2. 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)

3. 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 83 rd Annual Award)  Currently 24 categories  Best Director  Best Actor  Best Original Score…  The biggest award:  Best Picture.

4. 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

5. From 5 to 10 (cont’d)  The second reason: The Dark Knight. Video: http://www.youtube.com/watch?v=Terhj8mjPwY 2:57 – 3:23 http://www.youtube.com/watch?v=Terhj8mjPwY

6. Pick One From Ten

7. Plurality, Majority  Plurality The one that gets the largest number of votes wins  Majority >50%

8. 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

9. 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) 7525 40 60 b c b a a c 3565 75 25 b c b a a c

10. 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

11. How They Do It - Rank Preferential Voting (cont’d)

12. 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.

13. 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 50TSNTGWB… 150TGTKS… 50TGTSNTS3…

14. 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.

15. 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%)

16. Time For You

17. Real Life Example  content LG1LG5LG7 Leo132 Vivian123 Prof. Li312 Yung321

18. 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 1ABCDEFG 2ABDCEFG 3ACDBEFG 4BACDEFG 5GBCDAEF 6FABCDGE 7BACDEFG 8FBADCEG 9DBAEFGC 10BACDEFG 11ABCDEFG 12ABDCEFG 13ACDBEFG 14GBCDEFG 15GBCDAEF 16GABCDGF 17BACDEFG 18DBAFCEG 19DBCEFGA 20BACDEFG

19. 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?

20. Thank you. Discussion