest award:
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Best Picture.
From 5 to 10
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Best Picture nominees increased from 5 to 10 from 2010, for 2 reasons.
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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
From 5 to 10 (cont’d)
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The second reason: The Dark Knight.
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Video: http://www.youtube.com/watch?v=Terhj8mjPwY 2:57 – 3:23
Pick One From Ten
Plurality, Majority
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Plurality
The one that gets the largest number of votes wins
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Majority
>50%
Sequential Voting
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Determine the winner through multiple times of voting
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Pick the 3 strongest nominees to illustrate
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
Simplify the number of voters to 100
(a) “The King’s Speech”
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– 35
– Group B
A great film with experienced actors
(c) “The Social Network”
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– Group A
Actor-voters like experienced actors in a good film
(b) “True Grit”
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– 40
– 25
Other voters like the greatest film
– Group C
Sequential Voting (cont’d)
Sincere Voting vs. Strategic Voting
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
Group:
X
Y
Z

First choice:
a
b
c
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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
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75
a


Strategic Voting
25
b
40
vs.
35
b
c
c
60
b
a
65
c
a
b
75
25
a
c
Strategic Voting: Group A strategically votes (c) in the first round to eliminate (b).
Alternative: Elimination Runoff
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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!
Preferential Voting
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Voters can vote for multiple nominees at the same time
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One kind of Preferential Voting: Score
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Let’s add “Toy Story 3” (d) to the previous group
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
Assuming voters are all closed-minded, and won’t 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
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Percent:
40
35
25
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(a) “The King’s Speech”: (40)(3) + (35)(2) + (25)(1) = 215
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(b) “True Grit”:
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(c) “The Social Network”: (40)(1) + (35)(1) + (25)(3) = 150
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(d) “Toy Story 3”:
(40)(2) + (35)(3) + (25)(2) = 235 - winner
(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
Preferential Voting (cont’d)
How They Do It - Rank
How They Do It
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Number of voters: 5532
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Assume the distribution of voters’ first choices is:
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1. Inception: 1000
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2. The King’s Speech: 1000
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3. Winter’s Bone : 900
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4. 127 Hours: 800
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5. The Kids’ Are All Right: 500
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6. Black Swan: 400
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7. The Fighter: 382
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8. Toy Story 3: 250
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9. True Grit: 200
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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.
How They Do It (cont’d)
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
Assume 50 of them vote “Toy Story 3” as their second place and 50 vote
“True Grit” as their second place.
Then it becomes:
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1. Inception: 1000
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2. The King’s Speech: 1000
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3. Winter’s Bone: 900
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4. 127 Hours: 800
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5. The Kids’ Are All Right: 500
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6. Black Swan: 400
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7. The Fighter: 382
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8. Toy Story 3: 300
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9. True Grit: 250
50
TSN
TG
WB
150
TG
TKS
…
50
TG
TSN
TS3
…
…
How They Do It (cont’d)
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After assigning 150 to TKS, 50 to WB, and 50 to TS3, we have:
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1. The King’s Speech: 1150
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2. Inception: 1000
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3. Winter’s Bone: 950
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4. 127 Hours: 800
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5. The Kids’ Are All Right: 500
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6. Black Swan: 400
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7. The Fighter: 382
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8. Toy Story 3: 350
Eliminate one by one until one nominee gets 2766 votes.
Pick More Than One?
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Seats: 6
% to get a seat=100/6=16.667
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First: Tanya Chan (26.4%)
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Second: Regina Ip (19.5%)
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26.4 -16.667 = 9.733%
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%)
Time For You
Real Life Example
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content
LG1 LG5 LG7
Leo
1
3
2
Vivian
1
2
3
Prof. Li
3
1
2
Yung
3
2
1
Homework
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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 -> Seventh choice
1
A
B
C
D
E
F
G
11
A
B
C
D
E
F
G
2
A
B
D
C
E
F
G
12
A
B
D
C
E
F
G
3
A
C
D
B
E
F
G
13
A
C
D
B
E
F
G
4
B
A
C
D
E
F
G
14
G
B
C
D
E
F
G
5
G B
C
D
A E
F
15
G
B
C
D
A
E
F
6
F
A
B
C
D G
E
16
G
A
B
C
D
G F
7
B
A
C
D
E
F
G
17
B
A
C
D
E
F
G
8
F
B
A
D
C E
G
18
D
B
A
F
C
E
G
9
D
B
A
E
F
G
C
19
D
B
C
E
F
G A
10
B
A
C
D
E
F
G
20
B
A
C
D
E
F
G
Homework (cont’d)
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
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?
Thank you.
Discussion