Putting Fair Division on the Map

TL;DR

Using dimensionality reduction, a map of allocation instances is computed: a 2-dimensional embedding such that an instance's location on the map is predictive of the instance's origin and other key instance features.

Abstract

The fair division of indivisible goods is not only a subject of theoretical research, but also an important problem in practice, with solutions being offered on several online platforms. Little is known, however, about the characteristics of real-world allocation instances and how they compare to synthetic instances. Using dimensionality reduction, we compute a map of allocation instances: a 2-dimensional embedding such that an instance's location on the map is predictive of the instance's origin and other key instance features. Because the axes of this map closely align with the utility matrix's two largest singular values, we define a second, explicit map, which we theoretically characterize.