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...

We analyze a class of proportional cake-cutting algorithms that use a minimal number of cuts (n-1 if there are n players) to divide a cake that the players value along one dimension. While these algorithms may not produce an envy-free or efficient allocation – as these terms are used in the...

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...