Fair division in the age of the internet

Fair division, a key concern in the design of many social institutions, has for 70 years been the subject of interdisciplinary research at the interface of mathematics, economics, and game theory. Motivated by the proliferation of moneyless transactions on the internet, the computer science community has recently taken a deep interest in fairness principles and practical division rules. The resulting literature brings a fresh concern for computational simplicity (scalable rules) and realistic implementation. In this review of the most salient fair division results of the past 30 years, I concentrate on division rules with the best potential for practical implementation. The critical design parameter is the message space that the agents must use to report their individual preferences. A simple preference domain is key both to realistic implementation and to the existence of division rules with strong normative and incentive properties. I discuss successively the one-dimensional single-peaked domain, Leontief utilities, ordinal ranking, dichotomous preferences, and additive utilities. Some of the theoretical results in the latter domain are already implemented in the user-friendly SPLIDDIT platform (http://spliddit.org)