The difficulty of fairly allocating divisible goods

It is often necessary to divide a resource among a number of agents, and to do so in a way that does not leave any of the agents feeling cheated. There are a number of published methods for dealing with the problem of fairly dividing goods. Many of these methods are very successful, capable of finding allocations that satisfy the participating agents and distribute the goods being disputed in a way that they can agree to. These methods have done well in many real-world situations–from splitting desserts between squabbling siblings, to facilitating divorce settlements, to deciding international fishing rights. There are situations in which goods cannot be fairly divided, but must be allocated to agents in a way that they consider fair. Unfortunately, common methods of fair division cannot be easily applied, if at all, in cases where the items are of lesser or no value when taken apart. The applicability and likely success of an allocation method depends on whether or not the items to be allocated are divisible or indivisible. Finding agreeable rules for an envy-free division of a set of indivisible items is difficult. Many of the methods currently published do not meet the same criteria that divisible-goods methods do and are susceptible to strategic manipulation. Although there are ways of avoiding the most difficult situations involving indivisible goods, the methods remain fragile and apply in a narrower range of cases than do methods where items can be divided.