Assume two players, A and B, must divide a set of indivisible items that each strictly ranks from best to worst. If the number of items is even, assume that the players desire that the allocations be balanced (each player gets half the items), item-wise envy-free (EF), and Pareto-optimal (PO)....

Many procedures have been suggested for the venerable problem of dividing a set of indivisible items between two players. We propose a new algorithm (AL), related to one proposed by Brams and Taylor (BT), which requires only that the players strictly rank items from best to worst. Unlike BT, in...

Suppose two players wish to divide a finite set of indivisible items, over which each distributes a specified number of points. Assuming the utility of a player’s bundle is the sum of the points it assigns to the items it contains, we analyze what divisions are fair. We show that if there is...

An allocation of indivisible items among n ≥ 2 players is proportional if and only if each player receives a proportional subset — one that it thinks is worth at least 1/n of the total value of all the items. We show that a proportional allocation exists if and only if there is an allocation...

We propose a procedure for dividing indivisible items between two players in which each player ranks the items from best to worst. It ensures that each player receives a subset of items that it values more than the other player's complementary subset, given that such an envy-free division is...