Proportional division

A proportional division is a kind of fair division in which a resource is divided among n partners with subjective valuations, giving each partner at least 1/n of the resource by his/her own subjective valuation. A proportional division is a kind of fair division in which a resource is divided among n partners with subjective valuations, giving each partner at least 1/n of the resource by his/her own subjective valuation. Proportionality was the first fairness criterion studied in the literature; hence it is sometimes called 'simple fair division'. It was first conceived by Steinhaus. Consider a land asset that has to be divided among 3 heirs: Alice and Bob who think that it's worth 3 million dollars, and George who thinks that it's worth $4.5M. In a proportional division, Alice receives a land-plot that she believes to be worth at least $1M, Bob receives a land-plot that he believes to be worth at least $1M (even though Alice may think it is worth less), and George receives a land-plot that he believes to be worth at least $1.5M. A proportional division does not always exist. For example, if the resource contains several indivisible items and the number of people is larger than the number of items, then some people will get no item at all and their value will be zero. Nevertheless, such a division exists with high probability for indivisible items under certain assumptions on the valuations of the agents.