Divorce formula

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The divorce formula (sometimes also called the Adjusted Winner Method in German ) is a method from the mathematical negotiation theory of fair division in order to divide goods between two people or groups without envy . The Adjusted Winner algorithm for fair division goes back to Steven Brams and Alan D. Taylor (1996) and offers efficient, envy-free and equal division. Beyond the scientific context, the Adjusted Winner algorithm became famous as a divorce formula, according to which partners can save themselves the "post-marital war of roses". This algorithm always refers to the total wealth and takes this as the standard for the utility. This algorithm is also interesting for fair division problems, the subject of the evaluation cannot be expressed in monetary terms. The objects of dispute are assessed by both sides with points according to their subjective importance (material or ideal value) and distributed based on this assessment. Then, objects or portions thereof are passed from one to the other in order to score balance ( adjusted ).

example

First, all objects ( Object1, ..., Object5 ) are assessed separately by both parties ( A and B ). A total of 100 points are available for this.

Object 1 Object 2 Object 3 Object 4 Object 5 total
A. 45 20th 15th 10 10 100
B. 35 30th 10 10 15th 100

Then everyone receives the objects for which they have awarded more points. The subjective points for the objects obtained are added up.

A gets Object1 and Object3 (total: 60 points).
B receives Object2 and Object5 (total: 45 points).

There is a difference of 15 points between the two sums and an attempt is made to balance them out by handing over entire objects.

B has fewer points and also gets Object4 (new total: 55 points).

There is still a difference of 5 points that needs to be compensated. But there is no property worth 2.5 points (for both sides). The object is chosen for which the ratings are closest to one another. For this purpose, a coefficient is first calculated from the subjective evaluations for A's objects .

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

The object with the lesser value ( Object1 ) is selected and the proportion p of B is calculated by a simple formula so that both sides get the same score.

A so on are 1/16 of building1 to B . Both sides have now achieved 57 3/16 (over 50!) Points according to their subjective evaluation.

Others

The algorithm was patented in the USA in 1999 (such patents have not yet been recognized in Germany, see also software patents ). But it cannot simply be expanded to include more than two parties.

literature

  • Steven J. Brams, Alan D. Taylor: Fair Division: From Cake-Cutting to Dispute Resolution. Cambridge University Press, FD, 1996.

Web links

Individual evidence

  1. ↑ Raith (2000, p. 308)