Question

Suppose Fred and Maria are going to divide a cake using the divider-chooser method. However, Fred is only entitled to 30% of the cake, and Maria is entitled to 70% of the cake (maybe it was a $10 cake, and Fred put in $3 and Maria put in $7). Adapt the divider-choose method to allow them to divide the cake fairly. Assume that different parts of the cake may have different values to Fred and Maria, and that they don't communicate their preferences/values with each other.

Your goal is to come up with a method of fair division, meaning that although the participants may not receive equal shares, they should be guaranteed their fair share. Your method needs to be designed so that each person will always be guaranteed a share that they value as being worth at least as much as they're entitled to.

Please do not make Fred divide the cake in two pieces, one of value 30% and the other one of 70%. That way of dividing does not guarantee that Mary will get her own fair share. Also, please avoid mentioning the flavors of the cake.

Answer 1

As Fred is entitled for 30% of the cake, he can be asked to be the divider of the cake and can cut the cake into 3 equal pieces considering that he will get 1 of them ( as he is entitled to 30% of the cake.)

As Fred do not know which 2 pieces Maria will choose , therefore she will try cut the cake in 3 equal pieces for value 33.3 % each. assuming that he will definitely get 33.3 percent of the share of the piece.

In this way chooser -Maria can choose 2 pieces making it at least 66 % of the cake to be given to her or she can go for one piece that has high value for her than other two .Rest remaining piece can be taken by fred.