The following questions review the main ideas of this chapter. Write your answers to the...

The following questions review the main ideas of this chapter. Write your answers to the questions and then refer to the pages listed by number to make certain that you have mastered these ideas.

When the divide-and-choose method for three players is applied, what happens if the two choosers find the same piece acceptable and the other pieces unacceptable? pg. 213 What is the key to creating a fair-division procedure for three or more players? pg. 216

Note that in the divide-and-choose method for three players, the simplest case has a piece that only one player considers to be a fair share. The key to creating a fairdivision procedure for more players is to find a way to create a piece that one player considers a fair share and that no other player thinks is too large. In a sense, we are trying to find a player who will willingly take the smallest amount of the cake. Accordingly, we will have one player cut out what he or she considers a fair share of the cake. In turn, each of the other players must either (1) agree that the piece is no more than a fair share or (2) cut the piece down to a smaller one that is a fair share. The player who was the last one to cut the piece down to a smaller size believes it is a fair share and gets that piece. It is important to note that no other player thinks that piece is larger than a fair share. The strategy just described leads to the following method, which was named for the process of cutting down the size of a piece until it is acceptable to all.

Note that the process of judging and trimming is repeated for every piece of “cake” that is distributed. When using the last-diminisher method, the players repeat the process of judging and trimming for every piece of “cake” that is distributed. Some of the cake may wind up in small pieces, so a piece of cake must be considered just as desirable cut up as whole.