Two-player fair division of indivisible items: Comparison of algorithms

We study algorithms for allocating a set of indivisible items to two players who rank them differently. We compare eleven such algorithms, mostly taken from the literature, in a computational study, evaluating them according to fairness and efficiency criteria that are based on ordinal preferences as well as Borda counts. Our study is exhaustive in that, for every possible instance of up to twelve items, we compare the output of each algorithm to all possible allocations. We thus can search for “good” allocations that no algorithm finds. Overall, the algorithms do very well on ordinal properties but fall short on Borda properties. We also discuss the similarity of algorithms and suggest how they can be usefully combined.