Science behind cutting `fair pieces` of cake revealed
A new study has found the algorithm to divide goods such as cake and land.
Washington: A new study has found the algorithm to divide goods such as cake and land.
Mathematician Julius Barbanel of Union College, and political scientist Steven Brams of New York University have shown a way to optimally share cake between two people efficiently, in equal pieces and in such a way that no one feels robbed.
According to the method, an objective referee is essential so that the potential cake eaters first reveal which parts of the delicacy they value most. The referee then marks out the cake at all points were the probability density functions of the disgruntled would-be cake eaters cross, and assigns portions.
However, if at this point the two parties receive the same size of cake, the task is over, if not, then the giveback process starts.
The researchers believe that with a giveback procedure it is possible to make a perfect division between two people that is efficient, equitable and void of jealousy.
This method can be used to divide property as well, as it is not only equitable but also envy-free and efficient, which makes it perfect.
The algorithm was published in Springer`s The Mathematical Intelligencer.