Fair Division

Fair Division

A Fair Division Problem has a set of N players ( P1, P2, . . . , PN) and a set of goods S. We wish to divide S into N shares ( s1, s2, . . . , sN) so that each player gets a fair share of S. A fair share is a share that, in the opinion of the player receiving it, is worth 1/N of the total value of S. We will assume that any player is capable of deciding whether his share is fair; that is, we assume that any player is capable of assigning unambiguous values to S and to various parts of S (http://www.colorado.edu/education/DMP/fair_division.html).

The Lone Divider Method

This is just an extension of the Divider-Chooser Method to more than two players. Again we must pick our divider randomly. This fair division scheme requires three steps.

Step 1. Division--The divider slices the pizza into three pieces. This division is rational only if each piece has equal value to the divider.

Step 2. Declarations--Each chooser declares which pieces he or she considers acceptable (a fair share, in other words).

Step 3. Distribution--What happens here depends on the declarations (http://www.colorado.edu/education/DMP/fair_division.html).

The Lone Chooser Method

This is another three step process, and again we can extend it to more than three players. After a chooser and two dividers are chosen at random, they proceed as follows.

Step 1. First Division--The two dividers split the pizza by the divider-chooser method.

Step 2. Second Division--Each divider now divides his part into three parts he considers

equal.

Step 3. Selection--The chooser picks one piece from each divider, and each divider keeps

whatever he has left. Again, we have fair shares for everybody (http://www.colorado.edu/education/DMP/fair_division.html).

In the Lone Divider Method and Lone Chooser Method, they are played in steps that allow one person to be the divider and the rest of the players to be the choosers. Both of these have the ability to deal with multiple players, with...