Adjusted winner procedure

The divorce formula ( in German sometimes Adjusted Winner method) is a method from the mathematical theory of negotiating equitable distribution to divide goods envy-free between two people or groups. The algorithm for fair division Adjusted Winner goes back to Steven Brams and Alan D. Taylor (1996) and provides an efficient, envy -free and equal division. About the scientific context, the Adjusted Winner algorithm was famous as divorce formula, according to which partners can save the " post-marital War of the Roses ". This algorithm always refers to the entire assets and takes it as the default for the benefits. This algorithm is thus interesting for fair division problems with which the subject can not be expressed in monetary terms. The Armed objects are evaluated from both sides with points according to their subjective importance ( material or immaterial value) and distributed on the basis of this assessment. Then, objects or parts of it passed from one to the other to equalize the score (adjusted ).

Example

First of all objects ( object1, ..., object5 ) by both parties (A and B) are evaluated separately. This is accomplished with a total of 100 points available.

Then everyone gets the objects for which it has awarded more points. The subjective points for the objects obtained are added together.

There is a difference of 15 points between the two sums and attempts to achieve a balance by handing over entire objects.

There is still a difference of five points, which must be compensated for. An object with a value of 2.5 points ( for both sides) but there is no. It is selected the object, in which the ratings are closest to each other. For this purpose, a coefficient of the subjective ratings is calculated for the objects of A.

• Object1 45/35 = 1.29
• Object3 15/10 = 1.5

The object with the lower value ( object1 ) is selected and the proportion p of B is calculated by a simple formula, so that both sides received the same score.

So A is still about 1/16 of object1 to B. Both sides have now reached according to their subjective assessment 57 3/16 (ie over 50! ) Points.

Criticism

The divorce formula assumes that both parties have equal deserves a lot of goods. It is therefore not suitable for the solution of conflicts where one party to the other is morally superior.

Others

The algorithm was patented in the U.S. in 1999 ( in Germany these patents are not so far been recognized, see also Software patent). It can not simply be extended to more than two parties.