Chore division
From The Art and Popular Culture Encyclopedia
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Chore division is a fair division problem in which the divided resource is undesirable, so that each participant wants to get as little as possible. It is the mirror-image of the fair cake-cutting problem, in which the divided resource is desirable so that each participant wants to get as much as possible. Both problems have heterogeneous resources, meaning that the resources are nonuniform. In cake division, cakes can have edge, corner, and middle pieces along with different amounts of frosting. Whereas in chore division, there are different chore types and different amounts of time needed to finish each chore. Similarly, both problems assume that the resources are divisible. Chores can be infinitely divisible, because the finite set of chores can be partitioned by chore or by time. For example, a load of laundry could be partitioned by the number of articles of clothing and/or by the amount of time spent loading the machine. The problems differ, however, in the desirability of the resources. The chore division problem was introduced by Martin Gardner in 1978.
Chore division is often called fair division of bads, in contrast to the more common problem called "fair division of goods". Another name is dirty work problem. The same resource can be either good or bad, depending on the situation. For example, suppose the resource to be divided is the back-yard of a house. In a situation of dividing inheritance, this yard would be considered good, since each heir would like to have as much land as possible, so it is a cake-cutting problem. But in a situation of dividing house-chores such as lawn-mowing, this yard would be considered bad, since each child would probably like to have as little land as possible to mow, so it is a chore-cutting problem.
Some results from fair cake-cutting can be easily translated to the chore-cutting scenario. For example, the divide and choose procedure works equally well in both problems: one of the partners divides the resource to two parts that are equal in his eyes, and the other partner chooses the part that is "better" in his eyes. The only difference is that "better" means "larger" in cake-cutting and "smaller" in chore-cutting. However, not all results are so easy to translate. More details are given below.
See also
