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Fair Division. LOGO. MATHEMATICS IN DAILY LIFE. Hua Yinglei Hu Zhihao Fan Xin Si Peiyu. Assign Tasks. Amidakuji. Tasks. Divide Tasks. How to divide a cake? --two persons Taking more things into consideration. Proportional Division. P2. P1. P1. P2. P3.

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  1. Fair Division LOGO MATHEMATICS IN DAILY LIFE • Hua Yinglei • Hu Zhihao • Fan Xin • Si Peiyu

  2. Assign Tasks Amidakuji Tasks Divide Tasks

  3. How to divide a cake? --two persons Taking more things into consideration

  4. Proportional Division P2 P1 P1 P2 P3

  5. The Final Reduction Algorithm • Person who is the last one to cut the 1/n part will get this part of cake • Everyone has two choices: • Give the cut-cake to the next one directly • Cut down the size of the piece into 1/n according to his valuation

  6. If anyone cuts the cake into piece which is smaller than 1/n of the cake deliberately…… • If anyone gives a piece of cake which is bigger than 1/n of the cake to someone else deliberately……

  7. Selfridge-Conway Algorithm A1 A21 A22 A A23 C B • P1 divides the cake into three pieces • he considers of equal sizes • …… P2 P1 P3

  8. 2 3 1 Applications and Conclusions Fair division is the problem of dividing a set of goods between several people, such that each person receives his/her due share. Distribution of social welfare Divorce settlements Airport traffic management and so on

  9. Thanks

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