Fair division, also known as the cake-cutting problem, is the problem of dividing a resource in such a way that all recipients believe that they have received a fair amount. The problem is easier when recipients have different measures of value of the parts of the resource: in the "cake cutting" version, one recipient may like marzipan, another prefers cherries, and so on—then, and only then, the n recipients may get even more than what would be one n-th of the value of the "cake" for each of them. On the other hand, the presence of different measures opens a vast potential for many challenging questions and directions of further research.
There are a number of variants of the problem. The definition of 'fair' may simply mean that they get at least their fair proportion, or harder requirements like envy-freeness may also need to be satisfied. The theoretical algorithms mainly deal with goods that can be divided without losing value. The division of indivisible goods, as in for instance a divorce, is a major practical problem. Chore division is a variant where the goods are undesirable.
Fair division is often used to refer to just the simplest variant. That version is referred to here as proportional division or simple fair division.
Most of what is normally called a fair division is not considered so by the theory because of the use of arbitration. This kind of situation happens quite often with mathematical theories named after real life problems. The decisions in the Talmud on entitlement when an estate is bankrupt reflect some quite complex ideas about fairness, and most people would consider them fair. However they are the result of legal debates by rabbis rather than divisions according to the valuations of the claimants.
Read more about Fair Division: Assumptions, Criteria For A Fair Division, Two Players, Many Players, Variants, History, In Popular Culture
Famous quotes containing the words fair and/or division:
“Playing games with agreed upon rules helps children learn to live by rules, establish the delicate balance between competition and cooperation, between fair play and justice and exploitation and abuse of these for personal gain. It helps them learn to manage the warmth of winning and the hurt of losing; it helps them to believe that there will be another chance to win the next time.”
—James P. Comer (20th century)
“That crazed girl improvising her music,
Her poetry, dancing upon the shore,
Her soul in division from itself
Climbing, falling she knew not where,
Hiding amid the cargo of a steamship
Her knee-cap broken.”
—William Butler Yeats (1865–1939)