AF: Small: Fair Division at Scale

点击翻译按钮获取中文摘要

The mathematical study of fair division dates back to the 1940s. Nowadays the literature encompasses provably fair solutions for a wide variety of problems, many of them relevant to society at large. But, to date, very few fair division methods have been implemented. Building on its rich history, the field of fair division is poised to impact society on a grander scale, for example, via Spliddit (www.spliddit.org), a fair division website created by the PI. The overarching theme of this proposal is that the advent of fairness at scale gives rise to novel algorithmic challenges, revolving around the design of methods that are practical, widely applicable, and provably fair. Solutions to these challenges call for a synthesis of ideas from theoretical computer science and microeconomic theory. The evolution of Spliddit plays a key role in the project: Insights arising from the research will be implemented to improve Spliddit's publicly accessible methods. Moreover, new applications will be added in order to further widen the website's reach. The project also includes plans to enhance Spliddit's educational content through the creation of instructive videos, thereby making the website a valuable learning and teaching resource. Finally, the project contains plans to make a societal impact that extends beyond Spliddit. In particular, the PI will work with California school districts to develop a fair method for allocating unused space.On a technical level, the thrust of the project is twofold. (i) Dividing indivisible goods: One of five applications currently available on Spliddit, the division of indivisible goods is a notoriously difficult problem from a fair division perspective. To obtain a provably fair method, Spliddit relies on the notion of maximin share (MMS) guarantee. While exact MMS allocations may be infeasible, the project explores several notions of approximation. The project also explores the feasibility boundary of MMS allocations. Foundational algorithmic challenges lie at the heart of these research directions. (ii) Sharing credit: Spliddit's credit calculator fairly determines the contribution of each individual to a group project, using a method developed by de Clippel et al. Perhaps the method's most compelling guarantee is impartiality: a player's report does not affect her own share of the credit. Dividing credit for a scientific paper, with the goal of fairly ordering the authors by contribution, is an especially attractive potential application; but there is no guarantee that players will not be able to affect their position in the resultant ranking. The project aims to circumvent this obstacle via randomization and approximation.