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 83 rd 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: 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:  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) b c b a a c b c b a 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: (a) “The King’s Speech”: (40)(3) + (35)(2) + (25)(1) = 215 (b) “True Grit”: (40)(2) + (35)(3) + (25)(2) = 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) = loser

How They Do It - Rank Preferential 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  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  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: TSNTGWB… 150TGTKS… 50TGTSNTS3…

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  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=  First: Tanya Chan (26.4%)  = 9.733%  Second: Regina Ip (19.5%)  = 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 LG1LG5LG7 Leo132 Vivian123 Prof. Li312 Yung321

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

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. Discussion