Two people (often a divorcing couple) need to divide their assets (without selling them and dividing the cash). The objects are listed and each of the parties is given 100 points to distribute over the disputed items. Each item is tentatively given to the "high bidder," and their points thus received and totaled. If these totals are equal the distribution is complete. However, if one party received more points than the other, then the one (or more) of the items will have to be divided between them, as described below. Example:
| Item | John | Mary |
| A | 30 | 20 |
| B | 15 | 25 |
| C | 20 | 15 |
| D | 30 | 15 |
| E | 5 | 25 |
Note: A bolded value means that the corresponding item was awarded (tentatively) to that bidder.
John gets (tentatively) items A, C, and D (80 points), while Mary gets B and E (50 points). To equalize the points, we do the following. For each of the items that John got, we compute the ratio of points assigned by the two parties, with John's points being the numerator and Mary's the denominator. We then choose the item with the smallest ratio. In our example the ratios are:
A: 30 / 20 = 1.50
C: 20 / 15 = 1.33
D: 30 / 15 = 2.00
In this case, C has the smallest ratio, so it will be divided, as follows. John keeps A and D (60 points) and a certain fraction, x, of C. We will solve a simple equation to find the value of x. Mary will get the remaining fraction of C, wich is 1 - x, in addition to items B and E (50 points). The equation is
John's points Mary's points
60 + 20x = 50 + 15(1 - x)
Solving for x we get x = 5 / 35 = 1 / 7. Therefore, John keeps 1 / 7 of item C and Mary gets 1 - x = 6 / 7 of it. And John's total becomes 60 + (20)(1/7) = 62 6/7, while Mary's total is now 50 + (15)(6/7) = 62 6/7.
In the first portion of our applet, Opponent's Bids Unknown, you enter points to bid on each item. Click the Calculate button to see the distribution. Green point values go to that bidder. Click the New button to load a new set of items.
In the Calculate Distribution tab you must enter the initial totals, ratios, and a value for x (if necessary). Click the Check answers button to see if you are correct. Click the New button to load a new set of items and points.