Proportional Borda allocations

Abstract

In this paper we study the allocation of indivisible items among a group of agents, a problem which has received increased attention in recent years, especially in areas such as computer science and economics. A major fairness property in the fair division literature is proportionality, which is satisfied whenever each of the n agents receives at least 1n of the value attached to the whole set of items. To simplify the determination of values of (sets of) items from ordinal rankings of the items, we use the Borda rule, a concept used extensively and well-known in voting theory. Although, in general, proportionality cannot be guaranteed, we show that, under certain assumptions, proportional allocations of indivisible items are possible and finding such allocations is computationally easy.