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…” 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.

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

From 5 to 10 (cont’d)

The second reason: The Dark Knight. Video: http://www.youtube.com/watch?v=Terhj8mjPwY 2:57 – 3:23

Pick One From Ten

Plurality, Majority

Plurality

The one that gets the largest number of votes wins

Majority

>50%

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 King’s 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

Sincere Voting vs. Strategic Voting 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!

Sequential Voting (cont’d)

75 25

40 60

b c

ba a c

35 65

75 25

b c

ba a c

Preferential Voting

Voters can vote for multiple nominees at the same time One kind of Preferential Voting: Score

Let’s add “Toy Story 3” (d) to the previous group 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 Percent: 40 35 25 (a) “The King’s 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

How They Do It - RankPreferential Voting (cont’d)

How They Do It

Number of voters: 5532 Assume the distribution of voters’ first choices is:

1. Inception: 1000 2. The King’s Speech: 1000 3. Winter’s 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.

How They Do It (cont’d)

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 King’s Speech: 1000 3. Winter’s 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

…

How They Do It (cont’d)

After assigning 150 to TKS, 50 to WB, and 50 to TS3, we have:

1. The King’s Speech: 1150 2. Inception: 1000 3. Winter’s 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.

Pick More Than One?

Seats: 6 % to get a

seat=100/6=16.667

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%)

Time For You

Real Life Example

content

LG1 LG5 LG7Leo 1 3 2

Vivian 1 2 3

Prof. Li 3 1 2

Yung 3 2 1

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 -> 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

Homework (cont’d)

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.

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