Abebe, RedietKleinberg, JonParkes, David2019-10-22Abebe, Rediet, Jon Kleinberg, and David Parkes. 2017. Fair Division via Social Comparison. AAMAS '17 Proceedings of the 16th Conference on Autonomous Agents and MultiAgent Systems, São Paulo, Brazil, May 08- 12, 2017, 281-289.http://nrs.harvard.edu/urn-3:HUL.InstRepos:41593087We study cake cutting on a graph, where agents can only evaluate their shares relative to their neighbors. This is an extension of the classical problem of fair division to incorporate the notion of social comparison from the social sciences. We say an allocation is {\em locally envy-free} if no agent envies a neighbor's allocation, and locally proportional if each agent values its own allocation as much as the average value of its neighbors' allocations. We generalize the classical ``Cut and Choose" protocol for two agents to this setting, by fully characterizing the set of graphs for which an oblivious {\em single-cutter protocol} can give locally envy-free (thus also locally-proportional) allocations. We study the {\em price of envy-freeness}, which compares the total value of an optimal allocation with that of an optimal, locally envy-free allocation. Surprisingly, a lower bound of $\Omega(\sqrt{n})$ on the price of envy-freeness for global allocations also holds for local envy-freeness in any connected graph, so sparse graphs do not provide more flexibility asymptotically with respect to the quality of envy-free allocations.en-USSocial ChoiceFair DivisionGraph-Theoretic MethodsConference Paper2019-10-22