Proportional (fair Division)

Proportional (fair Division)

Proportional division or simple fair division is the original and simplest problem in fair division. Fair division problems are also called cake-cutting problems. A proportional division of a cake between people would ensure each of them got at least of the cake by their own valuation. The cake can have an irregular structure, for instance a fruit-cake with icing, and the recipients may value the different parts differently. There is no requirement for a division to be envy-free.

There are two main types of solution studied: discrete procedures require one person at a time to divide the resource, moving knife ones have one or more knives move over the resource and people can choose when to stop them.

The problem generalizes directly to other resources that can be split easily without losing value. The methods adapt easily to similar problems in chore division (dividing up an undesirable resource). Proportional division problems also include dividing a resource where each recipient is entitled to a different proportion. Fair division of indivisible good is however a much harder problem.