A Procedure for Exchanging Unwanted Items
Have you ever participated in a grab bag and ended up with an item that you felt someone else could put to infinitely better use? Having gotten a woman’s hairpiece at a white elephant grab bag, I know the feeling. It occurred to me that there must be a better way for people to exchange items so that the participants are more likely to end up with items that they find useful than is the case with the random redistribution of the items characteristic of a grab bag. To accomplish this goal, I developed the Systematic White-elephant Allocation Procedure (SWAP). The SWAP employs a sequence of multiperson exchanges designed to enable each participant to end up with, to the extent possible, the item that he (or she) most desires. An advantage of the SWAP is that unlike a grab bag, each person is guaranteed to receive an item that he likes at least as much as the one he brings; worst case, he ends up with the item he brought.
To participate in a SWAP meet, each person brings an unwrapped item he wishes to exchange, such as an unwanted Christmas present, grab bag prize, or white elephant. If the SWAP is to be conducted following a grab bag, it is advantageous to do so immediately after all of the prizes have been opened, while all persons are gathered together with their items. The details of this procedure are given below.
1. Those who wish to participate in the SWAP gather in a circle, facing inward. Each person holds his item so that it can be viewed by the other participants. Proceeding around the circle, each person, in turn, describes his object. Meanwhile, every other person examines all of the items and decides which of them he would most like to have. If his favorite item is the one he brought, he drops out of the circle. If a person desires an item possessed by someone who drops out, the former then chooses an item from those still remaining in the group and drops out if that item is his own. This process continues until no further dropouts occur, with the circle shrinking as necessary to close any gaps. If nobody remains in the circle, the procedure is complete; otherwise, continue. One person in the circle is chosen and designated as Person 1. How this person is selected is not important, since this choice will not affect the final allocation of items among the participants. The circle expands to allow one space (i.e., space enough for one person) to the left of Person 1 and two spaces to Person 1’s right. Designate the subgroup consisting of Person 1 as Group B; the remaining persons constitute Group A.
2. The rightmost person in Group B indicates the person possessing the item he most desires. The person so selected may be from either Group A or Group B. If he is from Group B, then go to Step 3; otherwise, continue. The selected person leaves Group A and joins Group B next to and to the right of the person who selected him. The resulting gap in Group A is closed by those persons in Group A to the left of the vacancy moving one space to the right, thus maintaining the separation between Group A and Group B. (These two groups form arcs along the circle.) Now go back to the beginning of Step 2.
3. Designate the subgroup of Group B consisting of the person most recently selected together with those persons (in Group B) to the right of him as Group C. Those in Group C now move one space to the right and curve around to form a circle, facing inward. Each person in this circle should have on his immediate right the item he most desires. Each person in Group C hands the item he possesses to the person on his left and accepts the item given to him by the person on his right. Processing is now complete for those in Group C. Any person whose favorite item is possessed by a member of Group C chooses a new item from those items remaining and drops out if that item is his own. If a person desires an item possessed by someone who drops out, the former then chooses an item from those still remaining in the group and drops out if that item is his own. This process continues until no further dropouts occur. If Group A and Group B are both empty, the procedure is complete; otherwise, continue. If Group A is empty, go to Step 2; otherwise, continue. If nobody remains in Group B, the rightmost person in Group A moves one space to the right to form the new Group B. The circle is shrunk to eliminate any spaces in Group A and reduce the gap to the left of Group B to one space and to the right of Group B to two spaces. Now go to Step 2.
If you do decide to hold a SWAP meet, feel free to share your experience in the comments.